Finite Element Vibration Analysis of Rotating Timoshenko Beams
Vibration-based Condition Monitoring of Rotating Machines
Transcript of Vibration-based Condition Monitoring of Rotating Machines
Vibration-based Condition
Monitoring of Rotating
Machines
A thesis submitted to
The University of Manchester
for the degree of
Doctor of Philosophy (PhD)
in the Faculty of Engineering and Physical Sciences
2015
Akilu Yunusa-Kaltungo
School of Mechanical, Aerospace and Civil
Engineering
Vibration-based Condition Monitoring of Rotating Machines
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Akilu Yunusa-Kaltungo 2
PhD in Mechanical Engineering (2015) University of Manchester (UK)
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Table of Contents
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Akilu Yunusa-Kaltungo 3
PhD in Mechanical Engineering (2015) University of Manchester (UK)
TABLE OF CONTENTS ----------------------------------------------------------------------------------------------
TABLE OF CONTENTS ...................................................................................................................... 3
LIST OF FIGURES ............................................................................................................................ 12
LIST OF TABLES .............................................................................................................................. 19
ABBREVIATIONS ............................................................................................................................. 21
NOMENCLATURE ............................................................................................................................ 23
LIST OF PUBLICATIONS ................................................................................................................. 25
ABSTRACT ....................................................................................................................................... 28
DECLARATION ................................................................................................................................. 29
COPYRIGHT STATEMENT .............................................................................................................. 30
ACKNOWLEDGEMENTS ................................................................................................................. 32
DEDICATION .................................................................................................................................... 33
SCIENTIFIC QUOTE ........................................................................................................................ 34
CHAPTER 1 INTRODUCTION ........................................................................... 35
1.1 Overview .............................................................................................................. 35
1.2 Research Objectives ........................................................................................... 39
1.3 Research Review ................................................................................................. 40
1.4 Outline of Thesis ................................................................................................. 42
CHAPTER 2 LITERATURE REVIEW ................................................................. 47
2.1 Typical VCM Process Framework ...................................................................... 47
2.1.1 Data collection ............................................................................................................... 49
2.1.2 Data processing ............................................................................................................ 52
2.1.2.1 Time domain analysis ............................................................................................... 52
2.1.2.2 Frequency domain analysis ...................................................................................... 53
2.1.2.3 Time-frequency analysis ........................................................................................... 53
2.1.3 Faults diagnosis ............................................................................................................ 54
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2.2 Standard Approaches to Vibration-based Fault Detection ............................... 55
2.2.1 Spectrum analysis ......................................................................................................... 56
2.2.1.1 Unbalance fault ......................................................................................................... 56
2.2.1.2 Shaft bow .................................................................................................................. 57
2.2.1.3 Shaft misalignment .................................................................................................... 58
2.2.1.4 Mechanical looseness ............................................................................................... 59
2.2.1.5 Shaft crack ................................................................................................................ 61
2.2.1.6 Shaft rub .................................................................................................................... 62
2.2.2 Rotor orbit analysis........................................................................................................ 63
2.2.3 Full spectrum analysis ................................................................................................... 65
2.2.4 Order tracking ................................................................................................................ 67
2.3 Overview of Standard Vibration Based Fault Detection Approaches .............. 68
2.4 Emerging Approaches to Vibration Based Fault Detection ............................. 70
2.4.1 Model-based approaches .............................................................................................. 70
2.4.2 Artificial intelligence and faults classification ................................................................ 74
2.4.3 Higher order signal processing tools ............................................................................. 77
2.4.4 Data Fusion ................................................................................................................... 80
2.4.4.1 Sensor level data fusion ............................................................................................ 83
2.4.4.2 Parameter level data fusion ...................................................................................... 85
2.5 Summary.............................................................................................................. 92
CHAPTER 3 EXPERIMENTS ............................................................................. 94
3.1 Experimental Rig and Components ................................................................... 94
3.1.1 Electric motor and speed controller............................................................................... 96
3.1.2 Anti-friction ball bearings ............................................................................................... 98
3.1.3 Couplings ...................................................................................................................... 99
3.1.4 Threaded bars ............................................................................................................. 100
3.2 Instrumentation ................................................................................................. 100
3.2.1 Accelerometers ........................................................................................................... 101
3.2.2 Proximity probes.......................................................................................................... 102
3.2.3 Measurement microphones ......................................................................................... 102
3.2.4 Instrumented hammer ................................................................................................. 103
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3.2.5 Signal conditioning units ............................................................................................. 105
3.2.6 Analogue-to-digital converter (ADC) ........................................................................... 107
3.2.7 Data acquisition software ............................................................................................ 108
3.3 Experimental Rig Foundations ......................................................................... 109
3.3.1 Rigid support (RS) ....................................................................................................... 109
3.3.2 Flexible supports ......................................................................................................... 111
3.4 Dynamic Characterisation ................................................................................ 114
3.5 Experimentally Simulated Faults ..................................................................... 122
3.5.1 Rigid support (RS) ....................................................................................................... 122
3.5.1.1 Case 1: Healthy ....................................................................................................... 122
3.5.1.2 Case 2: Misalignment .............................................................................................. 122
3.5.1.3 Case 3: Cracked shaft ............................................................................................. 123
3.5.1.4 Case 4: Shaft rub .................................................................................................... 124
3.5.2 Flexible supports (FS1 and FS2) ................................................................................ 125
3.6 Summary............................................................................................................ 126
CHAPTER 4 EXPERIMENTAL OBSERVATIONS OF ROTOR ORBIT
ANALYSIS IN ROTATING MACHINES ............................................................. 128
ABSTRACT ........................................................................................................ 128
4.1 Introduction ....................................................................................................... 129
4.2 Experimental Rigs ............................................................................................. 130
4.3 Vibration Experiments ...................................................................................... 131
4.3.1 Case 1: Healthy with residual misalignment (HRM) .................................................... 132
4.3.2 Case 2: Unbalance (UNB) ........................................................................................... 132
4.3.3 Case 3: Shaft crack (SC) ............................................................................................ 133
4.3.4 Cases 5-8: Shaft misalignment (SM) .......................................................................... 133
4.3.5 Case 9: Shaft rub (SR) ................................................................................................ 134
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4.4 Results and Observations ................................................................................ 135
4.5 Spectrum Analyses ........................................................................................... 137
4.6 Summary............................................................................................................ 139
CHAPTER 5 A COMPARISON OF SIGNAL PROCESSING TOOLS: HIGHER
ORDER SPECTRA VERSUS HIGHER ORDER COHERENCES ...................... 141
ABSTRACT ........................................................................................................ 142
5.1 Introduction ....................................................................................................... 142
5.2 Computational Approaches for Spectra and Coherences.............................. 144
5.3 Simulated Example ........................................................................................... 147
5.4 CSD and Ordinary Coherence Analysis ........................................................... 149
5.5 Bispectrum and Bicoherence Analysis ........................................................... 151
5.6 Trispectrum and Tricoherence Analysis ......................................................... 153
5.7 Signals with Noise ............................................................................................ 155
5.8 Summary............................................................................................................ 157
CHAPTER 6 COMBINED BISPECTRUM AND TRISPECTRUM FOR FAULTS
DIAGNOSIS IN ROTATING MACHINES ........................................................... 158
ABSTRACT ........................................................................................................ 159
6.1 Introduction ....................................................................................................... 159
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6.2 PSD and HOS Computations ............................................................................ 161
6.3 Experimental Setup ........................................................................................... 162
6.4 Simulation of Faults .......................................................................................... 164
6.5 Data Analysis .................................................................................................... 165
6.5.1 Spectrum analysis ....................................................................................................... 165
6.5.2 Bispectrum analysis .................................................................................................... 168
6.5.3 Trispectrum analysis ................................................................................................... 171
6.5.4 Diagnostic Features .................................................................................................... 176
6.6 Summary............................................................................................................ 178
CHAPTER 7 USE OF COMPOSITE HIGHER ORDER SPECTRA FOR FAULTS
DIAGNOSIS OF ROTATING MACHINES WITH DIFFERENT FOUNDATION
FLEXIBILITIES ................................................................................................... 179
ABSTRACT ........................................................................................................ 180
7.1 Introduction ....................................................................................................... 180
7.2 Composite Spectra Computations ................................................................... 183
7.3 Experimental Rig with Different Foundations ................................................. 185
7.3.1 Modal tests and data analysis ..................................................................................... 190
7.4 Experiments ...................................................................................................... 190
7.5 Data Analysis .................................................................................................... 192
7.6 CS Analysis and Observations ........................................................................ 192
7.7 CB Analysis and Observations ........................................................................ 193
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7.8 CT Analysis and Observations ......................................................................... 198
7.9 Combined Diagnostic Features ........................................................................ 203
7.9.1 Sensitivity analysis ...................................................................................................... 205
7.9.2 Practical application .................................................................................................... 206
7.10 Summary............................................................................................................ 207
CHAPTER 8 AN IMPROVED DATA FUSION TECHNIQUE FOR FAULTS
DIAGNOSIS OF ROTATING MACHINES .......................................................... 208
ABSTRACT ........................................................................................................ 208
8.1 Introduction ....................................................................................................... 209
8.2 Earlier Composite Spectrum ............................................................................ 210
8.3 Proposed poly-Coherent Composite Spectrum (pCCS) ................................. 211
8.4 Experiments and Observations ........................................................................ 212
8.4.1 Diagnosis features....................................................................................................... 215
8.5 Diagnosis with Earlier Composite Spectrum Method ..................................... 216
8.6 Summary............................................................................................................ 218
CHAPTER 9 A NOVEL FAULTS DIAGNOSIS TECHNIQUE FOR ENHANCING
MAINTENANCE AND RELIABILITY OF ROTATING MACHINES .................... 220
ABSTRACT ........................................................................................................ 220
9.1 Introduction ....................................................................................................... 221
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9.2 Composite Spectra Computations ................................................................... 225
9.2.1 Earlier method ............................................................................................................. 225
9.2.2 Improved method ........................................................................................................ 227
9.3 Proposed Fault Diagnosis Method ................................................................... 228
9.3.1 Concept of PCA........................................................................................................... 230
9.3.2 Computational approach of the proposed FD technique ............................................ 232
9.4 Experimental Example ...................................................................................... 234
9.4.1 Rig and faults simulation ............................................................................................. 236
9.4.2 Experimental modal analysis ...................................................................................... 238
9.4.3 Signal processing ........................................................................................................ 242
9.5 Faults Diagnosis ............................................................................................... 245
9.5.1 Data preparation.......................................................................................................... 245
9.5.2 Results and discussions .............................................................................................. 247
9.5.3 Comparison with Earlier Method ................................................................................. 249
9.6 Practical application of the proposed FD technique ...................................... 251
9.7 Summary............................................................................................................ 253
CHAPTER 10 SENSITIVITY ANALYSIS OF HIGHER ORDER COHERENT
SPECTRA IN MACHINE FAULTS DIAGNOSIS ................................................ 255
ABSTRACT ........................................................................................................ 255
10.1 Introduction ....................................................................................................... 256
10.2 poly-Coherent Composite Spectra ................................................................... 258
10.3 Example 1: Laboratory Scale Experimental Rig .............................................. 261
10.3.1 Earlier Faults Detection Method [251] ......................................................................... 264
10.4 Sensitivity Analysis Based on Experimental Data .......................................... 266
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PhD in Mechanical Engineering (2015) University of Manchester (UK)
10.5 Example 2: Industrial Fan ................................................................................. 270
10.5.1 The Case Study (RKIDF) ............................................................................................ 270
10.5.2 On-site vibration measurements ................................................................................. 272
10.5.3 Detection and Classification of RKIDF Operating Conditions using Earlier Method ... 273
10.6 Sensitivity Analysis Based on Industrial Data ................................................ 275
10.7 Summary............................................................................................................ 277
CHAPTER 11 CONCLUDING REMARKS AND FUTURE RESEARCH .......... 279
11.1 Overall Summary ............................................................................................... 279
11.2 Achieved Objectives ......................................................................................... 282
11.3 Concluding Remarks ........................................................................................ 287
11.4 Future Research ................................................................................................ 287
REFERENCES ................................................................................................... 289
APPENDIX A THEORETICAL BACKGROUND OF SPECTRUM BASED SIGNAL
PROCESSING TOOLS ....................................................................................... 311
A.1 Overview of Frequency Domain Signal Processing ....................................... 311
A.2 Power Spectrum ................................................................................................ 311
A.3 Cross-power Spectrum ..................................................................................... 313
A.4 Ordinary Coherence .......................................................................................... 313
A.5 Higher Order Signal Processing Tools ............................................................ 314
A.5.1 Bispectrum .................................................................................................................. 315
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PhD in Mechanical Engineering (2015) University of Manchester (UK)
A.5.2 Trispectrum ................................................................................................................. 315
A.6 Normalisation of Higher Order Signal Processing Tools ............................... 316
A.6.1 Bicoherence ................................................................................................................ 316
A.6.2 Tricoherence ............................................................................................................... 316
List of Figures
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LIST OF FIGURES ----------------------------------------------------------------------------------------------
Figure 1.1 Maintenance philosophies and their characteristics ............................. 36
Figure 1.2 Multi-shaft coal mill drive assembly layout, with locations and
orientations of VCM sensors. HO represents horizontal orientation, VO vertical
orientation and AO axial orientation [8], [9]. .......................................................... 38
Figure 1.3 Thesis chapters and contents .............................................................. 43
Figure 2.1 Basic stages of a typical VCM process ................................................ 49
Figure 2.2 Vibration data collection process for a typical rotating machine [20] .... 50
Figure 2.3 Typical spectrum-based VCM fault tree for a rotating machine ........... 55
Figure 2.4 Typical amplitude-spectrum of a rotating machine at 2040 RPM,
showing dominant 1x RPM peak as a result of unbalance fault. ........................... 57
Figure 2.5 A typical amplitude-spectrum of a rotating machine at 1200 RPM,
showing the appearance of several higher harmonics of machine speed due to
rotor bow. .............................................................................................................. 58
Figure 2.6 Typical amplitude-spectrum of a rotating machine at 2040 RPM,
showing dominant 1x RPM and 2x RPM peaks due to misalignment. .................. 59
Figure 2.7 A typical amplitude-spectrum of a rotating machine at 1200 RPM,
showing the appearance of several higher harmonics of machine speed due to
bearing looseness. ................................................................................................ 60
Figure 2.8 A typical amplitude-spectrum of a rotating machine at 2040 RPM,
showing the appearance of several harmonics of machine speed due to rotor
crack. .................................................................................................................... 62
Figure 2.9 A typical amplitude-spectrum of a rotating machine at 2040 RPM,
showing the appearance of sub-harmonics of machine speed due to rotor rub. ... 63
Figure 2.10 Rotor orbit plot of a typical rotating machine ...................................... 64
Figure 2.11 3D model of a typical rotating machine. ............................................. 71
Figure 2.12 Typical ANN-based model ................................................................. 75
Figure 2.13 Data fusion at sensor level ................................................................. 84
Figure 2.14 Multi-sensor data fusion [122]–[126] .................................................. 85
Figure 2.15 Data fusion at parameter level ........................................................... 86
List of Figures
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PhD in Mechanical Engineering (2015) University of Manchester (UK)
Figure 2.16 A typical multiple speeds cement plant roots blower with various
foundation options [132]–[136]. ............................................................................. 89
Figure 2.17 A unified data fusion approach .......................................................... 91
Figure 3.1 Typical experimental set-up ................................................................. 95
Figure 3.2 Picture of electric motor and speed controller ...................................... 97
Figure 3.3 Anti-friction ball bearings (a) Plummer block (b) Flange-mounted ....... 98
Figure 3.4 Couplings (a) Flexible (b) Rigid ............................................................ 99
Figure 3.5 Threaded bars for flexible foundations ............................................... 100
Figure 3.6 Accelerometers with their brass mounting studs ................................ 101
Figure 3.7 (a) MTN/ECPD+24V Proximity probes (b) EP080 drivers .................. 102
Figure 3.8 (a) Condenser microphone (b) Single channel power supply (c) sound
amplifier .............................................................................................................. 103
Figure 3.9 ICP-PCB 086C03 instrumented hammer ........................................... 104
Figure 3.10 PCB 482C signal conditioning unit ................................................... 106
Figure 3.11 NI 6229/16-bit/16-channel ADC ....................................................... 107
Figure 3.12 Picture of RS experimental rig ......................................................... 110
Figure 3.13 Schematic of RS experimental rig with dimensions ......................... 111
Figure 3.14 Picture of FS experimental rig .......................................................... 112
Figure 3.15 Schematic of FS experimental rig .................................................... 113
Figure 3.16 Picture of flexible supports (a) FS1 (b) FS2 ..................................... 114
Figure 3.17 Modal test setup for determining FS1 and FS2 natural frequencies 116
Figure 3.18 Typical FRF plots for FS1, measured at bearing 2 in the vertical
direction (a) FRF amplitude, (b) FRF phase ....................................................... 117
Figure 3.19 Typical FRF plots for FS1, measured at bearing 2 in the horizontal
direction (a) FRF amplitude, (b) FRF phase ....................................................... 117
Figure 3.20 Typical FRF plots for FS2, measured at bearing 2 in the vertical
direction (a) FRF amplitude, (b) FRF phase ....................................................... 118
Figure 3.21 Typical FRF plots for FS2, measured at bearing 2 in the horizontal
direction (a) FRF amplitude, (b) FRF phase ....................................................... 118
Figure 3.22 Modal test setup for determining FS1 and FS2 mode shapes ......... 119
Figure 3.23 Locations of ICP accelerometers for mode shapes’ determination .. 120
List of Figures
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Figure 3.24 FS1experimentally determined mode shapes (a) 50.66Hz, dominant in
vertical direction (b) 56.76Hz, dominant in horizontal direction ........................... 121
Figure 3.25 Cracked shaft ................................................................................... 124
Figure 3.26 Shaft rub .......................................................................................... 124
Figure 4.1 Experimental rig with flexible bearing foundation ............................... 131
Figure 4.2 Flexible anti-friction ball bearings foundations (a) FS1 (b) FS2 ......... 131
Figure 4.3 Unbalance case ................................................................................. 132
Figure 4.4 Loose bearing case............................................................................ 133
Figure 4.5 Shaft misalignment cases (a) SM1 (b) SM2 ....................................... 134
Figure 4.6 Shaft rub case .................................................................................... 135
Figure 4.7 Rotor orbit plots for FS1 (a) HRM (b) UNB (c) SC (d) LB (e) SM1 (f)
SM2 (g) SM3 (h) SM4 (i) SR ............................................................................... 136
Figure 4.8 Rotor orbit plots for FS2 (a) HRM (b) UNB (c) SC (d) LB (e) SM1 (f)
SM2 (g) SM3 (h) SM4 (i) SR ............................................................................... 137
Figure 4.9 Typical amplitude spectra for FS1 at 2400RPM (a) HRM (b) SC (c) SM4
(d) SR ................................................................................................................. 138
Figure 4.10 Typical amplitude spectra for FS2 at 2400RPM (a) HRM (b) SC (c)
SM4 (d) SR ......................................................................................................... 139
Figure 5.1 Typical amplitude spectra (a) Case 1 (healthy) and (b)-(d) Case 2-
Case 4 (different faulty conditions) ...................................................................... 149
Figure 5.2 Typical CSD plots (a) Signals 1&2, (b) Signals 1&4, (c) Signals 2&4,
and (d) Signals 3&4 ............................................................................................ 150
Figure 5.3 Typical ordinary coherence plots (a) Signals 1&2, (b) Signals 1&4, (c)
Signals 2&4, and (d) Signals 3&4 ....................................................................... 151
Figure 5.4 Typical amplitude-bispectra plots (a) Case 1 (healthy) and (b)-(d) Case
2-Case 4 (different fault conditions) .................................................................... 152
Figure 5.5 Typical bicoherence plots (a) Case 1 (healthy) and (b)-(d) Case 2-Case
4 (different fault conditions) ................................................................................. 153
Figure 5.6 Typical amplitude-trispectra plots (a) Case 1 (healthy) and (b) Case 2
(faulty) ................................................................................................................. 154
Figure 5.7 Typical tricoherence plots (a) Case 1 (healthy) and (b) Case 2 (faulty)
............................................................................................................................ 155
List of Figures
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Figure 6.1 Photographic representation of the experimental rig.......................... 163
Figure 6.2 Schematic representation of the experimental rig .............................. 164
Figure 6.3 Typical amplitude spectra at 34Hz for bearing 1 ................................ 166
Figure 6.4 Typical amplitude spectra at 50Hz for bearing 1 ................................ 167
Figure 6.5 Typical normalised amplitude spectrum components at 34Hz ((a)-(b))
and at 50Hz ((c)-(d)) for all the simulated cases ................................................. 168
Figure 6.6 Typical amplitude bispectra plots at 34Hz (a) healthy (b) misalignment
(c) cracked shaft (d) shaft rub ............................................................................. 169
Figure 6.7 Typical amplitude bispectra plots at 50Hz (a) healthy (b) misalignment
(c) cracked shaft (d) shaft rub ............................................................................. 169
Figure 6.8 Typical amplitude trispectra plots at 34Hz for bearings 1 (a-d) and 3 (e-
h); (a and e) healthy, (b and f) misalignment, (c and g) cracked shaft, (d and h)
shaft rub .............................................................................................................. 172
Figure 6.9 Typical amplitude trispectra at 50Hz (a) healthy (b) misalignment (c)
cracked shaft (d) shaft rub .................................................................................. 173
Figure 7.1 Abstract representation of rotating machine and foundation .............. 183
Figure 7.2 Photograph of the experimental rig .................................................... 187
Figure 7.3 Schematic of the experimental rig ...................................................... 188
Figure 7.4 Different rig supports (a) FS1 (b) FS2 ................................................ 189
Figure 7.5 Experimentally simulated cases (a) SC (b) LB (c) SM (d) SR ............ 191
Figure 7.6 Typical composite spectra at 1200RPM (a) HRM for FS1 (b) HRM for
FS2 (c) LB for FS1 (d) LB for FS2 ....................................................................... 193
Figure 7.7 Typical coherent composite bispectra (CB) at 1200RPM (a) HRM for
FS1 (b) HRM for FS2 (c) LB for FS1 (d) LB for FS2 ........................................... 194
Figure 7.8 Typical B11 CB component magnitude and phase (a) FS1 (1200RPM)
(b) FS2 (1200RPM) (c) FS1 (1800RPM) (d) FS2 (1800RPM) (e) FS1 (2400RPM)
(f) FS2 (2400RPM) .............................................................................................. 196
Figure 7.9 Typical B12 CB component magnitude and phase (a) FS1 (1200RPM)
(b) FS2 (1200RPM) (c) FS1 (1800RPM) (d) FS2 (1800RPM) (e) FS1 (2400RPM)
(f) FS2 (2400RPM) .............................................................................................. 197
Figure 7.10 Typical coherent composite trispectra (CT) at 1200RPM (a) HRM for
FS1 (b) HRM for FS2 (c) LB for FS1 (d) LB for FS2 ........................................... 199
List of Figures
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Figure 7.11 Typical T111 CT component magnitude and phase (a) FS1 (1200RPM)
(b) FS2 (1200RPM) (c) FS1 (1800RPM) (d) FS2 (1800RPM) (e) FS1 (2400RPM)
(f) FS2 (2400RPM) .............................................................................................. 201
Figure 7.12 Typical T112 CT component magnitude and phase (a) FS1 (1200RPM)
(b) FS2 (1200RPM) (c) FS1 (1800RPM) (d) FS2 (1800RPM) (e) FS1 (2400RPM)
(f) FS2 (2400RPM) .............................................................................................. 202
Figure 7.13 Typical combined magnitudes of B11 CB and T111 CT components
(a) FS1 (1200RPM) (b) FS2 (1200RPM) (c) FS1 (1800RPM) (d) FS2 (1800RPM)
(e) FS1 (2400RPM) (f) FS2 (2400RPM) ............................................................. 204
Figure 7.14 Typical combined magnitudes of B11 CB and T111 CT components at
1200RPM for FS2 foundation (a) scenario 1 (b) scenario 2 (c) scenario (d)
scenario 4 ........................................................................................................... 206
Figure 8.1 Photograph of experimental rig [128] ................................................. 213
Figure 8.2 Typical pCCS and phase plots at 2040RPM (a)-(b) Healthy and (c)-(d)
crack ................................................................................................................... 214
Figure 8.3 Typical pCCS and phase plots at 3000RPM (a)-(b) Healthy and (c)-(d)
crack ................................................................................................................... 214
Figure 8.4 Typical 1x and 2x pCCS amplitudes and phases for all four cases at
2040RPM ............................................................................................................ 215
Figure 8.5 Typical 1x and 2x pCCS amplitudes and phases for all four cases at
3000RPM ............................................................................................................ 216
Figure 8.6 Typical normalised CS amplitudes for all four cases at 2040RPM ..... 217
Figure 8.7 Typical normalised CS amplitudes for all four cases at 3000RPM ..... 218
Figure 9.1 Proposed faults diagnosis process flow chart .................................... 230
Figure 9.2 Experimental rig ................................................................................. 235
Figure 9.3 Different rig supports (a) FS1 (b) FS2 ................................................ 236
Figure 9.4 Experimentally simulated cases (a) SC (b) LB (c) SM (d) SR ............ 238
Figure 9.5 Experimental setup for modal test ..................................................... 239
Figure 9.6 Typical FRF amplitude and phase plots for FS1, measured at bearing 2
(a) vertical direction (b) horizontal direction ........................................................ 240
Figure 9.7 Typical FRF amplitude and phase plots for FS2, measured at bearing 2
(a) vertical direction (b) horizontal direction ........................................................ 241
List of Figures
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Figure 9.8 Typical CB plots for FS1 and FS2 at 1200RPM (a) HRM (FS1), (b)
HRM (FS2), (c) LB (FS1), (d) LB (FS2) ............................................................... 243
Figure 9.9 Typical CT plots for FS1 and FS2 at 1200RPM (a) HRM (FS1), (b) HRM
(FS2), (c) LB (FS1), (d) LB (FS2) ........................................................................ 244
Figure 9.10 Proposed faults diagnosis (a) multiple speeds – FS1 setup (b) multiple
speeds – FS2 foundation (c) multiple speeds and multiple foundations ............. 248
Figure 9.11 Faults diagnosis with earlier CB and CT method (a) multiple speeds –
FS1 setup (b) multiple speeds – FS2 setup (c) multiple speeds and multiple
foundations ......................................................................................................... 250
Figure 9.12 Continuous faults diagnosis, (a) Multiple speeds - FS1 setup (b)
Multiple speeds - FS2 foundation (c) Multiple speeds and multiple foundations . 252
Figure 10.1 Schematic representation of pCCS computational process ............. 260
Figure 10.2 Laboratory scale experimental rig .................................................... 262
Figure 10.3 Typical pCCB plots (a) C1 (b) C2..................................................... 265
Figure 10.4 Typical pCCT plots (a) C1 (b) C2 ..................................................... 265
Figure 10.5 Typical combined magnitudes of B11 pCCB and T111 pCCT
components for all cases under ideal laboratory scenario (LS0) of complete data
............................................................................................................................ 266
Figure 10.6 Typical combined magnitudes of B11 pCCB and T111 pCCT
components for all cases under different laboratory scenarios of missing data (a)
LS1 (b) LS2 (c) LS3 (d) LS4 .................................................................................. 268
Figure 10.7 Typical combined magnitudes of B11 pCCB and T111 pCCT
components for individual cases for all scenarios (a) C1 (b) C2 (c) C3 (d) C4 (e)
C5 ....................................................................................................................... 269
Figure 10.8 Schematic representation of RKIDF assembly [262] ....................... 271
Figure 10.9 Schematic representation of the burning line ................................... 272
Figure 10.10 Limestone deposits on RKIDF impeller and blades [263] .............. 272
Figure 10.11 Photograph of on-site vibration measurement setup [263] ............. 273
Figure 10.12 Typical pCCB plots (a) faulty (b) healthy ........................................ 274
Figure 10.13 Typical pCCT plots (a) faulty (b) healthy ........................................ 274
Figure 10.14 Typical combined magnitudes of B11 pCCB and T111 pCCT
components for all cases under ideal industrial scenario (IS0) of complete data 275
List of Figures
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PhD in Mechanical Engineering (2015) University of Manchester (UK)
Figure 10.15 Typical combined magnitudes of B11 pCCB and T111 pCCT
components for all cases under different industrial scenarios of missing data (a)
IS1 (b) IS2 (c) IS3 (d) IS4 ...................................................................................... 276
Figure 10.16 Typical combined magnitudes of B11 pCCB and T111 pCCT
components for individual cases for all scenarios (a) all faulty (b) all healthy ..... 277
List of Tables
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Akilu Yunusa-Kaltungo 19
PhD in Mechanical Engineering (2015) University of Manchester (UK)
LIST OF TABLES ----------------------------------------------------------------------------------------------
Table 2.1 Roots blower scenarios for 2 cement plants ......................................... 90
Table 3.1 Technical specifications of the electric motor ........................................ 97
Table 3.2 Technical specifications of the speed controller .................................... 97
Table 3.3 Technical specifications of anti-friction ball bearings ............................ 99
Table 3.4 Technical specifications of accelerometers ......................................... 101
Table 3.5 Technical specifications of condenser microphone and power supply 103
Table 3.6 Technical specifications of ICP-PCB 086C03 instrumented hammer . 105
Table 3.7 Technical specifications of ICP-PCB 086C03 instrumented hammer . 106
Table 3.8 Technical specifications of NI 6229/16-bit/16-channel ADC ................ 108
Table 3.9 LABVIEW-based (version 2.0) data acquisition software settings ....... 109
Table 3.10 Experimentally identified natural frequencies for FS1 and FS2 ......... 119
Table 3.11 Experimentally simulated cases, abbreviations, severities and locations
............................................................................................................................ 126
Table 4.1 Shaft misalignment severities and locations ....................................... 134
Table 5.1 Simulated amplitudes and phases ...................................................... 148
Table 5.2 Magnitudes of CSD components ........................................................ 151
Table 5.3 Magnitudes of bispectrum and bicoherence components ................... 156
Table 6.1 Summary of the diagnostic features for bispectrum and trispectrum .. 174
Table 7.1 Experimentally identified natural frequencies for FS1 and FS2 ........... 190
Table 7.2 Summary of cases, locations and abbreviations ................................. 192
Table 7.3 CB components for HRM and LB cases (FS1 and FS2) at 1200RPM 195
Table 7.4 CT components for HRM and LB cases (FS1 and FS2) at 1200RPM 199
Table 7.5 Different scenarios of signal processing parameters .......................... 205
Table 9.1 Experimentally identified natural frequencies for FS1 and FS2 ........... 239
Table 9.2 Experimental scenarios for FS1 and FS2 ............................................ 242
Table 10.1 Experimental rig components and their specifications ...................... 263
Table 10.2 Experimentally simulated cases ........................................................ 264
Table 10.3 Signal processing parameters for experimental data ........................ 267
Table 10.4 Description of laboratory scenarios ................................................... 267
List of Tables
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Akilu Yunusa-Kaltungo 20
PhD in Mechanical Engineering (2015) University of Manchester (UK)
Table 10.5 Technical specifications of RKIDF [262] ............................................ 270
Abbreviations
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Akilu Yunusa-Kaltungo 21
PhD in Mechanical Engineering (2015) University of Manchester (UK)
ABBREVIATIONS ----------------------------------------------------------------------------------------------
AI
artificial intelligence
ANN artificial neural networks
BM breakdown maintenance
BS bent shaft
CB composite bispectrum
CI condition indicator
CM condition monitoring
CS composite spectrum
CSD cross-power spectral density
CT composite trispectrum
EDM electric discharge machining
FC flexible coupling
FD fault diagnosis
FDS
FE
fault diagnosis scenario
finite element
FRF frequency response function
FS flexible support
FT
HOC
HOS
Fourier transformation
higher order coherences
higher order spectra
HRM
IP
ISO
healthy with residual misalignment
input parameters
international standards organisation
LB
MMF
MSMF
OEM
loose bearing
magneto motive force
multi-speed multi-foundation
original equipment manufacturer
PC principal components
PCA principal component analysis
Abbreviations
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Akilu Yunusa-Kaltungo 22
PhD in Mechanical Engineering (2015) University of Manchester (UK)
PCB printed circuit board
pCCS poly coherent composite spectrum
PMR planned maintenance regions
PPM
PSD
RB
planned preventive maintenance
power spectrum density
roots blower
RC rigid coupling
RMS root mean square
RPM revolutions per minute
SC shaft crack
SM shaft misalignment
SR
STFT
shaft rub
short time Fourier transformation
SVM
TM
UMA
support vector machine
target moduli
unified multi-speed analysis
VFD vibration-based fault diagnosis
WEC wind energy converter
Nomenclature
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Akilu Yunusa-Kaltungo 23
PhD in Mechanical Engineering (2015) University of Manchester (UK)
NOMENCLATURE ----------------------------------------------------------------------------------------------
A orthogonal matrix
B number of bearings
B number of flexible supports
composite bispectrum at frequencies and
composite bispectrum at engine orders and
, , ..., experimentally simulated cases
covariance matrix of p
, , , frequencies
, ,.....,
feature matrices for different experimentally simulated cases at rotor speed
,
, ..., feature matrices at rotor speeds , ,.....,
respectively
, , ..., identical ‘as installed’ rotating machines with flexible supports 1, 2, ..., B
ns number of equal segments for Fourier transformation
n1 n2
observations variables
P number of measured data sets at a particular rotor speed
, ,....., rotor speeds in revolutions per minute
coherent composite spectrum at frequency
poly Coherent composite spectrum at frequency
,
coherent cross-power spectrum of the rth segment between bearings 1 and 2; bearings 2 and 3 at frequency
Nomenclature
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Akilu Yunusa-Kaltungo 24
PhD in Mechanical Engineering (2015) University of Manchester (UK)
coherent cross-power spectrum of the rth segment between bearings (b-1) and b at frequency
T number of principal components
composite trispectrum at frequencies , and
, Fourier transformation of rth segment at frequency for
bearings (b-1) and b respectively
,
, ,
coherent composite Fourier transformation of rth segment at frequency , , and
,
complex conjugate of the Coherent composite Fourier transformation of rth segment at frequency and
complex conjugate of the Coherent composite Fourier transformation of rth segment at frequency
, poly coherent composite Fourier transformation of rth
segment at frequencies and
,
complex conjugate of poly coherent composite Fourier transformation of rth segment at frequencies and
,
, ,
Fourier transformation of rth segment at frequency for measurement locations 1-4 respectively
X1, X2, X3, ...., Xq individual features for “p” number of observations for a
particular case at rotor speed
, and engine orders
, ,
coherence between bearings 1 and 2; 2 and 3; ... (b-1) and b
diagonal matrix
List of Publications
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Akilu Yunusa-Kaltungo 25
PhD in Mechanical Engineering (2015) University of Manchester (UK)
LIST OF PUBLICATIONS ----------------------------------------------------------------------------------------------
Journal Publications
1. Paper title:- A comparison of signal processing tools: higher order spectra
versus higher order coherences
Authors: - A. Yunusa-Kaltungo, J.K. Sinha
Journal Name: - Journal of Vibration Engineering and Technologies
Status: - Published, Volume 3, Issue 4, August 2015
2. Paper title:- Combined bispectrum and trispectrum for faults diagnosis in
rotating machines
Authors: - A. Yunusa-Kaltungo, J.K. Sinha
Journal Name: - Proceedings of the Institution of Mechanical Engineers, Part
O: Journal of Risk and Reliability
Status: - Published, Volume 228, Issue 4, February 2014
3. Paper title:- An improved data fusion technique for faults diagnosis in rotating
machines
Authors: - A. Yunusa-Kaltungo, J.K. Sinha, K. Elbhbah
Journal Name: - Measurement
Status: - Published, Volume 58, August 2014
4. Paper title:- Use of composite higher order spectra for faults diagnosis of
rotating machines with different foundation flexibilities
Authors: - A. Yunusa-Kaltungo, J.K. Sinha, A.D. Nembhard
Journal Name: - Measurement
Status: - Published, Volume 70, March 2015
5. Paper title:- A novel faults diagnosis technique for enhancing maintenance and
reliability of rotating machines
Authors: - A. Yunusa-Kaltungo, J.K. Sinha, A.D. Nembhard
List of Publications
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Akilu Yunusa-Kaltungo 26
PhD in Mechanical Engineering (2015) University of Manchester (UK)
Journal Name: - Structural Health Monitoring
Status: - Available online (DOI: 10.1177/1475921715604388)
6. Paper title:- Sensitivity analysis of higher order coherent composite spectra in
machine faults diagnosis
Authors: - A. Yunusa-Kaltungo, J.K. Sinha, A.D. Nembhard
Journal Name: - Structural Health Monitoring
Status: - Under review
Peer-reviewed Conference Publications
1. Paper title:- HOS analysis of measured vibration data on rotating machines
with different simulated faults
Authors: - A. Yunusa-Kaltungo, J.K. Sinha, K. Elbhbah
Conference Name: - 3rd
International Conference on Condition Monitoring of
Machinery in Non-Stationary Operations (CMMNO 2013), Ferrara/Italy, May 8-
10 2013
Status: - Published
2. Paper title:- Faults diagnosis in rotating machines using higher order spectra
Authors: - A. Yunusa-Kaltungo, J.K. Sinha
Conference Name: - ASME Turbo Expo 2014: Turbine Technical Conference
and Exposition (GT2014), Dusseldorf/Germany, June 16-20 2014
Status: - Published
3. Paper title:- Coherent composite HOS analysis of rotating machines with
different support flexibilities
Authors: - A. Yunusa-Kaltungo, J.K. Sinha
Conference Name: - 10th International Conference on Vibration Engineering
Technology of Machinery (VETOMAC X 2014), Manchester/United Kingdom,
September 9-11 2014
Status: - Published
List of Publications
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Akilu Yunusa-Kaltungo 27
PhD in Mechanical Engineering (2015) University of Manchester (UK)
4. Paper title:- Experimental observations of rotor orbit analysis in rotating
machines
Authors: - A. Yunusa-Kaltungo, A.D. Nembhard, J.K. Sinha
Conference Name: - 9th IFToMM International Conference on Rotor Dynamics
(IFToMM ICORD 2014), Milan/Italy, September 22-25 2014
Status: - Published
5. Paper title:- Study on rotating machine vibration behaviour using measured
vibro-acoustic signals
Authors: - A. Yunusa-Kaltungo, J.K. Sinha, A.D. Nembhard
Conference Name: - 4th International Conference on Condition Monitoring of
Machinery in Non-Stationary Operations (CMMNO 2014), Lyon/France,
December 15-17 2014
Status: - Published
Abstract
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Akilu Yunusa-Kaltungo 28
PhD in Mechanical Engineering (2015) University of Manchester (UK)
ABSTRACT ------------------------------------------------------------------------------------------------ The University of Manchester Akilu Yunusa-Kaltungo PhD Mechanical Engineering Vibration-based Condition Monitoring of Rotating Machines (2015)
Vibration-based condition monitoring (VCM) is an accepted approach for classifying machines as healthy or faulty. Although tangible advancements have been made with acceptable VCM techniques such as amplitude spectrum analysis, phase analysis, orbits analysis, etc. This often warrants the acquisition of vibration data from all orthogonal directions using multiple sensors at each bearing pedestal. Consequently, the number of data sets to be processed and interpreted could become overwhelming, especially when dealing with large industrial rotating machines.
Rotating machine faults are generally detected by the presence of harmonics of rotating speed in vibration response. Several studies indicate that higher order spectrum (HOS) and higher order coherence (HOC) possess the capabilities to establish the amplitude and phase interactions of frequency components in measured vibration signals. Hence HOS or HOC may be useful for detecting rotating machine faults. However, applications of HOC dominate the literature, with no clarification on which class is more useful. A comparative study was conducted with numerically simulated (with and without noise) and experimental data from a rig. These studies clearly indicate that HOS offers more meaningful results than HOC, owing to the significant dependence of HOC on the signal noise content. Hence HOS was used for further research studies.
Earlier studies tried to eliminate the rigour of analysing separate spectrum per measurement location by constructing single composite spectrum (CS) and bispectrum (CB) irrespective of measurement locations. Observations were encouraging but confined to a rig with relatively rigid foundation. Since several industrial rotating machines possess flexible foundations, the current study examined a wider range of faults on identical rigs with different flexible foundations. Composite trispectrum (CT) was also introduced to enhance robustness and it was observed that fault classification was possible at all speeds by combining just one CB and CT components. Despite the encouraging results obtained from earlier CS, it was limited by phase information loss at intermediate measurement locations. Also, the power spectrum density (PSD) computational approach adopted for the final CS makes it phase blind, thereby relying solely on the amplitudes at individual frequencies. Consequently, an improved poly-coherent composite spectrum (pCCS) was developed which retained phase information at all measurement locations. By building upon the earlier successes achieved with CB and CT, poly-coherent composite bispectrum (pCCB) and trispectrum (pCCT) were similarly developed which provided better diagnosis features.
Equipment standardisation as a cost-effective means of rationalising maintenance spares has become a very common industrial strategy. As a consequence of this, the existence of several identical rotating machines with different natural frequencies due to variations in their foundation flexibilities is also common. The development of a reliable method that permits the application of measured vibration data from one machine on another identical machine is likely to be appreciated by the industry. Hence, this was achieved by fusing pCCB and pCCT components in a novel hybrid data fusion algorithm on the identical rigs with different flexible foundations. The insensitivity of the proposed method to various scenarios of data availability was also confirmed with experimental and industrial data.
Declaration
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Akilu Yunusa-Kaltungo 29
PhD in Mechanical Engineering (2015) University of Manchester (UK)
DECLARATION ------------------------------------------------------------------------------------------------
I hereby declare that no portion of the work referred to in the thesis has been
submitted in support of an application for another degree or qualification of this or
any other university or other institute of learning.
Copyright Statement
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Akilu Yunusa-Kaltungo 30
PhD in Mechanical Engineering (2015) University of Manchester (UK)
COPYRIGHT STATEMENT ------------------------------------------------------------------------------------------------
I. The author of this thesis (including any appendices and/or schedules to this
thesis) owns certain copyright or related rights in it (the “Copyright”) and he
has given The University of Manchester certain rights to use such Copyright,
including for administrative purposes.
II. Copies of this thesis, either in full or in extracts and whether in hard or
electronic copy, may be made only in accordance with the Copyright, Designs
and Patents Act 1988 (as amended) and regulations issued under it or, where
appropriate, in accordance with licensing agreements which the University
has from time to time. This page must form part of any such copies made.
III. The ownership of certain Copyright, patents, designs, trademarks and other
intellectual property (the “Intellectual Property”) and any reproductions of
copyright works in the thesis, for example graphs and tables
(“Reproductions”), which may be described in this thesis, may not be owned
by the author and may be owned by third parties. Such Intellectual Property
and Reproductions cannot and must not be made available for use without
written permission of the owner(s) of the relevant Intellectual Property and/or
Reproductions.
IV. Further information on the conditions under which disclosure, publication and
commercialisation of this thesis, the Copyright and any Intellectual Property
and/or Reproductions described in it may take place is available in the
University IP Policy (see
http://www.campus.manchester.ac.uk/medialibrary/policies/intellectual-
property.pdf), in any relevant Thesis restriction declarations deposited in the
University Library, The University Library’s regulations (see
Copyright Statement
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Akilu Yunusa-Kaltungo 31
PhD in Mechanical Engineering (2015) University of Manchester (UK)
http://www.manchester.ac.uk/library/aboutus/regulations) and in The
University’s Policy on presentation of Theses.
Acknowledgements
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Akilu Yunusa-Kaltungo 32
PhD in Mechanical Engineering (2015) University of Manchester (UK)
ACKNOWLEDGEMENTS ------------------------------------------------------------------------------------------------
My colossal gratitude goes to the Almighty Allah for the strength and wisdom I
received through His infinite mercies during my PhD research.
I would like to express my sincere appreciation to the Petroleum Technology
Development Fund (Federal Government of Nigeria) for wholly sponsoring each
element of my PhD research at the University of Manchester (UK).
I am also indebted to my friends and former colleagues at Lafarge Cement PLC
(Ashaka Plant, Nigeria) for providing all of the equipment technical specifications and
data used for the industrial validation aspect of this study.
I would also like to thank Dr. Jyoti Kumar Sinha (my PhD supervisor) for his
unabated support, guidance and drive during my PhD research, which transmogrified
into an extremely wonderful research environment at the University of Manchester
(UK). I am also indebted to all members of the School of Mechanical, Aerospace and
Civil Engineering (MACE) workshop team for accurately producing all the
components of my experimental rigs.
I extend my thanks to my colleagues and friends at D-Floor students’ village (Pariser
Building) and the Dynamics Laboratory at the School of MACE (University of
Manchester). In particular, Dr. Adrian D. Nembhard and Dr. Keri Elbhbah with whom
I built a formidable and result-oriented relationship during the last 3 years.
Finally, I would like to thank my family (immediate and extended) and friends for their
moral support and stoicism during more than 3 years of sedulous efforts committed
to this research, especially when the chips appeared to be down.
Dedication
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Akilu Yunusa-Kaltungo 33
PhD in Mechanical Engineering (2015) University of Manchester (UK)
DEDICATION ------------------------------------------------------------------------------------------------
I dedicate this work to my late father (died 26/12/2005), my mother, my wife, my kids,
my sisters and my brothers who supported and encouraged me during this PhD
research.
Scientific Quote
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Akilu Yunusa-Kaltungo 34
PhD in Mechanical Engineering (2015) University of Manchester (UK)
SCIENTIFIC QUOTE ------------------------------------------------------------------------------------------------
“The measure of greatness in a scientific idea is the extent to which
it stimulates thought and opens up new lines of research.”
- Paul A.M. Dirac
Introduction
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Akilu Yunusa-Kaltungo 35
PhD in Mechanical Engineering (2015) University of Manchester (UK)
1 Chapter 1 INTRODUCTION
----------------------------------------------------------------------------------------------
1.1 Overview
A significant number of modern industrial operations rely on various rotating
machines including pumps, compressors, induction motors, turbo-generators,
crushers, etc. Owing to the recent advances in design and manufacturing
technologies, the configurations and complexities of these rotating machines have
risen tremendously, which has correspondingly increased their failure modes. In
general, the attainment of the end of useful operating life of one or more rotating
machine components (e.g. rotors, discs, bearings, couplings, blades, gears, etc.)
can be either age-related (gradual) or random [1]. In most cases, age-related and
systematic failures are often tolerable, owing to the fact that they are more
predictable and offer appreciable lead time to failure [2]. On the contrary, random
failures are often associated with a significant degree of uncertainty, which makes
them less desirable to any operational process [1], [3], especially when they can
potentially lead to huge production downtimes and in extreme cases loss of human
life. For instance, previous statistics had indicated that as much as 20% of
accidents that occur in aircraft transmission systems are random in nature [4], [5],
which further emphasizes the need for early and accurate rotating machine faults
detection techniques.
For several decades, maintenance activities (repair or replace) have always
served as remedies to rotating machine failures, although earlier maintenance
strategies accommodated larger tolerances for equipment failure. However, owing
to increasingly tough sanctions associated with operational inefficiencies,
maintenance strategies have significantly transformed from the age of waiting for
Introduction
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Akilu Yunusa-Kaltungo 36
PhD in Mechanical Engineering (2015) University of Manchester (UK)
failures to occur before repair/replace actions are initiated (breakdown
maintenance (BM)) or assuming that all failures are gradual and time-based (time-
driven or planned preventive maintenance (PPM)) to the prediction of failures prior
to their occurrence (condition monitoring). Figure 1.1 presents an outline of the
popular maintenance philosophies and some of their characteristic features.
Figure 1.1 Maintenance philosophies and their characteristics
Condition monitoring (CM) of rotating machines fundamentally involves the
continuous application of measured and trended operational parameters (which
are often compared to pre-established baseline values) such as temperature,
pressure, sound, vibration, motor current, etc., to predict machine health [6].
Amongst all the CM techniques (infrared thermography (IRT), wear debris analysis
(WDA), vibration-based condition monitoring (VCM), acoustic emission (AE),
motor current analysis (MCA), etc.), VCM is the most established and most
tangible [7], owing to the fact that most rotating machine faults (unbalance,
misalignment, looseness, broken rotor bars, worn/damaged gears, damaged
Introduction
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Akilu Yunusa-Kaltungo 37
PhD in Mechanical Engineering (2015) University of Manchester (UK)
couplings, damaged bearings, etc.) exhibit their peculiar defect characteristics,
which often provide very strong indications of the sources of machine faults [7].
Although several VCM techniques have been used for detecting faults related to
rotating machines, however, spectrum analysis is the most commonly applied in
practice. A major drawback of the application of spectrum analysis alone is the
possibility to generate identical features for different rotating machine operating
conditions. This drawback is owing to the fact that spectrum analysis simply
compares the amplitudes at individual frequencies for different machine
conditions, since all phase information have been lost during the magnitude
squared operation leading to its computation. This is why additional analysis such
as rotor orbits and phase analysis are often required, which significantly increase
the complexity and subjectivity of the fault diagnosis process. The problem
becomes even bigger and more complicated when dealing with one or more large
multi-shaft rotating machines with several bearings and operating at multiple
speeds, such as large turbo generator sets for power generation or the coal mill
drive assembly schematically shown in Figure 1.2.
Introduction
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Akilu Yunusa-Kaltungo 38
PhD in Mechanical Engineering (2015) University of Manchester (UK)
Figure 1.2 Multi-shaft coal mill drive assembly layout, with locations and
orientations of VCM sensors. HO represents horizontal orientation, VO vertical
orientation and AO axial orientation [8], [9].
According to the provisions of popular vibration monitoring standards such as ISO
10816 [10], VCM faults diagnosis on a typical rotating machine such as that shown
in Figure 1.2 would entail the analysis of approximately 28 data sets (i.e. 10 VO
accelerometers, 10 HO accelerometers, 3 AO accelerometers, 4 proximity probes
and 1 tachometer), which will require separate analysis (e.g. amplitude spectra,
rotor orbits, phase plots, etc.). Therefore, taking advantage of the recent
advancements in computational technology, the development of a VCM technique
that will significantly minimise sensor/data requirements without necessarily
compromising the faults diagnosis process is highly desirable. Besides reducing
the rigour, complexity and subjectivity associated with the application of
Introduction
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Akilu Yunusa-Kaltungo 39
PhD in Mechanical Engineering (2015) University of Manchester (UK)
conventional VCM techniques such as spectrum analysis, the current approach
will foster the realisation of the global need for sensor reduction and management
of big data (especially when it can be applied to several identical rotating
machines irrespective of their foundation flexibilities and speeds), which has
topped the list of several research councils for the past decade [11].
1.2 Research Objectives
The aim of this research is to simplify the currently existing rotating machines’
faults diagnosis process, so that the influence of subjectivity and engineering
judgements can be significantly minimised. Hence, the objectives are:
Objective 1: Compare Higher order spectra and higher order coherences
in order to determine the usefulness of either class of signal processing
tools.
Objective 2: Observe the dynamics of different rotating machine faults with
reduced sensors, using higher order spectra.
Objective 3: Improve the existing frequency domain data fusion technique
used for constructing a single composite spectrum for a rotating machine,
so as to ease and enhance the accuracy of fault diagnosis.
Objective 4: Develop a fault diagnosis method that is independent of
machine speeds and foundation flexibilities, using composite spectra.
Objective 5: Determine the sensitivity of composite higher order spectra to
various scenarios of data availability.
Introduction
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Akilu Yunusa-Kaltungo 40
PhD in Mechanical Engineering (2015) University of Manchester (UK)
1.3 Research Review
As earlier mentioned, the aim of the current research is to simplify the VCM of
rotating machines by reducing the number of sensors required, and hence the
data sets to be analysed as well as developing a faults diagnosis approach that
will aid faults classification in identically configured rotating machines irrespective
of their operating speeds and foundation types. General vibration guidelines (e.g.
ISO 10816 [10]) commonly used in practice often recommend that vibration
measurements at each bearing location of a typical rotating machine should be
recorded from all orthogonal directions (i.e. vertical, horizontal and axial
directions), thereby resulting to the installation of approximately 3 vibration
sensors (and a corresponding number of vibration data sets to be analysed) per
bearing location. In order to realise the objective of reduced sensors and
measured vibration data, the current research only employs the use of a single
vibration sensor (accelerometer) per bearing location. The measured vibration
data are then processed using the higher order signal processing tools, which
exhibit a valuable faults diagnosis characteristic of establishing the relationships
that exist between the various frequency components of a signal. Besides
expressing the relationship that exists between frequency components of a
measured vibration signal (which is very vital for rotating machines’ faults
diagnosis, since measured vibration signals from practical rotating machines often
contain several harmonic components due to different faults), each higher order
signal processing component contains both amplitude and phase information,
thereby eliminating the need for additional analysis of phase information often
associated with the conventional spectrum analysis technique.
There are two very popular classes of higher order signal processing techniques,
higher order spectra (HOS) and its normalised form, higher order coherences
(HOC). The decision to select HOS for the current research was based on the
results of an initial sensitivity analysis conducted on both experimental and
numerically simulated vibration data. From these analyses, it was observed that
HOC components were significantly influenced by variations in measurement
Introduction
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Akilu Yunusa-Kaltungo 41
PhD in Mechanical Engineering (2015) University of Manchester (UK)
noise, while the HOS components remained relatively stable at different noise
levels.
Besides the aim of minimising the number of rotating machines’ VCM sensors and
data requirements, currently employed faults diagnosis approaches such as
spectrum analysis often entail the analysis of numerous amplitude spectra (which
are directly proportional to the number of vibration measurement locations on the
machine) prior to establishing the machine’s state of health. This implies that
routine establishment of the operating condition of large rotating machines
characterised by several measurement locations could be extremely rigorous and
costly, which may hinder the timely detection of incipient faults. Therefore, an
approach that generates a single composite spectrum (CS) that represents the
entire dynamics of a rotating machine irrespective of the number of vibration
measurement locations has been developed by an earlier study. The approach
entails the fusion of measured vibration data in the frequency domain, which
provided different composite spectral features for several experimentally simulated
rotor-related faults of an experimental rig. Despite the encouraging results
observed from the earlier CS approach, its absolute reliance on the amplitudes of
harmonic components limited its robustness. Hence, an improved frequency
domain data fusion approach has been developed in the current study, which
clearly offered better fault diagnosis results when compared to the earlier
approach.
It is a very common practical scenario to have identically configured rotating
machines (either installed at different locations in a particular plant or installed at
different plants) with varying foundation flexibilities and operating at various
speeds. Based on existing VCM techniques, faults classification under such
scenarios usually entail the conduction of separate analysis for individual
machines at different speeds, which is extremely demanding. Therefore, based on
the combination of a few composite HOS components, the current approach was
used to diagnose several rotor-related faults irrespective of machine foundation
and speed. Finally, the sensitivity of the current method was also tested against
Introduction
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Akilu Yunusa-Kaltungo 42
PhD in Mechanical Engineering (2015) University of Manchester (UK)
different signal processing parameters and measured vibration data availability,
and the faults diagnosis features under each case remained relatively stable.
1.4 Outline of Thesis
This thesis is not presented in the classical PhD thesis format, but rather
presented in the alternative format where the core context is provided in the form
of published/submitted research journal and peer-reviewed conference papers.
However, it should be noted that as in the classical PhD thesis format, the
alternative format requires that all cited references are compiled and grouped
under “References” at the end of the thesis. Figure 1.3 shows a graphical abstract
of the various chapters and their associated contents, which is further elaborated
in the subsequent paragraphs.
Introduction
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Akilu Yunusa-Kaltungo 43 PhD in Mechanical Engineering (2015) University of Manchester (UK)
Figure 1.3 Thesis chapters and contents
Introduction
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Akilu Yunusa-Kaltungo 44
PhD in Mechanical Engineering (2015) University of Manchester (UK)
Chapter 2 presents a review of academic and commercial research works related to
the general concepts of rotating machines’ VCM, as well as some of the common
causes of vibration in rotating machines. Owing to the alternative format adopted for
this thesis, the literature review conducted in Chapter 2 has been limited to a
general overview of rotating machines’ VCM process and the characteristics of some
of the most common causes of abnormal rotor-related vibrations. However, since
each of the “results” chapters (i.e. Chapters 4-10) is self-contained, a more specific
review of literature related to the questions addressed by that chapter is again
provided, so that it can be read without reference to the rest of the thesis.
In Chapter 3, detailed descriptions of the experimental rigs and experimentally
simulated cases are provided, including the technical specifications and settings of
the equipment, tools and instrumentation used for data collection and processing.
Prior to the simulation of different machine faults on the rigs, the natural frequencies
of each rig were experimentally determined through modal analysis, so as to
adequately understand the dynamic behaviours of the studied rotating machines.
With the exception of Chapter 5 and Chapter 11, the subsequent chapters are
constituted of the results obtained from the various experiments conducted and their
corresponding explanations. Although full details of the experimental setups and
faults simulation are provided in Chapter 3, however, the alternative format adopted
in this thesis (based on published/submitted research papers) may sometimes be
characterised by the repetition of information (in this case, the experimental setups
and faults simulation sections) in some chapters (i.e. Chapter 4 and Chapters 6-10),
especially when the same experimental rigs and faults were used to generate all the
analysed data. However, this approach enhances readability, as it eliminates the
need for constant reference to Chapter 3. Also, it preserves the original contents of
the already published/submitted research papers as much as possible.
Chapter 4 provides initial experimental observations on the detection of different
rotor-related faults, using common VCM techniques (spectrum and rotor orbits
analyses), so as to justify the need for the currently proposed approaches.
Introduction
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Based on some of the limitations observed to be associated with the commonly
applied VCM techniques studied in Chapter 4, a comparison of the faults diagnosis
abilities of the 2 most popular classes of higher order signal processing tools (i.e.
Higher Order Spectra and Higher Order Coherences) is provided in Chapter 5. The
results of the comparisons indicated that HOS (bispectrum and trispectrum) features
were unaffected by variations in measurement noise, which eventually led to the use
of HOS for diagnosing different faults associated with a rigidly supported rotating
machine in Chapter 6.
Once the ability of HOS to distinguish between different rotating machines’ operating
conditions was established in Chapter 6, the possibilities of simplifying faults
diagnosis through the construction of a single coherent composite higher order
spectrum (i.e. bispectrum and trispectrum) that represents the entire dynamics of a
typical rotating machine with various foundation flexibilities was then investigated in
Chapter 7. This investigation exposed the prospects of significantly reducing the
subjectivities and engineering judgements associated with faults diagnosis of rotating
machines, especially when dealing with large industrial rotating machines that are
supported by numerous bearings (e.g. large turbo generators).
Although the coherent composite higher order spectrum (CCS) data fusion technique
proposed in Chapter 7 provided encouraging rotating machines’ faults diagnosis
results, however, it was later observed that the cross-power spectral density (CSD)
approach adopted for the fusion of the measured vibration data from all
measurement locations led to the loss of phase information at successive bearing
locations, which eventually restricted the technique to faults diagnosis based on only
the amplitudes of several higher machine harmonics. In order to address this
limitation, an improved data fusion technique (i.e. poly-Coherent Composite
Spectrum) that retains all the amplitude and phase information at all the
measurement locations of a typical rotating machine was developed in Chapter 8.
The results obtained in Chapter 8 clearly indicated that faults diagnosis with the
improved poly-Coherent Composite Spectrum (pCCS) can be done based on just the
amplitudes and phase of the first or second harmonic alone, thereby eliminating the
need for investigating the higher harmonic components.
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Chapter 9 presents a novel faults diagnosis technique that is capable of detecting
and classifying different rotating machines’ conditions, irrespective of the machine
speed or foundation flexibility. In this chapter, pCCS components computed for
different machine conditions (i.e. operating speed, different foundation flexibility and
state of health) were used as the features in a principal components analysis (PCA)
based algorithm, so as to develop a multiple faults/multiple speeds/multiple
foundations faults diagnosis technique for enhancing maintenance and reliability of
industrial rotating machines. This approach aims to eliminate the current practice of
conducting separate faults diagnosis for identical rotating machines installed at
different plant locations and operating under different conditions of speed and health.
A comparison of the multiple faults/multiple speeds/multiple foundations faults
classification capabilities of features computed based on the earlier CCS and the
improved pCCS was also conducted in this chapter.
Based on the premise that industrial rotating machines often operate under severe
adverse conditions that sometimes lead to VCM sensors’ damage and eventual loss
of vibration data, Chapter 10 examines the ability of the proposed pCCS faults
diagnosis technique to classify machine faults under different scenarios of measured
vibration data availability.
Finally, Chapter 11 provides the concluding remarks (i.e. an overall summary of the
main findings from each chapter), and discusses the possibilities for future research.
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2 Chapter 2 LITERATURE REVIEW
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This chapter commences by presenting a general overview of rotating machines
and the VCM framework, including detailed explanations of the vital stages (i.e.
data collection, data processing and faults diagnosis) of the VCM process. The
chapter then proceeds to discuss some of the most commonly encountered rotor-
related faults in practice. Reviews of previously reported research studies on VCM
techniques that are commonly used to diagnose such rotor-related faults are
provided, as well as highlights of the need for more robust and simplified
approaches.
2.1 Typical VCM Process Framework
As previously mentioned, rotating machines form the heart of most industrial
activities, and more often than not, a reasonable amount of industrial failures are
usually associated with one or more components of these rotating machines. A
rotating machine may be simply described as an assembly of different
components (e.g. bearings, shafts, gears, couplings, impellers, blades, etc.) with
at least one of these components subjected to rotational motion, so as to aid the
achievement of a specific operational purpose [12]. The class of rotating machines
is quite enormous and vast, of which some of the most commonly used ones
across different industries include compressors, induction motors, fans, turbo-
generators, bucket elevators, belt conveyors, drag chains, crushers, drills, pumps,
etc. Owing to the extreme relevance of rotating machines, varying degrees of
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design and complexities have emerged over the years. These complexities and
sophistications correspondingly increase their proneness to failures, due to
increased failure modes. The implications of rotating machines’ (especially the
critical ones) failures to industries can range from short duration downtimes to
catastrophic and permanent stoppages, which often have very significant effects
on production, finance, safety and environment [12], [13]. Since rotating machines
form the backbone of most operations, it therefore becomes imperative to deduce
robust and reliable techniques that will accurately detect and diagnose their
incipient faults, so as to reduce the impacts of downtime to the barest minimum.
Over the years, a very popular means of prolonging the lead time to rotating
machines’ failures [14]–[17] is VCM, which is perhaps due to worrying statistics
indicating that up to 20-40% of casualties and unplanned outages could be directly
linked to vibration [18].
VCM is a branch of CM maintenance philosophy that employs vibration-based
techniques to ascertain the true conditions of machines and structures, so that
maintenance decisions (repair or replace) can be recommended based on
detected deviations from normal operational conditions. A correctly implemented
VCM program has the capability of significantly reducing maintenance costs,
through the elimination of sudden or abrupt failures. A typical VCM process is
often made up of the three basic stages shown in Figure 2.1 [19].
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Figure 2.1 Basic stages of a typical VCM process
2.1.1 Data collection
The initial stage of a typical VCM process for rotating machines is the
measurement and storage of vibration data. This stage of VCM usually entails the
installation of several instruments, which may slightly vary for different rotating
machines depending on complexity and fault types. However, most VCM systems
will usually require transducers, signal conditioners, analogue-to-digital converters
and means of storing the measured vibration data for further processing. A
transducer or sensor can be defined as an instrument that is capable of
transforming variations in physical quantities into an electrical signal. The vibration
signals measured from rotating machines by the transducers are usually analogue
signals which will need to be digitized for them to be admissible to the eventual
storage systems (usually a personal computer system). This digitization is
achieved through the aid of an analogue-to-digital converter (ADC). Sometimes,
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the range of the signals measured by the transducer may exceed or fall short of
the requirements of the ADC. Therefore, the incorporation of a signal conditioning
unit is always desired. Signal conditioning units perform various functions,
including the provision of required power to the transducers as well as the
amplification or attenuation of the measured signal, so as to ensure adequate
compatibility between measured signal range and the requirements of the ADC.
Figure 2.2 is a schematic representation of PC-based data collection and storage
stage of a typical rotating machine’s VCM system showing transducers
(accelerometers) A1-A4 installed at bearings B1-B4, flexible (FC) and rigid (RC)
couplings, signal conditioner, ADC and personal computer (PC).
Figure 2.2 Vibration data collection process for a typical rotating machine [20]
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In accordance with the theory of vibration, all vibrating components possess three
classes of closely related parameters (i.e. acceleration, velocity and displacement)
as shown by Equation (2.1). This therefore implies that the availability of any of
these parameters can adequately generate the other two parameters through
differentiation or integration [21].
(2.1)
In Equation (2.1), , and respectively denote the inertia, damping
and stiffness forces, while their sum is equivalent to the external force ( ). It is
therefore visible from the relationship that the inertia force is associated with
acceleration ( , while the damping and stiffness forces are respectively
associated with velocity ( ) and displacement ( ).
There are various types of transducers for measuring the vibration responses of
rotating machines in practice, including proximity probes for measuring the relative
displacement of a rotating shaft with respect to a fixed bearing pedestal,
seismometer for velocity measurements and accelerometers for acceleration
measurements. However, the setting up of a vibration data collection system
should be guided by certain precautions, which are not limited to but including [23]:
Knowledge of the technical specifications of the rotating machine on which
measurements are to be conducted.
Knowledge of the working principle and technical specifications of the
selected transducers (e.g. sensitivity, frequency range of measurement,
resonance frequency, etc.), so as to aid optimised selection.
Knowledge of the implications of different transducer mounting techniques
(e.g. stud, adhesive, wax and hand-held mounting techniques) on the
repeatability of measurements.
Knowledge of how the measured vibration data will be stored into the PC.
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2.1.2 Data processing
The vibration data measured and stored using the concepts described in Section
2.1.1 require processing, so as to extract the features that can be used to describe
the different operational conditions of the studied rotating machine. Measured
vibration signals are usually time domain signals which are complex in nature,
containing several frequency components with correspondingly different
amplitudes, due to the variety of responses generated by different components
(e.g. rotor, bearings, gears, blades, etc.) that form the machine train and possible
faults (e.g. misalignment, unbalance, crack, bend, rub, etc.). An earlier study by
Jardine et al. [19] classified rotating machinery data as waveform data, which can
be analysed using all or any of these three basic classes of techniques, namely;
time domain, frequency domain or time-frequency domain analyses techniques.
2.1.2.1 Time domain analysis
A time domain signal can be simply described as a plot of vibration amplitude
(displacement, velocity, acceleration, etc.) against time. During time domain
analysis, statistical features (e.g. peak, peak-to-peak, root-mean-square, crest
factor, kurtosis, etc.) that describe the time waveform are extracted in the time
domain. A very common application of time domain analysis in the industry is for
the overall comparison of the wave patterns of two “as installed” machines, so as
to establish their states of operational health with respect to each other, prior to
detailed analysis for detecting the exact sources of faults.
Time domain analysis has existed for a substantial period of time, with analysis in
earlier times involving the use of oscilloscopes and manual computation of the
different frequency components. A very popular and valuable kind of time-domain
analysis is the synchronous time averaging (STA) technique [22]–[24]. STA is very
useful in the localisation of vibration sources when there are several shafts running
at different speeds (e.g. in a multi-shaft drive assembly such as that shown in
Figure 1.1) in a machine train, as it directly measures vibrations that are
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associated with the running speed of the machine’s component of interest. This
therefore makes STA useful for eliminating vibrations that are not related (non-
synchronous) to the fundamental running speed of the reference shaft (such as
bearings faults, noise, etc.) through averaging, while retaining rotor related (such
as unbalance, rub, misalignment, looseness, etc.) vibrations.
Studies by Dalpiaz et al. [25] compared the effectiveness and sensitivities of
vibration signals processing techniques such as cepstrum and STA for the
detection of gear faults. The study [25] indicated that cepstrum analysis only
provided detailed information about the spectrum evolution, but was unable to
detect the gear faults from a single vibration measurement, due to the presence of
high energy activities (gear meshing frequencies) in both healthy and faulty gears.
On the other hand, STA provided absolute diagnostic information by effectively
identifying the location of the faulty gear.
2.1.2.2 Frequency domain analysis
Analysis in the frequency domain primarily entails the conversion of the complex
time domain vibration signal into the frequency domain, through the well-known
fast Fourier transformation (FFT) process. A significant merit of working in the
frequency domain over the time domain is its ability to easily isolate frequency
components of interest, which is further explained in Appendix A. One of the most
successful and widely used forms of frequency domain analysis is the spectrum
analysis, which involves either viewing the entire range of the machine spectrum
or focussing on a particular set of interesting frequency components [26]–[28].
2.1.2.3 Time-frequency analysis
The investigation of time-frequency analysis commenced due to the perceived
inabilities of the conventional spectrum analysis to effectively handle non-
stationary waveforms, which is quite possible with rotating machines. The
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conventional time-frequency analysis applies time-frequency distributions (which
represent the energy or power of the waveform signal in a dual dimensional
function of time as well as frequency) for more effective and revealing diagnosis of
rotating machinery faults. Some of the most popular time-frequency analysis
techniques are the short-time Fourier transform (STFT) or spectrogram [29]–[31].
STFT is based on the principle of dividing the entire waveform signal into various
segments with short-time windows, and subsequently performing a Fourier
transform on each segment.
2.1.3 Faults diagnosis
Faults diagnosis in VCM of rotating machines can also be referred to as the
interpretation of the measured vibration data. This stage of the VCM process
mainly involves the analysis of the various features (representing different
machine conditions) that have been extracted through any of the principles
described in Section 2.1.2, so as to ascertain the exact sources of the rotating
machine’s excessive vibration. Figure 2.3 shows a typical spectrum-based faults
diagnosis fault tree for some common rotating machine faults. As earlier
mentioned in Section 2.1.2, every component in a rotating machine train can be
described by its individual characteristic defect feature. Hence, the accurate
detection of these defect features provides significant guides towards the root
causes of abnormal rotating machines’ vibration.
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Figure 2.3 Typical spectrum-based VCM fault tree for a rotating machine
2.2 Standard Approaches to Vibration-based Fault Detection
Although a brief mention of the applications of some popular classes of VCM
techniques was made as part of Section 2.1.2 (Data processing), however, the
research and industrial maturity of VCM techniques such as amplitude spectrum
analysis for fault diagnosis makes it imperative to further highlight relevant
literature especially with respect to its sensitivity to different faults. This is then
followed by an overview of other standard VCM techniques such as rotor orbit
analysis, full spectrum analysis and order tracking.
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2.2.1 Spectrum analysis
Amongst the currently employed VCM techniques in practice, spectrum analysis
(based on the fast Fourier transformation (FFT)) is undoubtedly the most quotidian
due to its ease of computation and versatility. Once the FFT and eventual power
spectrum density (magnitude squared operation that leads to the loss of phase
information) operation is performed, the typical amplitude spectrum results to a
plot of amplitude at individual frequency components of the measured vibration
signal. Features (e.g. 1x, 2x, 3x, etc.) from several amplitude spectra representing
different machine operating conditions are then extracted and compared during
faults diagnosis. In this section, an overview of the spectrum-based characteristics
of some of the most commonly encountered rotating machine faults in practice will
be provided, so as to augment understanding. Additional theoretical explanation of
amplitude spectrum is provided in Appendix A.
2.2.1.1 Unbalance fault
Unbalance fault has been classified as one of the most common causes of
vibration in rotating machines [32]. Parkinson [33] and Foiles et al. [34]
respectively provided detailed and comprehensive reviews of some of the
conventional techniques commonly applied for correcting unbalance in rotors.
Machinery vibrations due to unbalance fault is usually characterised by a dominant
peak at the fundamental rotational frequency (1x RPM), which usually changes in
proportion to the square of the rotational speed and in the radial direction. Figure
2.4 provides a typical amplitude spectrum of a rotating machine with unbalance
fault. The total elimination of unbalance fault in rotating machines is almost
impracticable, due to the difficulties associated with achieving perfection in the
manufacture of components as well as their installation. Based on this premise, a
significant number of researches have been centred on estimating unbalance and
its correction.
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Figure 2.4 Typical amplitude-spectrum of a rotating machine at 2040 RPM,
showing dominant 1x RPM peak as a result of unbalance fault.
2.2.1.2 Shaft bow
The amplitude spectrum produced as a result of a bent or bowed shaft will usually
be characterised by the presence of 1x and 2x RPM components, which will
generally be transmitted in both radial and axial directions [35]. The location of the
bend will determine the dominance of the 1x RPM amplitude (if at the centre of the
shaft) or 2x RPM (if bend is located near the ends of the shaft). A detailed review
by Mehrjou et al. [36] on CM techniques for detecting rotor faults in squirrel-caged
induction machines pointed out that a bowed rotor complicates alignment and
could as well lead to other problems, depending on the location.
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Figure 2.5 A typical amplitude-spectrum of a rotating machine at 1200 RPM,
showing the appearance of several higher harmonics of machine speed due to
rotor bow.
2.2.1.3 Shaft misalignment
Another very common cause of vibration in almost all classes of rotating machines
is misalignment. Shaft misalignment in rotating machines refers to a state whereby
components that have been designed to be coaxial are not actually coaxial, owing
to assembly defects or deformation of certain machine sub-units [37].
Misalignment in rotating machines may either appear as angular or parallel. The
occurrence of angular misalignment is as a result of the formation of an angle by
the centre lines of the two coupled shafts. Vibration spectra produced by rotating
machines with angular misalignment will be characterised by pronounced peaks at
1x RPM, while the presence of 2x and 3x RPM components is highly possible [38].
Angular misalignments in rotating machines usually generate high axial vibrations.
In the case of parallel misalignment, the centrelines of the coupled shafts are
parallel to each other, but with a certain degree of offset and therefore do not
coincide at any point. Such misalignments produce dominant 2x RPM components
in the radial direction, due to the two hits that occur per rotational cycle. Owing to
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the fact that parallel misalignment rarely occurs in isolation, the appearance of 1x
RPM component is also very common.
Figure 2.6 Typical amplitude-spectrum of a rotating machine at 2040 RPM,
showing dominant 1x RPM and 2x RPM peaks due to misalignment.
2.2.1.4 Mechanical looseness
Mechanical looseness can either occur in the form of internal looseness between
the machine and its base mounting, internal looseness of the machine
components or structural looseness. Internal looseness occurs due to lack of
proper fit between the components of a machine (bearing-to-bearing housing,
shaft-to-bearing, coupling-to-shaft, etc.), which consequently leads to the
excitation of numerous harmonics of the machine running speed. These
harmonics are usually generated due to combined effects of exciting forces from
the rotor and the non-linear response from the loose components [35]. Looseness
between machine and base mounting is commonly the resultant of a crack in the
base structure or bearing pedestal, which may generate high 2x RPM component
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and some harmonics. Structural looseness on the other hand occurs when there is
a weakness in the foundation or looseness in the supporting structure.
The presence of mechanical looseness in a machine train is often characterised
by chaotic response, which have been observed to sometimes excite multiples of
x or
x RPM [39]. Other studies on mechanical looseness in rotating machines
such as those related to bearing caps or supports have also been seen to have
large numbers of harmonics and sub-harmonics, which were dependent on the
analysis direction and point [40]. The vibration signatures produced by a rotating
machine with mechanical looseness have also indicated that the vibration
amplitude at the higher order frequency region will usually be greater than half of
the vibration amplitude caused by the rotational speed, which will persist after
machine balancing operations [41].
Figure 2.7 A typical amplitude-spectrum of a rotating machine at 1200 RPM,
showing the appearance of several higher harmonics of machine speed due to
bearing looseness.
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2.2.1.5 Shaft crack
Another fault common to rotating machines is shaft crack. Although the primary
aim of studying shaft crack is for the purpose of fault detection and diagnosis,
however, the behaviour and responses that result from this fault also makes it an
interesting subject area. A cracked shaft will usually lose stiffness in a direction
perpendicular to the crack location. One of the most fundamental signs of the
emergence of a crack is the appearance of 1x RPM and 2x RPM components
(which is usually the outcome of the asymmetry in the shaft’s stiffness). The 2x
RPM component will usually be dominant when the operating speed is about half
the critical speed, which should disappear with a change in the rotational speed of
the machine [35]. Besides the second harmonic of the rotational speed (2x RPM)
and the sub-harmonics of the critical speed, additional higher order harmonics of
the rotational speed (i.e. 3x RPM, 4x RPM, etc.) may be observed due to the non-
linear effects associated with the crack breathing action (opening and closing) [42],
[43]. Research studies aimed at understanding the signatures of cracked rotors
have existed for decades, with some of the very early studies using the different
moments of inertia of rotors to detect the presence of cracks, once higher and sub-
harmonics are initially observed in the spectra [44]. Figure 2.8 shows the typical
amplitude spectrum for a rotating machine with a transverse crack on its rotor.
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Figure 2.8 A typical amplitude-spectrum of a rotating machine at 2040 RPM,
showing the appearance of several harmonics of machine speed due to rotor
crack.
2.2.1.6 Shaft rub
The response generated by a rotating shaft experiencing a rub action is very
similar to that of a loose machine, especially with its chaotic nature. Shaft rub
could be partial, (which occurs when the shaft only makes contact at some certain
points during its rotational cycle) or whole (where there is a constant and
continuous rub throughout the entire rotational cycle). Shaft rub is characterized by
the generation of a number of frequencies, excitation of one or more natural
frequencies and may also produce a band of white noise in the high frequency
region of the spectrum [35]. In addition, a rub action may also be characterised by
the presence of sub-harmonics, which will be integer fractions of the machine
rotational speed
. It is important to note that the appearance of
sub-harmonics in the spectrum of a machine experiencing shaft rub could be
highly dependent on the position of the shaft natural frequencies [35]. Although the
duration of a shaft rub action may be short, its severity could still significantly
depend on which component in the machine train the shaft rubs. Shaft rubs
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against seals, glands or coupling guards may be less severe. However, shaft rubs
against machine components such as bearings or turbine blades rubbing on
casing could have devastating consequences irrespective of the duration. Figure
2.9 shows a typical example of the spectral response that could be generated as a
result of shaft rub action.
Figure 2.9 A typical amplitude-spectrum of a rotating machine at 2040 RPM,
showing the appearance of sub-harmonics of machine speed due to rotor rub.
2.2.2 Rotor orbit analysis
Another well-established VCM technique for rotating machines is the rotor orbit
analysis. Rotor orbits generally represent the enlarged pathway of the exact
motion of a rotor’s centreline [45]. Rotor orbits are recreated from the vibration
signals measured by 2 vibration sensors (usually proximity probes) installed in the
vertical and horizontal directions of the rotor. Since it is often believed that
changes in rotor motions at certain times are always triggered by variations in the
rotor dynamic stiffness or changes in the forces exerted on it, rotor orbits can
sometimes provide meaningful information with regards to the rotor behaviour [45].
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Figure 2.10 shows how a rotor orbit can be constructed from measured vertical
and horizontal shaft displacements. The tachometer signal may also be used to
define the start and finish points of the orbit, so as to track phase changes.
Figure 2.10 Rotor orbit plot of a typical rotating machine
Several researchers have attempted to develop specific fault diagnosis patterns
for various rotor-related faults using orbit plots. For instance, Darpe et al. [46] and
Sinou [47] independently conducted experiments to investigate transverse crack
through the appearance of an inner loop orbit which varied in size when the
machine speed is approximately half of the first natural frequency, owing to the
presence of a dominant second harmonic of the machine speed. Although both
studies [46], [47] focussed on the detection of rotor crack, the experiments by
Darpe et al. [46] were done on an experimental rig with self-aligning ball bearings
with the aim of confirming earlier findings on the analysis of a Jeffcott rotor with
transverse breathing crack and passing through subcritical resonances. Also
based on a compendious experimental investigation of rotor cracks, Sinou [47]
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used rotors with slots (representing rotors with cracks) that are supported by bush
bearings. These investigations therefore led to the conclusions that rotor cracks
could be diagnosed based on variations in the orientation of the inner looped orbit
once it passes through sub-critical resonances [46].
The results of another experimental study conducted by Bai et al. [48] also
promulgated a rotor orbit with an inner loop for a small rig supported by ball
bearings. In this study [48] however, the inner loop was not due to a crack but
rather due to the occurrence of sub-harmonic resonance once the rig (under
unbalance load) speed was approximately twice its critical speed. In an attempt to
accurately establish specific diagnosis features for different machine operating
conditions based on rotor orbits, Muszynska and Goldman [49] simultaneously
investigated the dynamics of an unbalanced rotor supported by rolling element
bearings on several experimental rigs, including a rig with a loose bearing
pedestal and another with rotor-stator rub actions. Observations from the studies
stipulated that when partial rotor-stator rubbing occurred at high speeds, the orbits
display reverse precession loops as a consequence of the rub-generated
tangential force opposing the direction of rotation. Other research efforts aimed at
improving fault diagnosis using rotor orbit analysis include the detection of impact
rub phenomenon [50], cracked shaft [51], investigation of the causes of fractional
harmonic components in journal bearings as well as variations in oil temperature
and pressure [52], shaft misalignment [53], [54], backward whirl due to excessive
friction generated by rubbing components [49], etc.
2.2.3 Full spectrum analysis
The conventional spectrum analysis is based on vibration data acquired from only
one measurement direction (i.e. either vertical or horizontal), which therefore
makes it impossible for it to establish the relative phase correlation that exists
between vertical and horizontal spectral components [53]. But just as rotor orbit,
the full spectrum also offers information about the correlation that exists between
vibration data sets simultaneously measured in the vertical and horizontal
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directions (using vibration sensors). The initial steps of full spectrum analysis are
very similar to those applied for the conventional spectrum analysis, whereby the
time domain data from the vibration sensors are respectively broken down into
frequency components. A full spectrum is then created from the amplitudes of the
forward and backward whirl components of the filtered orbits. In concise terms, the
full spectrum can be regarded as the spectrum of an orbit. The vertical axis of the
full spectrum represents the peak-to-peak amplitude of the forward/backward
components, while the horizontal axis represents the ‘±’ frequency components.
The “+” represents forward components and are usually plotted on the right-hand-
side (RHS), while the “−” represents backward components and are
correspondingly plotted on the left-hand-side (LHS). More detailed and
comprehensive information, including the mathematical approach for generating
full spectra were presented in an earlier study conducted by Goldman and
Muszynska [55].
Industrial applications of full spectrum is not limited to but include the investigation
of axial run-out of shafts due to mechanical or electrical deformities [55]. Based on
the ambiguity often associated with the differentiation of certain rotor-related faults
such as shaft crack and shaft misalignment, some researchers have explored the
possibility of enhancing fault diagnosis quality by using full spectrum analysis. For
instance, using and experimental rig with 2 coupled rotors (each rotor carrying a
balance disc), Patel and Darpe [53] disclosed that although the vibration of rotors
due to parallel and/or angular misalignment is forward whirling (due to marginally
larger “+” harmonic components than “−” harmonic components), the presence of
backward whirl components at sub-critical speeds could provide a valuable means
of distinguishing misalignment and crack. The study [53] further emphasized that
the whirl nature of 2x and 3x components at 1/2 and 1/3 the critical speeds
respectively provide swift means differentiating shaft crack and shaft misalignment
faults. At 1/2 the critical speed, both +2x (forward) and -2x (backward) whirl
components are significant for shaft misalignment, unlike shaft crack that
possesses only significant +2x (forward) and very negligible -2x (backward) whirl
components. Similarly, at 1/3rd the critical speed, shaft crack exhibits prominent
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+2x and +3x whirl components [56], with correspondingly negligible -2x and -3x
components, while shaft misalignment fault showed very comparable +2x, -2x, 3x
and -3x components.
In another experimental study, Fengqi and Meng [57] examined the features of full
spectra for various kinds and severities of rub in rotating machines, where it was
concluded that stable 1x amplitude along with lower amplitudes of its harmonics
will be observable with relatively mild rub actions. On the other hand, the
amplitude of 1x decreases as the magnitude of rub increases, which will also
trigger the generation of more higher harmonic components. Additionally,
Goldmann and Muszynzka [55] provided a detailed summary of the observable
features from full spectrum when diagnosing commonly encountered rotating
machine faults such as unbalance, rotor crack, partial rub, full rub, etc.
2.2.4 Order tracking
The behaviours of rotating machines during transient operations often provide very
vital information that aid the detection or verification of impending faults that may
lead to very costly downtimes. During order tracking, 1x and other higher
harmonics of the machine speed need to be extracted from the measured vibration
data [58], [59], so as to establish amplitude-to-phase relationship of the extracted
harmonics (e.g. 1x, 2x, etc.) with the change in machine speed (which is
sometimes plotted as the Bode plot).
In a study conducted by Wang et al. [60] to accurately monitor the propagation of a
transverse crack on a shaft with variable speed, it was proclaimed that though
small in amplitude, transient vibrations due to cracks often modulate and distort
the prominent harmonic vibration orders which makes the phenomenon extremely
difficult to extract based on time waveform reconstructed order tracking alone.
Therefore, through the individual application as well as combinations of various
signal processing techniques (e.g. Vold-Kalman filter order tracking (VKF-OT),
Gabor order tracking (GOT), Fourier analysis, time-frequency analysis, computed
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order tracking (COT), etc.) on a set of simulated data representing a machine with
cracked rotor, Wang et al. [60] concluded that an integration of COT [61], VKF-OT
or GOT techniques offer the best possibilities for detecting both the prominent
harmonic and the small transient vibrations.
In another study, Abdul-Aziz et al. [62] experimentally monitored the behaviour of
a growing crack through spin tests conducted on a rotating rig, with the primary
aim of simulating the mission profile of a space aircraft engine. Crack detection in
this study [62] entailed comparing the bode plots of 2 scenarios (healthy toothed
disc and a toothed disc with a small artificially induced notch) on the same
experimental rig. In the bode plot for the experimental setup with a cracked disk, a
sharp rise in the amplitude response after settling past the 1st critical speed was
clearly observed and this behaviour was attributed to the crack. The response for
the healthy disk however remained smooth after crossing the 1st critical speed.
The findings from this study further affirms the observations from earlier studies
[63], [64], whereby a sharp rise in amplitude upon surpassing the 1st critical speed
was also reported.
2.3 Overview of Standard Vibration Based Fault Detection
Approaches
Over the years, a lot has been achieved in VCM of rotating machines through the
application of standard VCM techniques such as simple amplitude spectrum.
These achievements are immensely owed to a variety of factors such as the
sensitivity of the technique (i.e. amplitude spectrum) to a wide range of machine
faults (e.g. shaft bow, shaft misalignment, shaft crack, loose bearings, gear wear,
unbalance, bent shaft, gear crack, etc.), relative computational simplicity as well as
its applicability to different kinds of rotating machines. However, despite the
maturity level of the generally used amplitude spectrum (based on power spectrum
density), fault diagnosis based on this technique is tedious and often requires a
significant level of engineering judgement from an experienced analyst. Although
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the computation of amplitude spectra from measured vibration data is relatively
simple, however its lack of phase information often leads to over reliance on the
amplitudes at individual frequencies during fault diagnosis. In practice, the
amplitude/frequency relationship for different machine faults could appear similar.
For instance, the amplitude spectra due to shaft misalignment, loose bearing and
cracked shaft respectively shown in Figures 2.4-2.7 all contain several harmonics
of the machine speed.
Besides the loss of phase information, the limitations of diagnosis based on the
simple amplitude spectrum alone is further compounded by the fact that popular
vibration standards [10] recommend that vibration measurements should be
conducted at all orthogonal (xyz) axes of the bearing pedestals of rotating
machines. Consequently, several vibration sensors are often required at each
bearing pedestal, which leads to the generation of large volumes of data. The
method then becomes computationally intensive and complex for even the most
experienced analysts, especially when dealing with large rotating machines that
are supported by numerous bearings. Perhaps, a combination of these limitations
especially the lack of phase is the reason why spectrum analysis is usually
conducted in conjunction with other techniques such as orbit and phase analyses,
so as to enhance the confidence levels of the results.
The efficacy of monitoring the dynamic behaviour of rotating machines under
different operating conditions is well-known. However, the ambiguity associated
with rotor orbits representing clearly different machine operating conditions
sometimes introduces appreciable levels of inconsistency to the fault diagnosis
process. Thus, overcoming such inconsistencies would entail the introduction and
eventual analysis of additional parameters such as phase, using techniques such
as order tracking and full spectrum analysis. Effectively integrating all of these
techniques when analysing each machine condition will not only require
substantial expertise, but could also lead to expensive delays and plant
downtimes. As a consequence of the subjectivity and over dependence on human
engineering judgement associated with standard VCM techniques, VCM related
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researches have significantly diversified towards the application of model-based
fault detection techniques, artificial intelligence and pattern classification
techniques, higher order signal processing techniques, etc.
2.4 Emerging Approaches to Vibration Based Fault Detection
Recent advancements in computational and information technologies have offered
researchers ample opportunities to accurately detect and classify rotating machine
faults, using a variety of approaches. In this section, some of the emerging VCM
fault detection approaches will be highlighted.
2.4.1 Model-based approaches
Model-based fault diagnosis of rotating machines fundamentally entails the
development of an explicit mathematical model of the studied machine. Upon the
creation of a representative model, residual generation techniques (e.g. parameter
estimation) are then used to extract signals (also known as residuals) that will aid
fault detection and identification. The emergence of super-computers has provided
so much flexibility to model-based fault detection activities, with models ranging
from simplified 2D models to more complicated 3D models (Figure 2.11).
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Figure 2.11 3D model of a typical rotating machine.
In an attempt to obtain more precise and reliable understanding of the progression
of machine faults (e.g. crack propagation) based on previously deduced
information, considerable research has been done on model-based fault
identification. For instance, earlier studies by Sekhar [65] applied a model-based
identification technique to detect the presence of a breathing crack on a shaft that
is supported by 2 flexible bearings and carrying 2 discs. The crack location and
depth were identifiable even at fewer degrees of freedom (4 and 8). However, as
degrees of freedom (DOF) reduced, the accuracy of the estimated crack depth
also reduced due to the impossibility of accurately estimating full vibration data
from fewer data points. Using the same model and capitalising on the prospects of
the initial findings, Sekhar [66] extended the study to the detection of 2 transverse
breathing cracks. An FFT of estimated equivalent loads (which were dominant at
the nodes of the cracked elements) showed the appearance of 2x and 3x
harmonic components, which is an indication of crack.
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Despite shaft misalignment being one of the most commonly encountered rotor-
related faults in practice, an absolute understanding of the characteristic features
of this fault is yet to be established. This is sometimes due to the similarities
between the features exhibited by shaft misalignment fault and other rotor-related
faults such as crack. A quest for better understanding of the effects of
misalignment on the couplings has driven researchers including Sekhar and
Prabhu [37] to apply higher order finite element model to ascertain the presence
and location of misalignment in two coupled shafts. In this approach,
considerations were given to several parameters (shear force, slope, deflection,
bending moment, etc.) at each node. The study [37] deduced that both parallel
and angular misalignments of the connected shafts cause bending of the
coupling’s flexible diaphragms, and that the vibration response obtained contained
1x and 2x components. Research contributions from Patel and Darpe [54] also
indicated that the stiffness coefficients of rotors coupled with angular misalignment
vary with each cycle of rotation, and could exhibit up to the first 6 harmonics (i.e.
1x, 2x, 3x, …., 6x) of the rotational speed. Pennacchi et al. [67] elaborated on the
non-linearity generated as a result of coupling misalignment [67] in rotors with
journal bearings, while Jalan and Mohanty [68] differentiated between two
common rotating machine faults (i.e. misalignment and unbalance) as well as
detecting their locations, using residual generation model-based technique.
Besides the detection of shaft misalignment and crack faults, model-based
approaches have been extensively used to detect and quantify other rotor-related
faults. To mention a few, Sudhakar and Sekhar [69] highlighted that the
modification of equivalent loads and vibration minimization methods with a
theoretical fault model were less prone to errors and more effective in the
detection of unbalance when compared to the initial equivalent loads minimization
method. Other researchers have also estimated unbalance in rotating machines by
applying measured vibration data during a unit transient (a single run-down) of the
machine, while incorporating the rotor and bearing models for the estimation of the
multi-plane unbalance [32], [70]. This method proved fast and presented the
potential of overcoming some of the practical difficulties associated with the
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construction of a reliable finite element (FE) model that will adequately account for
the dynamics of the foundation [71].
A significant number of critical process machines (e.g. the rotary kilns in cement
manufacturing plants) that operate under extreme temperatures and loads require
near perfect temperature profiles (especially when restarting after a long
stoppage). This high level of perfection is sometimes unachievable due to
unforeseen failures of some auxiliary equipment (e.g. gearbox lubrication pump or
cooling water pump). This therefore leads to uneven heat/load distributions in the
shaft, which sometimes leads to shaft bow. Studies aimed at effectively detecting
and differentiating shaft bow include a model-based study of the dynamic
behaviour of a gear-rotor system with visco-elastic supports and a bowed shaft. It
was shown that the magnitude and phase of the bow exhibit significant effects on
the first critical speed [72]. Since the occurrence of multiple faults in typical
industrial rotating machines is quite common, efforts aimed at differentiating single
and multiple faults in rotating machines triggered earlier investigations into the
resultant responses generated by a bowed shaft with the presence of a transverse
crack [73]. In this study, a simulation of the responses from both faults (i.e. shaft
bow and crack) was conducted. Observations from the study [73] indicated that
slight shaft bows may not significantly affect the non-linear responses due to shaft
cracks, but could disguise the orbital response sensitivity of the cracked shaft at
half the critical speed. Pennacchi and Vania [74] also applied statistical methods
for studying the accuracy of faults identification of the bowed shaft of a power unit
generator during coast down. The study [74] concluded that the model-based
technique developed for the identification and differentiation of the faults was quite
reliable, based on insignificant differences observed (particularly at the points at
which the bow generated the highest vibration amplitudes) when compared to the
experimental technique.
Mechanical looseness is another common rotating machine fault that could have
devastating effects if undetected at its inchoate stage. The effects of mechanical
looseness sometimes extend beyond the machine with the loose components. For
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instance, looseness in machine foundation could lead to the transmission of
vibration to adjacent rotating machines. Some researchers have studied looseness
combined with impact rub by applying binary approaches such as non-linear finite
element method and contact theory on dual-disc rotor-bearing systems [75], [76],
where it was gleaned that the amplitude of vibration in the low frequency region
(due to looseness) is usually suppressed by the impact rub of the rotor and stator.
It was also concluded that impact rub induced as a result of bearing pedestal
looseness is directional.
However, despite the commendable research advances made in VCM of rotating
machines through the application of model-based techniques, the questions that
still linger around the ability to develop theoretical models that will accurately
represent the actual dynamics of rotating machines with extremely complex
configurations [19] has somewhat confined a significant aspect of its applications
to research.
2.4.2 Artificial intelligence and faults classification
Most of the matured rotating machines’ VCM techniques currently employed in the
industries still rely solely on human experiences for interpretation of diagnosis
features. This total reliance on human experience sometimes leads to significant
levels of subjectivity and errors. In order to minimise this reliance on personal
judgements, some researchers have explored the possibility of applying
techniques that can mimic the operations of the human brain. Such techniques are
generally referred to as artificial intelligence (AI) techniques. In the literature, some
of the most popular AI techniques for rotating machine faults diagnosis are artificial
neural networks (ANN), support vector machine (SVM), fuzzy logic, etc. AI
techniques such as ANN are based on computational models that imitate the
structure of the human brain [19]. A typical ANN model comprises of several
simple processing elements that are joined via a complicated layer structure that
allows the model to evaluate complicated tasks which are often characterised by
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multiple inputs and outputs. Figure 2.12 shows a typical ANN-based model with
multiple inputs (IP) and several target outputs (TM).
Figure 2.12 Typical ANN-based model
Noteworthy researchers have explored the possibility of completely automating
VCM of rotating machines using AI techniques such as ANN [77]–[84], so as to
create a smart approach that can effectively evade the elements of human
dependence associated with currently used techniques [85]. Among others, ANN
has been used to detect gear faults [80]–[82], rotor loading conditions [79] and
rolling element bearing faults [84]. While the research-based performance of AI
techniques such as ANN have continuously improved in comparison to
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conventional techniques, the deployment of ANN to the field is still restricted by
the lack of clearly stated guidelines for acquiring the training data as well as the
exact approach needed to train the model. This is perhaps why most of the studies
applying ANN for rotating machine faults diagnosis are still limited to the use of
experimental data for model training.
Another AI-based VCM technique for rotating machine faults diagnosis that is
growing in popularity is SVM. The real time analysis capability of SVM as well as
its supplemented decision boundary [86], [87] particularly makes it very attractive
for VCM of rotating machines. In an attempt to diagnose common rotating
machinery faults including crack, Jiang et al. [88] used SVM for classifying time
domain vibration features obtained via a multiple-sensor/feature-level fusion
approach. The authors [88] hinged the rationale behind this approach on the fact
that the sensitivity of single sensor-based diagnosis approaches may be low to
incipient faults, especially when dealing with complex machinery [89]. It is also
believed that the integration of several types of CM sensors may enhance the
accuracy with which quantities can be examined [89]. Based on these notions,
Jiang et al. [88] simulated various faults on a laboratory scale rig and the results
obtained were quite promising. However, the confidence levels of the study [88]
findings are still limited by the lack of clearly stated standards for selecting the
fundamental process for SVM (i.e. the Kernel function) [90].
In an attempt to simplify rotating machine fault diagnosis and at the same time
evade the aforementioned convolutions associated with popular AI-based
techniques including ANN and SVM, some researchers have examined the
possibilities of performing rotating machine faults diagnosis using classification
techniques such as principal components analysis (PCA). PCA is a multivariate
statistical analysis technique that is capable of reducing the dimensionality of data
sets. Original data sets such as measured vibration signal from a typical rotating
machine is often characterised by a large number of interrelated variables. PCA
transforms these interrelated variables onto a new subspace with significantly
lower dimensionality [91]. Thus the new subspace called PCs [91], [92], represent
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a set of uncorrelated valuables that retained the maximum variations available in
the original data set.
To attest to the opportunities that exist with the application of PCA-based
approaches for rotating machine faults classification, Malhi and Gao [93] showed
how the effectiveness of bearing faults classification can be significantly enhanced
through the application of PCA-based methods. In the study [93], several artificial
defects which varied in severities were seeded on the inner and outer rings of 5
different rolling element bearings. Initially, 13 machine condition indicators (i.e. 5
time domain features, 4 frequency domain features and 4 wavelet domain
features) were considered as input features of the faults classification algorithm.
However, through the application of PCA for dimensionality reduction, only 3 input
features namely RMS (time domain), power in defect frequency range (frequency
domain) and wavelet & Fourier ball pass frequency outer amplitude (wavelet
domain) were selected as input features for the PCA-based faults classification
algorithm. The study showed that based on the examination of the directionality of
all the initially considered machine condition indicators, the 3 selected features
exhibited the most significant variance due to changing defects conditions.
Furthermore, the results of the study indicated that the 3 features selected via
PCA significantly improved the accuracy of bearing faults classification when
compared to classification obtained from using features that were not selected by
PCA. Using the same principle of dimensionality reduction, other studies have
similarly detected and classified rolling element bearing [94], [95] and gear [91],
[96] faults. However, despite the knowledge about the potential of PCA-based
methods, the literature is still starved of studies that have applied PCA-based
methods for the detection and classification of rotor-related faults.
2.4.3 Higher order signal processing tools
The emergence of faults in rotating machines is always associated with the
appearance of several harmonics (i.e. 1x, 2x, 3x, 4x, etc.) of the machine speed.
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Understanding the relationship that exists between these harmonics is very vital
for detecting and differentiating incipient machine faults before they lead to
catastrophic failures. Unfortunately, the very common and popular VCM
techniques that dominate the field at present are unable to provide insights about
such harmonic relationships. Therefore, taking advantage of the continuously
improving technological advancements that has erupted within the past few
decades; researchers have sorted for ways to enhance the understanding of
rotating machine faults. A prominent step towards this endeavour is the
introduction of higher order signal processing techniques for detecting and
differentiating rotating machine faults. In order to foster a better understanding of
higher order signal processing techniques, the concise theoretical background
provided in Appendix A can be very useful. In practice, the 2 most popular higher
order signal processing techniques are the higher order spectra (HOS) and its
normalised form, which is also referred to as higher order coherences (HOC).
HOS is further divided into 2 main classes, namely the bispectrum [97] and
trispectrum [98]. The bispectrum and trispectrum are respectively the double and
triple Fourier transformations of the third and fourth order moments of a time
domain signal. The normalisation of HOS generates the HOC (i.e. bicoherence
and tricoherence), where bicoherence and tricoherence respectively represent the
normalised forms of bispectrum and trispectrum [98]. Since HOC is fundamentally
a normalisation of HOS, it is believed that fault diagnostic features generated by
both tools will not differ except that the amplitudes of the HOC will be bounded
between 0 and 1.
In order to demonstrate the relevance of higher order signal processing tools in
CM of rotating machines, Hassan et al. [99] showed how bicoherence can be used
to detect and monitor the progression of tail rotor gearbox failure due to lack of
lubrication. During the experimental study, the scenario of a leaking gearbox was
artificially created by wrecking the output seals, which eventually led to gear tooth
failure. Measured vibration data were then analysed using the power spectrum
density (PSD) and bicoherence techniques at different stages (i.e. 3 days, 2 days
and 1 day before total gearbox failure) of the gear fault. Results obtained from the
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PSD analysis were very similar for the different stages of the gear fault. On the
contrary, the study showed that the bicoherence amplitudes showed steady
progressions from 3 days before failure down to the point of failure. The
observations from this study further affirm the inadequacy of solely using PSD for
CM. Based on the bicoherence trends, the study also established that the tail
gearbox can safely run for additional 480 hours with continuous tail gearbox
lubrication oil leakage, which is very useful for maintenance planning. Jang et al.
[100] also used bicoherence to detect and distinguish balanced and unbalanced
stator current conditions of a 3-phase induction motor, which was adjudged to be
due to the magneto motive force (MMF) equalling the second harmonic (2x) of the
line frequency (i.e. 60Hz). The study [100] also showed how bicoherence can be
used to explain that quadratic interaction involves the product of 2 frequency
components.
According to another study conducted by Bouillaut and Sidahmed [101], it is
possible to better interpret gear vibrations that occur as a result of the rotational
frequency modulating the gear meshing frequency which leads to the appearance
of sidebands that will be spaced at the rotational frequency around the harmonics
of the meshing frequency. The study compared the abilities of VCM methods such
as PSD and HOCs to detect several operating conditions (healthy, spalling, crack,
etc.) of CH64 helicopter gearbox unit. The HOCs adequately detected the coupling
relationships that existed between the different frequency components of the
vibration signals measured for each case. However, the PSD was unable to
accurately distinguish between some of the cases as it only compares the
amplitudes at a particular frequency for each of the cases (owing to its lack of
phase information). Li et al. [102] also used bicoherence to detect and differentiate
5 operating conditions (healthy and 4 artificially seeded faults of varying severities
using the electric discharge machining method) of a taper roller bearing. As
observed from other studies, the PSD appeared similar for healthy and fault
conditions while the bicoherence provided distinct features for different conditions.
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Significant amounts of research [99]–[105] have clearly demonstrated the benefits
of fault diagnosis with higher order techniques over the commonly used PSD.
However, these studies have been grossly biased towards the application of the
normalised forms of HOS, also known as the HOC. Such bias led to the theoretical
and experimental exploration of HOS for detecting 2 rotating machine faults (i.e.
crack and misalignment) [106], where distinct bispectrum and trispectrum features
were observed for both faults [106]. However, the experiments were conducted on
a very simple rig supported by just 2 bearings. In practice, most industrial rotating
machines possess far more complex configurations and several bearings which
again triggered the use of bispectrum for detecting 3 faults (i.e. misalignment,
crack and rub) on a relatively rigid experimental rig with 4 bearings at 2 machine
speeds [107]. The diagnosis results obtained from the study were again
encouraging. However, it was observed that the detection of rub with bispectrum
alone was inconsistent at both machine speeds. In fact, the rub case exhibited
similar features to the healthy case.
Based on the mixture of the applications of HOC and HOS, it is still unclear from
the available literature whether both classes of higher order signal processing
tools are exactly same with respect to their fault diagnosis capabilities or whether
one of the classes outperforms the other.
2.4.4 Data Fusion
In practice, routine CM activities often involve the continuous measurement of
various operational parameters (e.g. vibration, temperature, airflow, speed,
pressure, energy consumption, sound, wear debris, etc.) at predefined intervals,
also referred to as the condition monitoring interval. The measured CM
parameters are then separately analysed and trended overtime, so as to detect
the emergence of incipient machine faults. For instance, Yang et al. [108]
established the relationship between temperature profiles and fatigue damage of a
reactor pressure vessel. The study [108] proposed a model for quantifying the
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stress-strain and fatigue failure from the observed temperatures, which can prove
very useful for the CM of rotating machines operating under extreme temperature
such as the cement plant rotary kilns. Similarly, Avdelidis and Almond [109]
conducted a study on the application of temperature profiles (thermal imaging) for
determining and monitoring the integrity of aircraft structure anchor points, using
conventional aluminium alloys and carbon fibre reinforced plastic skins.
Another useful parameter for rotating machine CM is the wear particle distribution
obtained from lubricating oils. Lubricating oils perform various vital functions in
rotating machines including the prevention of metal-to-metal contact between
critical machine components, cooling agents for hot surfaces, transport systems
for additives that enhance resistance of metal surfaces to wear, as well as the
movement of wear particles and contaminants away from the contact surfaces of
vital machine components. Through a careful analysis of the types, sizes, shapes,
and composition of wear particles, insights about the health of rotating machines
can be obtained [110]. Based on this premise, the study conducted by Peng and
Kirk [111] showed that boundary features such as particle size distribution and
shape were adequate for identifying cutting, spherical and rubbing wear particles,
but contained insufficient information for detecting laminar, fatigue chunk and
extreme sliding wear particles.
Other researchers [112]–[115] have explored the use of power characteristics for
monitoring changes in the operating conditions of critical rotating machines.
Hameed et al. [112] provided a comprehensive review of health monitoring
techniques for wind turbines, where it was shown that accurate information on the
overall condition of the rotor (a very important component of the wind energy
converter) can be obtained by trending the relation between wind speed and active
power output of the wind energy converter (WEC). The study [112] also showed
that the use of higher order signal processing tools (bispectrum and bicoherence)
for detecting the presence or absence of phase coupling between the frequency
components of the electrical power signal can be used to classify the WEC as
faulty or healthy.
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Despite the significant advances achieved through the separate applications of the
CM parameters, accurate analysis of all parameters would require the services of
a well-experienced and highly versatile CM analyst. Also, the complexity of
separately processing and analysing individual CM parameters is enormous.
However, with the current emphasis on sensor reduction and management of big
data [11], providing a holistic view of an entire rotating machine through
combinations of several sets of a particular CM parameter (e.g. vibration
measurements from several bearings) or combinations of different CM parameters
(e.g. vibration and temperature measurements from several bearings) will
significantly simplify CM. Such approaches are often referred to as data fusion,
data integration or data combination.
Though rapidly gaining attention in CM, the general concept of data/parameter
fusion cannot be described as completely new since it dates back to the existence
of human senses (i.e. taste, touch, sight, hearing and smell) [116]. Humans have
always combined several senses in order to enhance their survival rates. For
instance, it would require a combination of vision, touch, taste and possible smell
to adequately judge the quality of an edible fruit. Also, the combination of sights
and sounds helps an animal detect the exact location of its prey or predator.
Similarly, data fusion in applied sciences is built around the premise that enhanced
and simplified descriptions of the monitored system can be achieved through a
combination of different sensors and/or parameters [89]. Historically, data fusion
techniques were mainly developed for military activities such as automated target
recognition, battlefield surveillance and remote sensing [116]. However, ongoing
cross-functional knowledge transfer through research has significantly promoted
the application of the concept in other fields including CM of rotating machines.
Data fusion in CM of rotating machines can be performed at sensor level (also
referred to as multi-sensor data fusion) or at parameter level (also referred to as
feature or parameter fusion)
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2.4.4.1 Sensor level data fusion
Sensor level data fusion refers to the merging of measured data from several
condition monitoring (CM) sensors (e.g. vibration, sound, temperature, pressure,
etc.) installed on an equipment, so as to obtain precise and comprehensive fault
diagnosis features that could eventually simplify and/or enhance the overall CM
process [117]–[121]. In the context of rotating machine CM, multi-sensor data
fusion can be approached in 2 main ways. The former is the fusion of data
acquired by similar sensors (e.g. the fusion of vibration signals measured by 4
similar accelerometers installed on the bearings of a rotating machine), while the
latter entails the fusion of data acquired by different sensors measuring different
CM parameters. Figure 2.13 shows a schematic representation of steps involved
in a typical sensor level data fusion process, while Figure 2.14 shows an
integrated CM system for a typical industrial centrifugal fan, where 5 different CM
parameters (vibration, sound, airflow, wear particles and temperature) are fused
together to develop a unique condition indicator (CI). The CI can then be trended
over time and eventually used to define the appropriate planned maintenance
regions (PMR) for the monitored rotating machine. It is vital to note that data fusion
at sensor level is usually done prior to the extraction of the parameters or features
that will be used for actual fault diagnosis.
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Figure 2.13 Data fusion at sensor level
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Figure 2.14 Multi-sensor data fusion [122]–[126]
2.4.4.2 Parameter level data fusion
In contrary to the data fusion that occurs at sensor level, parameter level data
fusion requires that the fault diagnosis features (e.g. RMS, crest factor, 1x
amplitude, etc.) embedded in the signals measured by individual CM sensors are
separately extracted prior to fusion. Figure 2.15 shows a schematic representation
of the steps involved in a typical parameter/feature level data fusion process
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PhD in Mechanical Engineering (2015) University of Manchester (UK)
Figure 2.15 Data fusion at parameter level
In light of the potential opportunities available for simplifying VCM of rotating
machines through data fusion, Sinha and Elbhbah [127] proposed a technique that
fuses measured vibration data in the frequency domain so as to generate a single
composite spectrum (CS) that effectively represents the dynamics of the entire
machine. Based on the vibration data acquired from a laboratory scale rotating
machine with relatively rigid bearing supports, the proposed CS technique
provided clearly distinct and consistent features for 4 rotating machine conditions
(healthy, shaft misalignment, shaft crack and shaft rub) at 2 machine speeds
(34Hz and 50Hz). In contrary to the data intensiveness and rigour associated with
common approach to rotating machine fault diagnosis whereby separate amplitude
spectra are individually computed at each measurement location, the CS method
only generates a single composite spectrum irrespective of the number of
measurement locations therefore minimising fault diagnosis time, and this is highly
desired for enhancing machine uptime.
Although the CS frequency domain data fusion technique simplifies fault
diagnosis, however, the robustness of the technique is limited by two factors.
Firstly, the computed CS for each of the equal segments in the measured vibration
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PhD in Mechanical Engineering (2015) University of Manchester (UK)
signal loses phase information at intermediate measurement locations, owing to
the cross power spectrum density approach adopted whereby the Fourier
transformation (FT) at a particular bearing location is multiplied by the complex
conjugate of the FT at a successive measurement location. This therefore limits
the available phase information only to the first and last measurement locations.
Secondly, faults diagnosis based on CS is limited to comparisons of amplitudes at
individual frequencies for different machine conditions, owing to the complete loss
of phase information associated with the power spectrum density (PSD) approach
used to compute the final averaged CS. In order to address the latter limitation of
the CS being limited to just amplitudes at individual frequencies, Elbhbah and
Sinha [128] then developed the composite bispectrum (CB) data fusion method. It
is worth noting that exactly same experimentally simulated cases and rig were
used for developing the CS and CB data fusion methods. However, besides fusing
measured vibration data from several measurement locations, each computed CB
component is a representation of the interaction that exists between 2 frequency
components and a third that is equivalent to their sum. Hence the CB data fusion
is expected to provide better diagnosis, since it is not limited to amplitudes at
individual frequencies but the interaction that exist between several frequency
components.
In principle, the CB data fusion method provides significant advantages over CS
data fusion as well as other commonly applied VCM methods. However, the
following gaps still limit the confidence level of the method. Firstly, the computation
of CB components relies solely on the CS obtained from each of the equal FT
segments. This infallibly means that the CB components are also associated with
limited phase information, which may reduce the accuracy of fault diagnosis.
Secondly, the concept of CB is based on the theory of bispectrum computation.
While the capability of the bispectrum to establish the relationship between the
frequency components of a signal (i.e. relates 2 frequency components of a
measured signal to a third frequency component that equals the sum of the initial
2.) is known, earlier studies by Elbhbah and Sinha [107], [129] have also shown
the inability of bispectrum alone to distinguish certain rotating machine conditions
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(e.g. healthy and shaft rub at 50Hz machine speed). Thirdly, all the studies
conducted on the application of CS and CB data fusion methods were conducted
for only a rotating machine with rigid bearing supports and at separate machine
speeds.
However, it is known that rotating machines operate under all sorts of changing
conditions, with speed constituting a significant part of these changes. Some
researchers [130] have developed VCM techniques for detecting unbalance and
misalignment faults, based on the processing of vibration data measured during
acceleration and deceleration stages of a machine’s operation. Fault diagnosis
was then conducted through a comparison of the patterns obtained from various
features generated in time waveform and waterfall diagrams to an existing
database of known engine faults. Similarly, Modgil et al. [131] proposed an
advanced vibration diagnostic system which acquired data for engine test cells
from idle through to maximum power operations. The proposed VCM approach
(based on transient operations) could be very useful for monitoring aircraft
engines, particularly during landing and takeoff stages where the operations are
transient. However, the waterfall diagrams adopted entails the combination of data
obtained from the amplitude spectra at different machine speeds with diagnosis
being based at a particular speed, which undermines the usefulness of the
technique under continuously changing speed operations. Also, fault diagnosis
with these methods [130], [131] was based on FE models, which reignites the
widely asked question about the ability to accurately develop a FE model that
represents the actual rotating machine dynamics [19].
Significant levels of development have been attained with VCM techniques that
focus on transient operations. However, it is doubtful that the basic data
processing techniques would be robust enough to handle continuous operations
with variable speeds. Based on this premise, the development of a VCM technique
which is insensitive to changing speeds is highly justified. In addition to changing
speeds, there exist practical scenarios where identical rotating machines possess
slightly different dynamic behaviours owing to variations in the flexibilities of their
foundations. For instance, it is common for a plant or group of plants to purchase a
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number of the same rotating machine (e.g. multiple speeds roots blowers of
cement manufacturing plants) from an original equipment manufacturer (OEM).
Though the configuration of these machines is same, however, their dynamic
behaviours may slightly vary due to differences in the flexibilities of their
foundations. Figure 2.16 shows the picture of a typical multiple speeds roots
blower with various foundation options (e.g. steel, concrete, springs, etc.).
Figure 2.16 A typical multiple speeds cement plant roots blower with various
foundation options [132]–[136].
Currently, the detection of faults under such scenarios (i.e. identical multiple
speeds machines with different foundations) would involve separate analysis of
measured vibration data for each machine (e.g. roots blower 1 with concrete
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foundation, roots blower 2 with steel foundation, etc.) at different speeds and plant
locations. Therefore, if a typical cement manufacturing organisation owns 2
separate cement plants and each of the plants transports fine materials (e.g. raw
meal, cement, fine coal, etc.) through the aid of 3 multiple speeds roots blowers.
Depending on the practical requirements for each installation location (e.g. soil,
adjoining structures and vibration isolation requirements), the foundation
flexibilities for the blowers will vary and thus their dynamic characteristics. Table
2.1 shows that as many as 15 different sets of measured vibration data could be
available for analysis from each of the 3 blowers with different foundations and
operating at 5 speeds (i.e. 30 data sets for both cement plants).
Table 2.1 Roots blower scenarios for 2 cement plants
Operating Speeds (rpm)
Cement Plant 1 Cement Plant 2
RB1Concrete RB2Steel RB3Springs RB1Concrete RB2Steel RB3Springs
600 1 2 3 1 2 3
1200 4 5 6 4 5 6
1800 7 8 9 7 8 9
2400 10 11 12 10 11 12
3000 13 14 15 13 14 15
Based on the practical scenarios described in Table 2.1, it is obvious that
continuously monitoring several multiple speeds identical rotating machines will be
highly complicated especially using conventional VCM techniques including
amplitude spectrum, rotor orbits analysis, bode plots, waterfall analysis, etc.
Although relatively recent data fusion methods such as CS and CB offer significant
simplicity over the conventional techniques, however, the process of separately
fusing measured vibration data for a single machine at individual speeds could
also be associated with considerable levels of complexity. Hence, there exists the
need to develop a hybrid (i.e. combination of sensor level and feature level data
fusion approaches) data fusion technique that can effectively combine measured
vibration data from several VCM sensors at various speeds for different rotating
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machines. Figure 2.17 shows a unified data fusion approach, where data from
several CM sensors are fused together and features extracted for different
machine speeds. The features extracted at multiple speeds for multiple machine
foundations are again fused together to generate a unified fault diagnosis
technique that could be used for different speeds and foundation flexibilities.
Figure 2.17 A unified data fusion approach
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2.5 Summary
The significance of the achievements recorded in VCM of rotating machines using
standard techniques such as amplitude spectrum is irrefutable. Most of these
achievements are largely owed to its simplicity and sensitivity to most commonly
encountered rotating machine faults. Despite its usefulness, diagnosis based on
amplitude spectrum analysis alone sometimes leads to inconclusive results,
largely due to its utter reliance on the amplitudes at individual frequencies. As
such, other standard VCM techniques such as orbit analysis, order tracking and
full spectrum are often applied in conjunction with amplitude spectrum so as to
raise the credence level of the technique. It is rational to admit that such
combinations of several standard VCM techniques have also yielded tangible
results in some instances. However, standard techniques such as rotor orbits have
also been observed to generate indeterminate results. Besides the impediments
associated with individual standard VCM techniques, a combination of several
techniques is also associated with appreciable levels of complexity and expertise.
In an attempt to evade some of the limitations associated with standard VCM
techniques (particularly the over-reliance on human experience), some
researchers have ventured into techniques such as ANN and SVM. Although
useful and encouraging research results have been achieved with ANN and SVM
with respect to automatic faults classification, their deployment to the industry are
still impeded by the lack of clearly stipulated procedure for acquiring the training
data for ANN as well as a lack of clearly defined standard for selecting the SVM
Kernel function. Approaches involving the construction of FE models that attempt
to simulate the dynamic responses generated by typical rotating machines due to
changing operating conditions have also been attempted by several researchers.
While FE methods possess the ability to provide intricate understanding of
machine behaviour due to faults, it is sometimes impracticable to construct FE
models that are absolute replicas of complex industrial rotating machines.
In order to adequately respond to the industrial need for developing a simplified
but reliable fault diagnosis approach that will equally address the growing research
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need for management of large data and pattern classification, data fusion methods
appear to be the most auspicious especially under different speeds and
foundations. Based on the currently existing literature, fault diagnosis of rotating
machines has been restricted to a solitary machine. This therefore implies that a
significant research gap still exists with respect to the development of a robust
fault diagnosis approach that would accommodate the sharing of data between
several identical rotating machines. Such an approach would eliminate the need
for keeping separate data history for each of the identical rotating machines
available in a plant.
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3 Chapter 3 EXPERIMENTS
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In order to foster a substantial acceptability of any newly proposed technique, an
experimental validation is often required, and this is commonly achieved through
the aid of an experimental test rig. A representative test rig may be described as
that which has been adequately set-up to correctly simulate the investigated faults
in the research. This chapter however presents details of various components that
make-up the test rig and the experimental simulation of the studied rotating
machine conditions. Prior to the experimental simulation of the different machine
conditions, the dynamic characteristics of the different experimental rigs were
determined, so as to adequately understand their dynamic behaviours.
Additionally, the chapter highlights the types, quantities and mounting positions of
instruments (transducers, data acquisition systems, signal conditioners, speed
controller, etc.) used for the collection and storage of the different experimental
data.
3.1 Experimental Rig and Components
In addition to the introductory description of a representative test rig, it should also
possess the capability of generating representative as well as repeatable
experimental data. Since the rig is an assembly of different components
(mechanical and electrical), a good understanding of the characteristics of these
components is required, so as to optimise their outputs. Such characteristics are
not limited to, but may include; operating ranges, material properties, stable
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ranges, frequency of calibration, operating environment, operational (input/output)
settings, etc. As these components will be used to generate data for VCM, it is
very vital that they are in perfectly healthy conditions at the commencement of the
experiment, so as to set-up reliable baseline parameters upon which all future
readings will be compared.
Furthermore, the setting up of the test rig and its associated components should
be correctly done. In accordance with the safety requirements of the University of
Manchester Dynamics Laboratory, a detailed risk assessment of all the tasks
associated with the experiments was conducted. Hence, this section will provide
details of how the test rig was set-up and the settings used for data collection.
Figure 3.1 shows pictorial representations of the major components that make-up
the experimental set-up.
Figure 3.1 Typical experimental set-up
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From Figure 3.1, it can be seen that rig rotation is achieved through the aid of an
induction motor that is flexibly coupled to the shaft (which is supported by 4 anti-
friction ball bearings). The variation of rig rotational speed is remotely done
through the aid of a PC-based motor speed controller. Vibration measurements
are then collected via sensors such as accelerometers (one diagonally mounted
on each bearing), proximity probes (2 mounted on bearings 1 and 3 pedestals in
the vertical and horizontal directions) and measurement microphones (mounted on
the rig protective cover near bearings 1 and 3 respectively). Signal conditioning
units are used to power each of the sensors as well as condition (amplify or
attenuate) the sensor outputs, so that it adequately matches the requirements of
the analogue-to-digital converter (ADC) that transforms the measured analogue
signals into digital forms that can be recorded onto a PC, using the customised
PC-based data acquisition software. The technical characteristics of the
experimental rig components will then be highlighted in the subsequent parts of
this section, while Section 3.2 describes the different instrumentation.
3.1.1 Electric motor and speed controller
The electric motor that drives the experimental rig is a 3-phase induction motor
and speed variation on the motor was achieved through the aid of a speed
controller. Figures 3.2(a)-(b) respectively shows pictures of the electric motor and
speed controller, while Tables 3.1-3.2 respectively provide their technical
specifications.
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Figure 3.2 Picture of electric motor and speed controller
Table 3.1 Technical specifications of the electric motor
S/No. Criteria Description
1 Manufacturer Crompton Greaves Ltd, India
2 Model GF 7965
3 Part No. IM 456
4 Serial No. KLG 18298
5 Power 0.75 kW
6 Voltage range 380v-415V
7 Phase 3
8 Frequency 50 Hz
9 Speed 2800 RPM
10 Current 1.85 A
11 Enclosure TEFC
12 Mounting Base foot + flange
Table 3.2 Technical specifications of the speed controller
S/No. Criteria Description
1 Manufacturer Newton Tesla
2 Input voltage 200-240 Volts AC
3 Input frequency 50/60 Hz
4 Output voltage 0-200 Volts AC
5 Output frequency 5-60 Hz
6 Power rating 0.75 kW
7 Output current 4.1 A
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3.1.2 Anti-friction ball bearings
Vibration data under healthy machine condition and several rotor-related faults
were collected from experimental rigs with various foundation flexibilities, owing to
the fact that similarly configured industrial rotating machines sometimes exhibit
different foundations in practice. The initial sets of vibration data were collected
from an experimental rig with relatively rigid foundation, where the rotor assembly
was supported by 4 Plummer block anti-friction ball bearings (Figure 3.3(a)). Since
a significant number of practical rotating machines are flexibly mounted, further
vibration measurements were conducted on flexible foundations. This was
however achieved by replacing the initial Plummer block anti-friction ball bearings
with flange-mounted anti-friction ball bearings (Figure 3.3(b)).
Figure 3.3 Anti-friction ball bearings (a) Plummer block (b) Flange-mounted
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Table 3.3 Technical specifications of anti-friction ball bearings
S/No Criteria Bearing Type
Plummer Block Flange Mounted
1 Manufacturer SKF
2 Model No. SY20TF/RA SEY20/NP20 FY20TF/RCJY20/SF20
3 Number of rolling elements 8
4 Diameter of rolling elements (mm) 7.938
5 Bearing width (mm) 31
6 External diameter (mm) 47
7 Internal diameter (mm) 20
8 Bearing pitch circle diameter (mm) 33.5
3.1.3 Couplings
The experimental rigs consist of 3 separate shafts (i.e. 1m, 0.5m and motor
shafts), which were connected by two different types of couplings (i.e. flexible and
rigid). The electric motor shaft was flexibly (Figure 3.4(a)) coupled to the 1m shaft
on one hand, while the 0.5m and 1m shafts were rigidly (Figure 3.4(b)) coupled
together on the other hand.
Figure 3.4 Couplings (a) Flexible (b) Rigid
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3.1.4 Threaded bars
Vibration measurements for the flexibly supported experimental rig were
conducted under 2 distinct foundation flexibilities, so as to experimentally simulate
the practical case of identically configured rotating machines installed at different
plant locations. Therefore, the flexibilities of the foundations were adjusted using
the 2 sets of mild steel threaded bars shown in Figure 3.5. Initially, both sets of
threaded bars were 10mm in diameter (Type: TB-58BZP-M10). However, the
geometries of the threaded bars used for the second flexibly supported
experimental rig (Figure 3.5(b)) were slightly modified, where aL = cL = 40 mm
(length) x 10 mm (diameter) and bL = 50 mm (length) x 6 mm (diameter).
Figure 3.5 Threaded bars for flexible foundations
3.2 Instrumentation
The measurement of vibration response from all experimental rigs under different
experimentally simulated conditions (faults and speeds) was achieved through the
installation of several transducers (e.g. accelerometers, proximity probes,
instrumented hammer and microphones), signal conditioning units and data
acquisition systems. In this section, some of the properties and specifications of
the instruments used for this research will be briefly discussed.
aL
bL
cL
a b
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3.2.1 Accelerometers
Accelerometers are contact transducers that are capable of measuring dynamic
acceleration of vibrating systems. During the current research, 4 accelerometers
(1 on each bearing, mounted at 45° to the shaft’s axis of rotation) were used to
collect vibration data from all the experimental rigs. Figure 3.6 and Table 3.4
respective provide the picture and technical specifications of the accelerometers.
Figure 3.6 Accelerometers with their brass mounting studs
Table 3.4 Technical specifications of accelerometers
S/No. Criteria Description
1 Model No. 352C33
2 ECN No. 28610
3 Sensitivity (±10%) 100mV/g
4 Frequency range (±5%) 0.5 to 10000 Hz
5 Resonant frequency ≥50 KHz
6 Temperature range -65 to +200 oF
7 Settling time (within 10% of bias) <10 seconds
8 Electrical connector 10-32 coaxial jack
10 Excitation voltage 18 to 32 VDC
11 Mounting torque 10 to 20 in-lb
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3.2.2 Proximity probes
Proximity probes are displacement transducers used to measure the gap or
relative displacement of a metal object in motion (e.g. the shaft of a rotating
machine) from the probe. In practice, proximity probes are commonly used for
protecting critical rotating machines (e.g. the rotary kilns of cement process plants)
by interrupting power supply to the machine once a preset shaft displacement
level is approached [137]. During the current study, the relative displacement of
the shaft under different experimentally simulated machine conditions were
measured using 4 MTN/ECPD+24V types of proximity probes (with a pair installed
at bearings 1 and 4 respectively in the vertical and horizontal directions as shown
in Figure 3.7(a)). Each proximity probe is powered by an EP080 driver (Figure
3.7(b)).
Figure 3.7 (a) MTN/ECPD+24V Proximity probes (b) EP080 drivers
3.2.3 Measurement microphones
Since changes in rotating machine sound pressure levels are also valuable
indications of changes in operating conditions, 2 high sensitivity condenser
measurement microphones (Figure 3.8(a)) were also installed on the experimental
rigs with flexible foundations (1 microphone installed at bearing 1 and the other at
mid-way between bearings 2 and 3) for sound pressure level measurements. Both
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measurement microphones were mounted on the experimental rig cover at a
distance of approximately 50 mm from bearing 1 and the rigid coupling
respectively. Each condenser microphone is powered by a type 2801 single-
channel power supply (Figure 3.8b), and the voltage output from the condenser
microphone is passed to the data acquisition card, through a sound amplifier
(Figure 3.8c).
Figure 3.8 (a) Condenser microphone (b) Single channel power supply (c) sound
amplifier
Table 3.5 Technical specifications of condenser microphone and power supply
S/No. Criteria Description
1 Manufacturer Bruel & Kjaer
2 Power supply input voltage range 110-240 V AC
3 Power supply output voltage Max. 28 V RMS
4 Power supply frequency range 2 Hz - 200 kHz
5 Microphone Resonance frequency Approx. 25 kHz
6 Sensitivity 12.5 mV/Pascal
3.2.4 Instrumented hammer
An impact hammer was used for identifying the natural frequencies and mode
shapes of the experimental rigs. In practice, the identification of the natural
frequencies of rotating machines or structures through impact hammer test usually
entails striking the test structure or machine with an instrumented hammer and
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then acquiring the response with a transducer (e.g. accelerometer). The impulse
from the hammer contains an almost steady force, over a broad frequency range,
which is why it is able to excite all resonant frequencies within that range [138].
The selection of hammer size is often guided by the structure or machine to be
excited. For instance, large rotating machines (e.g. large turbo generator sets,
cement rotary kilns, induced draft fans, etc.) or structures (e.g. bridges) may
require instrumented sledge hammers, while small to moderate experimental rigs
may require mini-hammers [138]. The hammer senses the applied force through
the aid of an integrated ICP quartz element (mounted on the striking head), which
transfers the impact force to the analogue-to-digital converter (ADC), after
adequate signal conditioning. Additionally, the frequency range to be excited can
be varied by replacing the hammer tip (i.e. harder hammer tips excite higher
frequency ranges than softer hammer tips) [21]. Figure 3.9 and Table 3.6
respectively show the picture and technical specifications of the instrumented
hammer used during this research.
Figure 3.9 ICP-PCB 086C03 instrumented hammer
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Table 3.6 Technical specifications of ICP-PCB 086C03 instrumented hammer
S/No. Criteria Description
Performance
1 Sensitivity (±15%) 10 mV/N
2 Measurement range ±224 N pk
3 Resonant frequency ≥22 kHz
4 Non-linearity ≤1%
Electrical
1 Excitation voltage 20-30 VDC
2 Constant current excitation 2 to 20 mA
4 Output bias voltage 8 to 14 VDC
Physical
1 Sensing element Quartz
2 Sealing Epoxy
3 Hammer mass 0.16 kg
4 Head diameter 1.57 cm
5 Tip diameter 0.63 cm
6 Hammer length 21.6 cm
7 Electrical connection position Bottom handle
8 Extender mass weight 75 g
9 Electrical connector BNC jack
3.2.5 Signal conditioning units
Transducers such as accelerometers and impact hammers require electrical
power supply. Additionally, the magnitudes of the output signals from these
transducers are often very small, and associated with different forms of
contamination, which therefore necessitates the need for some form of
amplification or filtration prior to digitization [139]. This preparation of the output
signals from the transducers is often referred to as signal conditioning. In this
research, PCB 482C signal conditioning units (picture and technical specifications
are respectively shown in Figure 3.10 and Table 3.7) were used for the realisation
of these purposes.
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Figure 3.10 PCB 482C signal conditioning unit
Table 3.7 Technical specifications of ICP-PCB 086C03 instrumented hammer
S/No. Criteria Description
Performance
1 Channels 4
2 Input sensor type ICP, voltage, charge
3 Voltage gain X0.1 to x200
4 Voltage gain increment 0.1
5 Charge conversion (selectable) 0.1, 1.0, 10.0 mV/pC
6 Frequency range (gain <100) 0.05 to 100 kHz
7 Frequency range (gain 100) 0.05 to 75 kHz
Electrical
1 Sensor excitation +24 VDC
2 Excitation current 0 to 20 mA
3 Computer control RS-232
4 LED fault monitor Open/short/overload
5 Power required +9 to -18 VDC
Physical
1 Input power connector 6-socket mini DIN
2 Sensor input connectors BNC
3 Signal output connectors BNC
4 Size (H x W x D) 8.1 x 20 x 15 cm
5 Temperature range +32 to +120 0F or 0 to +50 0C
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3.2.6 Analogue-to-digital converter (ADC)
Outputs generated by the different VCM transducers (i.e. accelerometers,
proximity probes and microphones) used for collecting the vibration data during
the current research are often in analogue forms. For these analogue signals to be
compatible with the PC onto which they will be stored for further data processing,
an analogue-to-digital converter (ADC) is required. ADCs convert continuous time
signals into discrete forms [140]–[143], which enables data storage onto computer
systems for eventual signal processing and rotating machine faults diagnosis. The
NI 6229, 16-bit, 16-channel ADC (picture and technical specifications are
respectively shown in Figure 3.11 and Table 3.8) was used during this research.
Figure 3.11 NI 6229/16-bit/16-channel ADC
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Table 3.8 Technical specifications of NI 6229/16-bit/16-channel ADC
S/No. Criteria Description
Analogue Input
1 Number of channels 16 differential or 32 single ended
2 ADC resolution 16 bits
3 Sampling rate 250 kS/s single channel; 250 kS/s multi-channel (aggregate)
4 Input range ±10 V, ±5 V; ±1 V, ±0.2 V
5 Input FIFO size 4,095 samples
Analogue Output
1 Number of channels 4
2 DAC resolution 16 bits
3
Maximum update rate
1 channel-833 kS/s, 2 channels-740 kS/s/channel, 3 channels-666 kS/s/channel and 4 channels-625 kS/s/channel
4 Output FIFO size 8,191 samples shared amongst channels used
Digital I/O/PFI
1 Number of channels 48 total; 32 (PO.<0...31>), 16 (PFI<0…7>/P1, PFI<8…15>/P2)
3.2.7 Data acquisition software
The measured vibration data from the various VCM transducers (after analogue-
to-digital conversion) were then stored on to a Dell Optiplex 990 (with Intel(R)
Core(TM) i7-2600 CPU @ 3.40GHz; 4.00 GB RAM and 64-bit operating system)
PC, through the aid of the customized LABVIEW-based (version 2.0) data
acquisition software (designed by Austin consultants for the University of
Manchester) shown in Figure 3.1. Although this software is quite simplified and
user friendly, however, care must be taken while entering the various fields (for
instance transducer channels, sampling frequency, voltage ranges and file
names). Table 3.9 provides a summary of the software settings used for acquiring
the research data.
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Table 3.9 LABVIEW-based (version 2.0) data acquisition software settings
ADC Channel
Transducer Type
Transducer Location
Voltage Range
Sampling Frequency
Dev1/ ai 0
Accelerometer
Bearing 1
-2 to +2
10kS/s (flexible supports)
&
5kS/s (for rigid support)
Dev1/ ai 1 Bearing 2
Dev1/ ai 2 Bearing 3
Dev1/ ai 3 Bearing 4
Dev1/ ai 4
Proximity
probes
Bearing 1 (vertical)
-10 to +10
Dev1/ ai 5 Bearing 1 (horizontal)
Dev1/ ai 6 Bearing 4 (vertical)
Dev1/ ai 7 Bearing 4 (horizontal)
Dev1/ ai 16 Microphones
Bearing 1 -2 to +2
Dev1/ ai 17 Bearings 2 & 3
3.3 Experimental Rig Foundations
In the current research, vibration data (under different faults and rotating machine
speeds) were collected from an experimental rig with 3 distinct foundations (i.e.
rigid support, flexible support 1 and flexible support 2), so as to experimentally
simulate the practical scenario of a particular rotating machine (e.g. pump)
acquired from an original equipment manufacturer (OEM) by different users in
different plant locations. Such differences in locations and/or users often result to
variations in the flexibility of the machines’ foundations and hence their dynamic
characteristics. Therefore, this section provides the details of the 3 experimental
rigs, with particular emphasis on their foundations.
3.3.1 Rigid support (RS)
In the RS experimental rig (Figures 3.12-3.13), two mild steel shafts of similar
diameters (20mm) and respective lengths of 1000mm and 500mm were connected
together through the aid of the rigid coupling shown in Figure 3.4(b). The 1000mm
shaft was then coupled to the electric motor shaft using the helical “W” series
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metric single piece flexible coupling shown in Figure 3.4(a). Three mild steel
balance discs of similar dimensions (100mm (outer diameter), 20mm (inner
diameter) and 15mm (thickness)) were mounted on the shafts (i.e. two balance
discs on the 1000mm shaft, between bearings 1 and 2; and the third balance disc
on the 500mm shaft, between bearings 3 and 4). Each of the balance discs
contains 12 radial holes of 6mm diameter each, and spaced at 30 degrees apart.
The shafts were then supported by 4 Plummer block anti-friction ball bearings,
which are tightly fastened to a lathe bed, through the aid of mild steel base plates.
The entire experimental rig assembly is placed on neoprene rubber pads (for
isolating vibration from adjacent machines). A total of 4 accelerometers (1 per
bearing pedestal in the horizontal direction) were installed on the experimental rig
for vibration data collection.
Figure 3.12 Picture of RS experimental rig
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Figure 3.13 Schematic of RS experimental rig with dimensions
It is very crucial to highlight that the original design and construction of the RS
experimental rig shown in Figures 3.12-3.13 formed part of an earlier research
conducted by Elbhbah and Sinha [107] at the Dynamics Laboratory of the
University of Manchester.
3.3.2 Flexible supports
In addition to the vibration data collected from the RS experimental rig, two flexibly
supported (i.e. FS1 and FS2) experimental rigs were also considered. It must be
noted that the majority of the components (i.e. electric motor, 1000mm shaft, 500m
shaft, base plates, lathe bed, neoprene dampers, balance discs, etc.) that make up
the RS, FS1 and FS2 experimental rigs are identical and similarly sized. However,
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RS supports are relatively rigid while FS1 and FS2 supports are flexibly mounted
(Figure 3.14-3.15).
Figure 3.14 Picture of FS experimental rig
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Figure 3.15 Schematic of FS experimental rig
In Figure 3.15, the components labelled a-m respectively represent accelerometer,
rigid coupling, shaft, balance disc, bearing flange, threaded bar, flange-mounted
anti-friction ball bearing, flexible coupling, tachometer, electric motor, electric
motor base mount, lathe bed and neoprene rubber pad. Additionally, Figure 3.16
shows that the flexibilities of FS1 and FS2 vary slightly, owing to the different
geometries of the threaded bars (Figure 3.5) that connect their bearings to the
pedestals.
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Figure 3.16 Picture of flexible supports (a) FS1 (b) FS2
3.4 Dynamic Characterisation
In order to better understand the dynamic behaviours of the different experimental
rigs, their natural frequencies (by appearance) and mode shapes were
experimentally identified using the impact response method of modal analysis.
Experimental modal analysis is a widely known design testing and qualification
technique in various disciplines [144]. The knowledge of the modal properties of a
system greatly paves way for design improvements and useful life enhancement
[145], [146]. In order to ensure a structured and guided approach to modal testing,
the UK Dynamic Testing Agency (DTA) further recommended a four-stage
approach, namely [144], [147]; preparation (i.e. clear definition of experimental
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objectives and identification of relevant resources), exploration (i.e. the definition
of data acquisition parameters such as number of averages, acquisition duration,
frequency resolution, sampling frequency, etc., which may involve some initial trial
runs), measuring (i.e. actual collection of experimental data) and analysis.
According to earlier studies by Elbhbah and Sinha [127], the first few natural
frequencies (by appearance) of the RS experimental rig were experimentally
identified using the impact response method as 68Hz, 144Hz and 352.5Hz. Similar
approaches were again adopted for the determination of the natural frequencies of
FS1 and FS2 experimental rigs, where responses were measured in both vertical
and horizontal planes, owing to the flexibilities of the rigs (i.e. FS1 and FS2) in
both planes. During the experiments, FS1 and FS2 were respectively excited by
the ICP-PCB instrumented hammer shown in Figure 3.9 and the vibration
responses were measured using an ICP accelerometer similar to that shown in
Figure 3.6. Hence, Figure 3.17 shows a picture of the experimental setup for
determining the natural frequencies of FS1 and FS2 experimental rigs.
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Figure 3.17 Modal test setup for determining FS1 and FS2 natural frequencies
The first few natural frequencies (by appearance) for FS1 and FS2 in both vertical
and horizontal directions (based on response measurements at bearing 2) were
identified using the peak picking method. Figures 3.18-3.21 and Table 3.10
respectively show plots of the frequency response functions (FRF) and a summary
of the natural frequencies.
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Figure 3.18 Typical FRF plots for FS1, measured at bearing 2 in the vertical
direction (a) FRF amplitude, (b) FRF phase
Figure 3.19 Typical FRF plots for FS1, measured at bearing 2 in the horizontal
direction (a) FRF amplitude, (b) FRF phase
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Figure 3.20 Typical FRF plots for FS2, measured at bearing 2 in the vertical
direction (a) FRF amplitude, (b) FRF phase
Figure 3.21 Typical FRF plots for FS2, measured at bearing 2 in the horizontal
direction (a) FRF amplitude, (b) FRF phase
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Table 3.10 Experimentally identified natural frequencies for FS1 and FS2
Experimental Rig Natural Frequencies (Hz)
1st
2nd
3rd
4th
FS1 50.66 56.76 59.2 127.6
FS2 47 55.54 57.98 127
In order to experimentally determine the mode shapes, an experimental approach
similar to that applied for natural frequencies’ determination was adopted, except
for the fact that 9 ICP accelerometers (distributed across the length of the
experimental rigs) were used to measure the responses. Figures 3.22-3.23
respectively show a picture of the experimental setup and the schematic
representation of the exact locations (in millimetres) of the 9 ICP accelerometers
used for measuring the responses, while Figure 3.24 shows samples of the first
few mode shapes (by appearance) for FS1. In Figure 3.23, B1-B4, FC and RC
respectively denote bearings 1-4, flexible and rigid couplings. Locations 1-9 (L1-
L9) in Figure 3.24 represent the locations at which the responses were measured,
which also correspond to the distances shown in Figure 3.23.
Figure 3.22 Modal test setup for determining FS1 and FS2 mode shapes
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Figure 3.23 Locations of ICP accelerometers for mode shapes’ determination
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Figure 3.24 FS1experimentally determined mode shapes (a) 50.66Hz, dominant in vertical direction (b) 56.76Hz, dominant in
horizontal direction
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3.5 Experimentally Simulated Faults
On all the experimental rigs (i.e. RS, FS1 and FS2), several cases were simulated,
which represented different operating conditions of typical rotating machines in
practise. Hence, this section provides detailed descriptions of the experimental
simulation of the different cases on all the experimental rigs.
3.5.1 Rigid support (RS)
Although, details of the experimental simulation of the 4 cases (healthy,
misalignment, cracked shaft and shaft rub) studied on the RS rig have been
provided in an earlier study conducted by Elbhbah and Sinha [107], however,
similar information will be repeated here, so as to further enhance clarity.
3.5.1.1 Case 1: Healthy
The healthy case was intended to simulate a near perfect machine, through the
alignment of all the coupled shafts. However, the impossibilities of practically
manufacturing error-free components still imposed some residual unbalances on
the healthy case. Additionally, a perfect alignment between the coupled shafts was
unrealistic (as is often the case in practise), thereby inducing some residual
misalignment between the coupled shafts (especially at the rigid coupling).
Therefore, the healthy case still contained some degree of residual unbalance and
residual misalignment.
3.5.1.2 Case 2: Misalignment
A 2mm misalignment was induced in both vertical and horizontal directions of
bearing 1 (i.e. near the flexible coupling shown in Figure 3.12). The misalignment
in the vertical direction was induced by placing a 2mm thick mild steel shim
underneath bearing 1 base mount, while horizontal misalignment was achieved by
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moving the bearing 2mm (using a calibrated dial indicator for distance
measurement) from its axis in the horizontal direction, through the aid of the
pedestal slots.
3.5.1.3 Case 3: Cracked shaft
A crack of 0.25mm (width) by 4mm (depth) was created on the 1000mm (length)
shaft, using the spark erosion electric discharge machining (EDM) technique [107].
EDM has continuously gained popularity amongst machining processes. Its
application of heat energy for material reduction from electrically conductive
components has particularly made it (EDM) very relevant to various industries,
including; medical, aerospace, automobile and general manufacturing [148].
Another merit of EDM lies in the fact that the electrode does not make direct
contact with the work piece, thereby eliminating mechanical stresses and
vibrations during the machining process [148]. With the recent advancements in
technology, EDM electrodes go as low as 0.1mm, which makes them very suitable
for the precise manufacture of intricate shapes and components [149]. During the
EDM process, the mechanism that erodes materials from the work piece converts
electrical energy to heat energy, through a variety of high frequency
(approximately between 20-30 kHz) electrical discharges between the electrode
and the work piece, which is soaked in a dielectric fluid [150], [151]. The amount of
heat energy produced, leads to the creation of a plasma channel between the
anode and cathode (at temperatures as high as 8000-20000 degrees Celsius)
[152], which leads to the melting of materials at the surface of the electric poles
[148]. Upon cutting-off the direct current supply, the plasma layer breaks down,
thereby leading to a drastic reduction in temperature, which consequently leads to
the removal of molten materials (in the form of microscopic debris) from the
surfaces of the poles [148]. In order to therefore simulate an incipient rotor crack,
which will be quantifiable (i.e. width and depth), EDM process was applied, as
shown on Figure 3.25.
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Figure 3.25 Cracked shaft
3.5.1.4 Case 4: Shaft rub
The shaft rub case was simulated through the use of a Perspex sheet, with a
centrally located hole of 21mm diameter. The 1000mm (length) x 20mm (diameter)
shaft was then passed through the hole in the Perspex sheet, near bearing 1.
Figure 3.26 Shaft rub
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3.5.2 Flexible supports (FS1 and FS2)
In the flexibly supported rigs (FS1 and FS2), a total of ten (10) cases were
experimentally simulated, so as to cover a reasonably wide range of practical
operating conditions of typical industrial rotating machines. Although there are two
different flexible support set-ups (FS1 and FS2), however, all cases have been
simulated in exactly the same manner, so as to allow direct comparisons between
FS1 and FS2. Since it often impossible to achieve a perfect alignment in the
reference case, all the experimentally simulated cases contained additional
residual misalignment (which is often the case in practice). Vibration data were
then collected at 3 distinct machine speeds; 1200 RPM (20 Hz), 1800 RPM (30
Hz) and 2400 RPM (40 Hz) for each case under FS1 and FS2 supports, so as to
extensively understand the dynamics of the machines under different operating
conditions. Since full details of the specific experiments will be provided in the
subsequent chapters (including figures), only a summarised list of the
experimentally simulated cases and their abbreviations are provided in Table 3.11.
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Table 3.11 Experimentally simulated cases, abbreviations, severities and locations
Case Description Abbreviation Severity and Location
1 Healthy with residual
misalignment HRM
Some residual misalignment, possibly
at couplings
2 Unbalance UNB
M5 x 25mm grub screw of 2.6g mass
was inserted in one of the 12
equidistant holes on the balance disk
positioned at 190mm from bearing 2.
3 Bent shaft BS 3.4mm run-out was created at the
centre of the 1000mm shaft.
4 Shaft crack SC
4mm (depth) x 0.25mm (width) crack
on 1000mm shaft at 160mm from
bearing 1
5 Loose bearing LB Loosening some of the bearing 3
threaded bar nuts
6
Shaft misalignment
SM1 0.4mm mild steel shim beneath LHS of
bearing 1 foundation
7 SM2 0.4mm mild steel shim beneath LHS
and RHS of bearing 1 foundation
8 SM3 0.8mm mild steel shim beneath LHS of
bearing 1 foundation
9 SM4 0.8mm mild steel shim beneath LHS
and RHS of bearing 1 foundation
10 Shaft rub SR
Partial rub using 2 Perspex blades
(TDC and BDC of 1000mm shaft),
275mm from bearing 1
3.6 Summary
This chapter provided details of the different experimental rigs (RS, FS1 and FS2),
as well as the various components (mechanical and electrical) that constitute
them. Details of the transducers and instrumentation that aided vibration data
collection and storage were also provided. The chapter also highlighted the
experimental determination of the dynamic characteristics (natural frequencies and
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mode shapes) of the rigs as well as the experimental simulation of different cases
that represented practical operating conditions of industrial rotating machines.
Hence, the subsequent chapters of this thesis will focus on the research findings
and their corresponding explanations.
Experimental Observations of Rotor Orbit Analysis in Rotating Machines
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4 Chapter 4 EXPERIMENTAL OBSERVATIONS
OF ROTOR ORBIT ANALYSIS IN ROTATING MACHINES
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Reformatted version of the following paper:
Paper title: Experimental observations of rotor orbit analysis in rotating
machines
Authors: A. Yunusa-Kaltungo, A.D. Nembhard and J.K. Sinha
Published in: Proceedings of 9th IFToMM International Conference on Rotor
Dynamics (IFToMM ICORD 2014), Milan/Italy, September 22-25 2014
Series title: Mechanisms and Machine Science
Volume: 21
DOI: 10.1007/978-3-319-06590-8
Publisher: Springer International Publishing
Abstract
A better understanding of the characteristic features of different faults associated
with rotating machines is very vital, so that appropriate and timely maintenance
interventions can be recommended prior to the occurrence of catastrophic failures.
Experimental Observations of Rotor Orbit Analysis in Rotating Machines
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Akilu Yunusa-Kaltungo 129 PhD in Mechanical Engineering (2015) University of Manchester (UK)
Rotor orbit analysis of machine vibration data collected using proximity probes has
been observed to be useful for faults diagnosis in rotating machines. Although this
analysis is extensively applied for rotating machine faults diagnosis in several
industries, however, very limited experimental results are still available in
literatures. In the current study, rotor orbit analysis has been conducted on an
experimental rig of 1500mm rotor length, supported by 4 flexibly mounted anti-
friction ball bearings. A number of faults have also been experimentally simulated
on the rig for the purpose of this study. Hence, the paper presents the experiments
conducted, the rotor orbit analysis and observations, which may further enhance
the understanding of rotating machines’ behaviours under different faults.
Keywords: Condition monitoring, faults diagnosis, rotating machines, flexible
foundation, rotor orbits
4.1 Introduction
A highly desired attribute of any vibration-based fault diagnosis (VFD) technique is
its ability to develop unique, reliable and consistent features that express the
changes in operating conditions of a rotating machine due to the emergence of
faults. One of such VFD techniques that have been considerably applied over the
years for detecting and estimating malfunctions in rotating machines is the rotor
orbit analysis of vibration data, measured using proximity probes. Measuring
vibration signals for rotor orbit analysis as already detailed in earlier studies [55],
[153]–[155], involves installing two orthogonal proximity probes, where the
measured vibration signal by each of the probes is indicative of the rotor peak-to-
peak displacement in that particular direction. The rotor orbit plot is then
constructed by combining the measured vibration displacements from the two
orthogonal proximity probes. Rotor orbit analysis has been applied for the
diagnosis of different rotating machine conditions, such as; analysis of impact rub
phenomenon [50]; rotor misalignment [53], [54]; detecting the causes of the
appearance of sub-harmonic components in journal bearings, including oil
Experimental Observations of Rotor Orbit Analysis in Rotating Machines
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temperature and pressure variations [52]; influence of rotor cracks [51]; etc. While
these studies [50]–[55], [153]–[155] have shown the usefulness of rotor orbit
analysis for diagnosing rotating machine faults, very limited experimental results
on the technique are still currently available in literatures, which consequently
restrict the detailed understanding of the technique with different rotating machine
faults. Hence, the current study conducts rotor orbit analysis on vibration
displacements measured by proximity probes from two identical rotating rigs with
different foundation flexibilities, so as to further enhance the understanding of
rotating machines’ behaviours under different faults.
4.2 Experimental Rigs
The experiments were conducted on two identical rotating machines with slightly
different foundation flexibilities (i.e. FS1 and FS2), which aims to simulate a
practical case of installing the same rotating machine at two different locations.
Figure 4.1 shows the first experimental rig (i.e. FS1), containing two mild steel
shafts of 1000mm and 500mm lengths respectively. Both shafts are of similar
diameters (i.e. 20mm) and are rigidly coupled together, while the 1000mm shaft is
flexibly coupled to a 0.75 kW electric motor. Three mild steel balance discs with
125mm outside diameter, 15mm thickness and 20mm inside diameter were
respectively mounted on the 1000mm and 500mm shafts. Two of the balance
discs were mounted on the 1000mm shaft at distances of 300mm from the flexible
coupling and 190mm from bearing 2 respectively, while the third balance disc was
mounted on the 500mm shaft at 210mm from both bearings 3 and 4. The
experimental rig is however supported by 4 flange-mounted anti-friction ball
bearings. The second experimental rig (i.e. FS2) is an exact replica of FS1 with
respect to configuration, components and capacity. However, both FS1 and FS2
are slightly unique in the stiffness of their foundations (Figure 4.2), due to the fact
that FS1 and FS2 bearings were respectively mounted using 10mm and 6mm
thick threaded bars (Figure 4.2).
Experimental Observations of Rotor Orbit Analysis in Rotating Machines
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Figure 4.1 Experimental rig with flexible bearing foundation
Figure 4.2 Flexible anti-friction ball bearings foundations (a) FS1 (b) FS2
4.3 Vibration Experiments
A total of 9 experimentally simulated cases on both rigs (FS1 and FS2) at 2400
RPM machine speed were used in the current study, and the vibration
displacements were collected using 2 orthogonally mounted (near bearing 1)
proximity probes for further signal processing. It is salient to note that the machine
Experimental Observations of Rotor Orbit Analysis in Rotating Machines
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speed is below the first critical speeds (Hz) for FS1 and FS2 foundations
respectively. In order to better understand the dynamic behaviours of both rigs,
impact-response experimental modal analysis technique was used to identify the
first few natural frequencies (by appearance) of FS1 rig as; 50.66Hz, 56.76Hz,
59.2Hz and 127.6Hz. As in the case of FS1, the first few natural frequencies (by
appearance) of FS2 rig were similarly identified as; 47Hz, 55.54Hz, 57.98Hz and
127Hz.
4.3.1 Case 1: Healthy with residual misalignment (HRM)
A healthy case adjudged to be containing some residual misalignment was
considered as the reference case, since it was practically difficult to achieve a
perfectly aligned rig.
4.3.2 Case 2: Unbalance (UNB)
The unbalance case was experimentally simulated by inserting an M5 x 25mm
grub screw of 2.6g mass in one of the 12 equal divisions on the balance disc near
bearing 2 (i.e. 190mm from bearing 2).
Figure 4.3 Unbalance case
Experimental Observations of Rotor Orbit Analysis in Rotating Machines
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4.3.3 Case 3: Shaft crack (SC)
A 4mm deep crack with width of 0.25mm was created on the 1000mm shaft, at a
location of 160mm from bearing 1, through the aid of the wire electric discharge
machining (EDM) process. As it was unlikely for the crack to breathe, a 0.23mm
mild steel shim was then inserted in the crack to ensure breathing action.
Figure 4.4 Loose bearing case
4.3.4 Cases 5-8: Shaft misalignment (SM)
Four different severities of shaft misalignment (i.e. SM1, SM2, SM3 and SM4)
were experimentally simulated by inserting mild steel shims of different
thicknesses beneath bearing 1 foundation, which are shown in Table 4.1 and
Figure 4.5.
Experimental Observations of Rotor Orbit Analysis in Rotating Machines
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Table 4.1 Shaft misalignment severities and locations
Case Misalignment Abbreviation Severity and Location
5 Scenario 1 SM1 0.4mm mild steel shim beneath LHS of bearing 1 foundation
6 Scenario 2 SM2 0.4mm mild steel shim beneath LHS and RHS of bearing 1 foundation
7 Scenario 3 SM3 0.8mm mild steel shim beneath LHS of bearing 1 foundation
8 Scenario 4 SM4 0.4mm mild steel shim beneath LHS and RHS of bearing 1 foundation
Figure 4.5 Shaft misalignment cases (a) SM1 (b) SM2
4.3.5 Case 9: Shaft rub (SR)
Finally, the shaft rub case was simulated by installing 2 Perspex blades (i.e. one at
the top and the other at the bottom) at 275mm from bearing 1, which was aimed at
experimentally simulating a practical case of rotating blades (e.g. turbine or fan
blades) rubbing against the casing at some locations.
Experimental Observations of Rotor Orbit Analysis in Rotating Machines
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Akilu Yunusa-Kaltungo 135 PhD in Mechanical Engineering (2015) University of Manchester (UK)
Figure 4.6 Shaft rub case
4.4 Results and Observations
The vibration data measured by 2 proximity probes for all the experimentally
simulated cases on the rig with 2 different foundation flexibilities (i.e. FS1 and
FS2) at 2400RPM machine speed, have been used to construct the typical rotor
orbit plots shown in Figures 4.7-4.8. The LB cases clearly yielded the highest shaft
displacement in both FS1 (Figure 4.7(d)) and FS2 (Figure 4.8(d)), which is quite
evident in the rotor orbit size. However, with the exception of SR cases (Figure
4.7(i) and Figure 4.8(i)) on both FS1 (Figure 4.7) and FS2 (Figure 4.8), the rotor
orbits for all the experimentally simulated cases are very identical in shape and
size. This observation however deviates from suggestions from earlier studies
[53], [54]. For instance, the rotor orbits due misalignment have been earlier
described as containing inner loops, which may sometimes constitute a shape
similar to the “figure-8” [53], depending on severity. Hence, based on the specific
cases experimentally simulated in the current study, it has been observed that the
application of rotor orbits for absolute faults diagnosis in rotating machines may be
Experimental Observations of Rotor Orbit Analysis in Rotating Machines
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Akilu Yunusa-Kaltungo 136 PhD in Mechanical Engineering (2015) University of Manchester (UK)
difficult and limited under certain machine operating conditions (e.g. support
flexibility, type and location of fault).
Figure 4.7 Rotor orbit plots for FS1 (a) HRM (b) UNB (c) SC (d) LB (e) SM1 (f)
SM2 (g) SM3 (h) SM4 (i) SR
Experimental Observations of Rotor Orbit Analysis in Rotating Machines
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Akilu Yunusa-Kaltungo 137 PhD in Mechanical Engineering (2015) University of Manchester (UK)
Figure 4.8 Rotor orbit plots for FS2 (a) HRM (b) UNB (c) SC (d) LB (e) SM1 (f)
SM2 (g) SM3 (h) SM4 (i) SR
4.5 Spectrum Analyses
Figures 4.9-4.10 show the typical amplitude spectra for just 4 cases (HRM, SC,
SM4 and SR) on both FS1 (Figure 4.9) and FS2 (Figure 4.10) at 2400RPM, which
have been computed using a 95% overlap; frequency resolution ( ) = 0.6104Hz;
sampling frequency (fs ) = 10000Hz and number of data points (N) = 16384. The
amplitude spectra clearly show some depictions through the changes in harmonic
patterns for each of the experimentally simulated cases on both FS1 and FS2 rigs.
Experimental Observations of Rotor Orbit Analysis in Rotating Machines
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Akilu Yunusa-Kaltungo 138 PhD in Mechanical Engineering (2015) University of Manchester (UK)
Figure 4.9 Typical amplitude spectra for FS1 at 2400RPM (a) HRM (b) SC (c) SM4
(d) SR
Experimental Observations of Rotor Orbit Analysis in Rotating Machines
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Akilu Yunusa-Kaltungo 139 PhD in Mechanical Engineering (2015) University of Manchester (UK)
Figure 4.10 Typical amplitude spectra for FS2 at 2400RPM (a) HRM (b) SC (c)
SM4 (d) SR
4.6 Summary
Experimental observations on orbit plots have been presented for a number of
faults on a rotating machine with 2 different foundations. Under both installation
conditions, the machine speed was below the first critical speed. Therefore, the
dynamics of the machines for both installations are expected to be identical, which
has also been observed here. However, based on the cases experimentally
simulated in the current study, there is no significant change in the orbit features
for the different experimentally simulated faults for both installation conditions,
except for the shaft rub case (SR). However, changes in the harmonic patterns for
different faults are clearly visible in the amplitude spectra. Hence, the consistency
Experimental Observations of Rotor Orbit Analysis in Rotating Machines
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Akilu Yunusa-Kaltungo 140 PhD in Mechanical Engineering (2015) University of Manchester (UK)
of the present observations and the general understanding of rotor orbit analysis
could be significantly enhanced through a series of planned future investigations of
more cases at different locations and severities.
A Comparison of Signal Processing Tools: Higher Order Spectra Versus Higher Order Coherences
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Akilu Yunusa-Kaltungo 141 PhD in Mechanical Engineering (2015) University of Manchester (UK)
5 Chapter 5 A COMPARISON OF SIGNAL PROCESSING TOOLS: HIGHER ORDER
SPECTRA VERSUS HIGHER ORDER COHERENCES
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Reformatted version of the following papers:
Paper 1 title: A comparison of signal processing tools: Higher order spectra
versus higher order coherences
Authors: A. Yunusa-Kaltungo and J.K. Sinha
Published in: Journal of Vibration Engineering & Technologies, Volume 3, Issue 4,
August 2015, Pages 461-472
Paper 2 title: Faults diagnosis in rotating machines using higher order
spectra
Authors: A. Yunusa-Kaltungo and J.K. Sinha
Published in: Proceedings of ASME Turbo Expo 2014: Turbine Conference and
Exposition, Dusseldorf/Germany, June 16-20 2014
Series title: Structures and Dynamics
Volume: 7A
A Comparison of Signal Processing Tools: Higher Order Spectra Versus Higher Order Coherences
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Akilu Yunusa-Kaltungo 142 PhD in Mechanical Engineering (2015) University of Manchester (UK)
DOI: 10.1115/GT2014-25090
Publisher: American Society of Mechanical Engineers
Abstract
A class of signal processing tools, higher order spectra (HOS) and their
normalised amplitudes higher order coherences (HOC) have been receiving
attentions in numerous applications, including health monitoring (HM) techniques
for structures and machines. It is however difficult to decide which of the tools
(HOS or HOC) gives the best diagnostic features. In this paper, HOS and HOCs
have been compared using numerically simulated signals with and without noise.
The cross-power spectral density (CSD) between two signals and its ordinary
coherence are also compared. The results and observations on the different
spectra and their coherences are discussed here. It is observed that the use of
HOS may be more advantageous over HOC analysis.
Keywords: Cross-power spectrum, bispectrum, trispectrum, ordinary coherence,
bicoherence, tricoherence
5.1 Introduction
The cross-power spectral density (CSD) between two signals and its normalised
amplitude between 0 and 1 known as ordinary coherence are well-known signal
processing tools, used to find the relation between the two signals at each
frequency component within both signals [146], [156]. Similarly, the existence of a
relationship between the different frequency components within a signal is also
possible. Over the past few decades [98], [103], [157]–[160], the detection of such
relation between the frequency components within a signal using higher order
signal processing tools (higher order spectra and higher order coherences) has
gained tremendous attention. The two most popular higher order statistical
A Comparison of Signal Processing Tools: Higher Order Spectra Versus Higher Order Coherences
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Akilu Yunusa-Kaltungo 143 PhD in Mechanical Engineering (2015) University of Manchester (UK)
techniques are the higher order spectra (HOS) and the higher order coherences
(HOC). HOS, mainly bispectrum [97], [98], [103], [107], [129], [146], [158]–[164]
and trispectrum [98], [159] are respectively the double and triple Fourier
transforms of the third and fourth order moments of a time domain signal. The
normalisation of the amplitudes of HOS produces the HOC, where bicoherence
represents normalised bispectrum and tricoherence similarly represents
normalised trispectrum [98], [159]. It is therefore believed that this normalisation
should not alter the characteristics of the spectrum pattern except that the
amplitudes have been limited to a range of between 0 and 1. However the
amplitude normalisation process adopted for the HOS is based on the concept of
the cross-power spectral density (CSD) between two signals and its ordinary
coherence [146], [156]. Hence it is unlikely that the HOC may appear like the HOS
with just normalised amplitude between 0 and 1.
HOS and HOC have been extensively used in a number of applications, including
structural health monitoring, fault detection and characterisation in medicine, rotor-
dynamics, electronics, aerospace, etc. In rotor-dynamics, machinery faults such as
misalignment, crack and shaft rub have been detected using bispectrum [107],
[129], [161]. In a similar study, both bispectrum and trispectrum were used to
identify crack and misalignment in the shaft of a rotating machine [106], [165],
while bispectrum has also been specifically used to detect faults associated with
induction motors [166]. Medical applications of higher order statistical tools include
the use of bispectrum components of the heart rate variability for the detection of
congestive heart failure [167], the classification of different electrocardiogram
(ECG) signals using a combination of bispectrum components and principal
components analysis [168], [169], detection and analysis of epileptic conditions
[170]–[172], etc. In aerospace, bicoherence has been used to separately detect
unbalance, misalignment and a combination of both faults in AH-64 helicopter
drive train assembly [173] and the gearbox of the American NAVY CH-46
helicopter [101]. HOS has similarly been used for studying the non-linear effects of
vibration signals in helicopter drive trains [173]. Structural applications include the
use of HOC for fatigue crack detection in a cantilever beam [174] as well as
A Comparison of Signal Processing Tools: Higher Order Spectra Versus Higher Order Coherences
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Akilu Yunusa-Kaltungo 144 PhD in Mechanical Engineering (2015) University of Manchester (UK)
determining the early contact between two components [175]–[177]. Other
applications of HOS and HOC include rolling element bearings condition
monitoring using bicoherence [100], [102], [164], [178], [179]; hidden mines
detection in coastal systems [180]; analysis of the cutting process in
manufacturing systems [181]; study of material properties [182]; the analysis of
speech and sound in audio processing [183]–[185]; and for the assessment of the
performance of measurement instruments [186].
Some of the above applications have made use of HOS, while others have used
HOC. However, it still remains unclear whether HOS or HOC provide the best
diagnostic features, or whether the two classes of signal processing tools (HOS
and HOC) offer similar features. In this paper therefore, a number of numerically
simulated signals with different amplitudes, frequency components and phases
have been used for the computation of HOS and HOC, with and without noise to
bring out their usefulness and impact on the data analysis and diagnosis. The
cross-power spectral density (CSD) between two signals and its ordinary
coherence are also compared. The results and observations suggest that the HOS
has clear advantages over the HOC which are illustrated in the paper.
5.2 Computational Approaches for Spectra and Coherences
The averaged power spectrum density (PSD) of a time domain signal is
computed as;
=
(5.1)
where =
N is the number of data points for
DFT analysis; is the sampling frequency; is the frequency resolution; is the
A Comparison of Signal Processing Tools: Higher Order Spectra Versus Higher Order Coherences
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Akilu Yunusa-Kaltungo 145 PhD in Mechanical Engineering (2015) University of Manchester (UK)
number of segments of size N; and are respectively the discrete
Fourier transform (DFT) and its complex conjugate at frequency for the rth
segment of the time domain signal that is characterised by a time length of t,
with a reasonable amount of overlap.
Similarly, the CSD between two time domain signals and was computed
as;
(5.2)
The HOS however provide the relation that exists between frequencies within a
time domain signal , since they involve both amplitudes and phases [98],
[157]–[159]. In simpler terms, the bispectrum (which is the double Fourier
transform of the third order moment of a time domain signal, ) basically
involves the combination of two frequencies, and (with both having
amplitudes and phases) with a third frequency which is the summation of the
first two, and computed as [98], [157]–[159], [163];
(5.3)
Similarly, the trispectrum (which is the triple Fourier transform of the fourth order
moment of a time domain signal ) involves the combination of three
frequencies, , and (all having amplitudes and phases) with a fourth
frequency which is the summation of the first three, and computed as
[98], [157]–[159], [163];
A Comparison of Signal Processing Tools: Higher Order Spectra Versus Higher Order Coherences
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Akilu Yunusa-Kaltungo 146 PhD in Mechanical Engineering (2015) University of Manchester (UK)
(5.4)
Furthermore, the normalization of the HOS between amplitude scales of 0 and 1
produces the HOC (where little or no coherence tends to 0 and high coherence
tends to 1). In other words, the normalization of the bispectrum results to
bicoherence, while that of the trispectrum similarly results to tricoherence. The
HOC have been computed as [98], [157]–[159], [163];
Bicoherence, b2 (fl, fm) =
(5.5)
Tricoherence, t2 (fl, fm, fn) =
(5.6)
The coherence between two time domain signals and is a measure of the
linear correlation between them, at a given frequency , where a coherence
nearer to unity signifies that the time domain signals and are linearly
correlated [156], [186]. On the other hand, a reduction in coherence from unity
between the two time domain signals and , may either signify the
presence of noise or a nonlinear relationship [156]. Therefore, the ordinary
coherence between the time domain signals and is computed as [156];
(5.7)
A Comparison of Signal Processing Tools: Higher Order Spectra Versus Higher Order Coherences
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Akilu Yunusa-Kaltungo 147 PhD in Mechanical Engineering (2015) University of Manchester (UK)
where represents the CSD between the time domain signals and ,
while and are their respective PSD at frequency , as shown by Equations
(5.1)-(5.2).
5.3 Simulated Example
In the simulated example, a typical rotating machine with a rotating speed of 3000
RPM (50Hz) has been considered. Vibration response of rotating machines
usually generates responses at rotating speed, which is referred to as the
fundamental frequency (50Hz), and also known as 1x. Due to the emergence of
different faulty conditions [128], rotating machines produce higher harmonics i.e.
100Hz (2x), 150Hz (3x), 200Hz (4x), ….., etc. Hence, the time domain signal
in Equation (5.8), is used to describe a rotating machine with different health
conditions.
(5.8)
where , , , ...., represent the vibration amplitudes at the various
frequency harmonics ( , , ,..., ) and their respective
phases.
A total of 4 cases were simulated (as shown in Table 5.1), and Figure 5.1 shows
the amplitude spectra of the 4 simulated cases computed as per Equation (5.1),
using number of data points (N) of 4096, sampling frequency ( ) of 3000Hz,
frequency resolution ( ) of 0.7324Hz and an overlap of 80% for the averaging.
In case 1, the vibration amplitudes are general low, with 1x amplitude being
slightly higher than those at the higher harmonics (2x, 3x, 4x, …, etc.), which is a
A Comparison of Signal Processing Tools: Higher Order Spectra Versus Higher Order Coherences
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Akilu Yunusa-Kaltungo 148 PhD in Mechanical Engineering (2015) University of Manchester (UK)
representation of a typical healthy case. In the other 3 cases, the vibration
amplitudes have changed (i.e. higher than observed in case 1), which indicates 3
different fault conditions.
Table 5.1 Simulated amplitudes and phases
Simulation Vibration amplitude (g) Frequency (Hz) Phase (degrees)
Case 1
a1 0.15 f1 50 -60
a2 0.06 f2 100 95
a3 0.02 f3 150 160
a4 0.008 f4 200 120
a5 0.001 f5 250 37
a6 0.0006 f6 300 -52
Case 2
a1 1 f1 50 25
a2 0.8 f2 100 35
a3 0.64 f3 150 45
a4 0.48 f4 200 75
a5 0.32 f5 250 105
a6 0.06 f6 300 130
Case 3
a1 0.7 f1 50 48
a2 0.4 f2 100 92
a3 0.33 f3 150 145
a4 0.18 f4 200 90
a5 0.08 f5 250 175
a6 0.04 f6 300 45
Case 4
a1 0.4 f1 50 -130
a2 0.8 f2 100 -55
a3 0.2 f3 150 75
a4 0.6 f4 200 175
a5 0.3 f5 250 125
a6 0.02 f6 300 60
A Comparison of Signal Processing Tools: Higher Order Spectra Versus Higher Order Coherences
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Akilu Yunusa-Kaltungo 149 PhD in Mechanical Engineering (2015) University of Manchester (UK)
Figure 5.1 Typical amplitude spectra (a) Case 1 (healthy) and (b)-(d) Case 2-
Case 4 (different faulty conditions)
5.4 CSD and Ordinary Coherence Analysis
For all 4 simulated cases, the CSD and ordinary coherence have been computed,
using Equations (5.2) and (5.7), and Figures 5.2-5.3 show the CSD and ordinary
coherence plots. In Figures 5.2(a)-5.2(d), all the CSD plots displayed different
features, (showing different magnitudes at the various harmonics of the
fundamental frequency) which clearly show the responsiveness of the CSD to
amplitude and phase changes between the different signals. Amplitudes of
different CSD components shown in Figure 5.2 are also summarized in Table 5.2
for easy comparison. Furthermore, their ordinary coherence plots are shown in
Figure 5.3, with all the magnitudes at the different harmonics of the fundamental
A Comparison of Signal Processing Tools: Higher Order Spectra Versus Higher Order Coherences
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Akilu Yunusa-Kaltungo 150 PhD in Mechanical Engineering (2015) University of Manchester (UK)
frequency tending towards unity as expected, irrespective of the amplitude and
phase changes. This simply indicates and further confirms the well known fact that
the ordinary coherence generally provides the relation between 2 signals at a
frequency, and hence frequently used in several applications including modal tests
[146].
Figure 5.2 Typical CSD plots (a) Signals 1&2, (b) Signals 1&4, (c) Signals 2&4,
and (d) Signals 3&4
(a) (b)
(c) (d)
A Comparison of Signal Processing Tools: Higher Order Spectra Versus Higher Order Coherences
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Akilu Yunusa-Kaltungo 151 PhD in Mechanical Engineering (2015) University of Manchester (UK)
Figure 5.3 Typical ordinary coherence plots (a) Signals 1&2, (b) Signals 1&4, (c)
Signals 2&4, and (d) Signals 3&4
Table 5.2 Magnitudes of CSD components
Frequency, Hz
CSD, Sxy
1 and 2 1 and 4 2 and 4 3 and 4
50 0.3501 0.7003 0.2802 0.2005
100 0.12 0.3202 0.3198 0.2401
150 0.08237 0.2105 0.06592 0.05002
200 0.01798 0.08671 0.1081 0.6003
250 0.003929 0.02552 0.02386 0.01486
300 0.0004179 0.002422 0.0008087 0
5.5 Bispectrum and Bicoherence Analysis
The bispectrum and bicoherence have also been computed for all 4 simulated
cases, using Equations (5.3) and (5.5), for which the typical amplitude-bispectra
and the bicoherence plots are shown on Figures 5.4-5.5. In Figure 5.4, B11
A Comparison of Signal Processing Tools: Higher Order Spectra Versus Higher Order Coherences
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Akilu Yunusa-Kaltungo 152 PhD in Mechanical Engineering (2015) University of Manchester (UK)
represents the relationship between 1x (twice) and 2x components; B12 = B21
represents the relationship between 1x, 2x and 3x components; B22 represents the
relationship between 2x (twice) and 4x components; etc. Similarly, in Figure 5.5,
b211 represents the relationship between 1x (twice) and 2x components; b2
12 = b221
represents the relationship between 1x, 2x and 3x components; b233 represents the
relationship between 3x (twice) and 6x components; etc. It can be seen that all the
amplitude-bispectra plots in Figures 5.4(a)-5.4(d) displayed different
characteristics, with Figure 5.4(a) showing no visible peaks at any location,
representing a healthy condition, while Figures 5.4(b)-5.4(d) show various
bispectrum components with different magnitudes, which clearly represents
different fault conditions. On the contrary, the bicoherence plots in Figures 5.5(a)-
5.5(d) showed identical patterns, with numerous bicoherence components for all
the simulated cases.
Figure 5.4 Typical amplitude-bispectra plots (a) Case 1 (healthy) and (b)-(d) Case
2-Case 4 (different fault conditions)
A Comparison of Signal Processing Tools: Higher Order Spectra Versus Higher Order Coherences
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Akilu Yunusa-Kaltungo 153 PhD in Mechanical Engineering (2015) University of Manchester (UK)
Figure 5.5 Typical bicoherence plots (a) Case 1 (healthy) and (b)-(d) Case 2-Case
4 (different fault conditions)
5.6 Trispectrum and Tricoherence Analysis
Similarly, the trispectrum and tricoherence were computed for all the simulated
cases using Equations (5.4) and (5.6), for which the typical amplitude-trispectra
patterns for 2 of the 4 cases are shown in Figure 5.6. T111 represents the
relationship between 1x (thrice) and 3x components; T112=T121=T211 represents the
relationship between 1x (twice), 2x and 4x components; etc. Similarly, in Figure
5.7, t2111 represents relationship between 1x (thrice) and 3x components; t2112 =
t2121 = t2211 represents relationship between 1x (twice), 2x and 4x components; etc.
The amplitude-trispectra plots shown in Figures 5.6(a)-5.6(b) possessed very
different features, with Figure 5.6(a) showing only the T111 trispectrum component
or sphere (where sphere diameter represents amplitudes of vibration and spheres
presence at certain locations indicating the intersection of 3 frequencies in l, m and
b233
b211
b212
(a)
b233
b211
b212
(b)
b233
b211
b212
(c)
b233
b211
b212
(d)
A Comparison of Signal Processing Tools: Higher Order Spectra Versus Higher Order Coherences
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Akilu Yunusa-Kaltungo 154 PhD in Mechanical Engineering (2015) University of Manchester (UK)
n axes), which is a representation of a typically healthy machine. Figure 5.6(b)
however displayed additional components (T112= T121= T211) to the T111 component,
which is an outcome of the changes in the amplitudes and phases (representing a
typical faulty condition). The tricoherence plots in Figure 5.7 however show very
identical features for both healthy and faulty conditions, as shown in Figures
5.7(a)-5.7(b) respectively.
Figures 5.4-5.7 have clearly showed that irrespective of amplitude or phase
changes, HOC (bicoherence and tricoherence) will always tend towards 1. On the
other hand, HOS (bispectrum and trispectrum) adequately respond to amplitude
and phase changes. This observation was consistent for all the 4 simulated cases.
Figure 5.6 Typical amplitude-trispectra plots (a) Case 1 (healthy) and (b) Case 2
(faulty)
A Comparison of Signal Processing Tools: Higher Order Spectra Versus Higher Order Coherences
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Akilu Yunusa-Kaltungo 155 PhD in Mechanical Engineering (2015) University of Manchester (UK)
Figure 5.7 Typical tricoherence plots (a) Case 1 (healthy) and (b) Case 2 (faulty)
5.7 Signals with Noise
Now, different levels of noise are also added to the signals in Table 5.1, so as to
further understand the behaviors of HOS and HOC. The 3 noise levels considered
are at 10 dB, 20 dB and 30 dB (with 10 dB being the noisiest). The magnitudes of
the HOS components as well as the plot patterns remained unchanged at all noise
levels. On the contrary, as the noise levels increased towards 10 dB, the
magnitudes of the HOC components (e.g. b233 and b2
23 significantly reduced from
1 at zero noise to 0.304 and 0.454 respectively) began to decrease, which shows
the dependency of HOC on noise levels, and this is further illustrated by Table 5.3.
A Comparison of Signal Processing Tools: Higher Order Spectra Versus Higher Order Coherences
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Akilu Yunusa-Kaltungo 156
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Table 5.3 Magnitudes of bispectrum and bicoherence components
SNR (dB) Case Bispectrum Components Bicoherence Components
B11 B12 B13 B22 B23 B33 b211 b
212 b
213 b
222 b
223 b
233
10
1 0.001 0 0 0 0 0 0.999 0.998 0.981 0.981 0.454 0.304
2 0.805 0.513 0.313 0.305 0.166 0.025 1 1 1 1 0.999 0.973
3 0.196 0.092 0.04 0.028 0.011 0.004 1 1 0.999 0.999 0.996 0.977
4 0.129 0.063 0.048 0.386 0.047 0.001 0.999 0.998 0.999 1 0.998 0.924
20
1 0.001 0 0 0 0 0 1 1 1 0.998 0.921 0.824
2 0.799 0.512 0.308 0.306 0.165 0.025 1 1 1 1 1 0.996
3 0.195 0.092 0.042 0.029 0.011 0.005 1 1 1 1 1 0.997
4 0.128 0.064 0.048 0.385 0.048 0.001 1 1 1 1 0.921 0.997
30
1 0.001 0 0 0 0 0 1 1 1 1 0.989 0.981
2 0.8 0.512 0.308 0.308 0.164 0.025 1 1 1 1 1 1
3 0.196 0.092 0.042 0.029 0.011 0.004 1 1 1 1 1 1
4 0.128 0.064 0.048 0.385 0.048 0.001 1 1 1 1 1 0.999
zero noise
1 0.001 0 0 0 0 0 1 1 1 1 1 1
2 0.8 0.512 0.307 0.307 0.164 0.025 1 1 1 1 1 1
3 0.196 0.092 0.042 0.029 0.011 0.004 1 1 1 1 1 1
4 0.128 0.064 0.048 0.384 0.048 0.001 1 1 1 1 1 1
A Comparison of Signal Processing Tools: Higher Order Spectra Versus Higher Order Coherences
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5.8 Summary
A total of 4 signal cases have been simulated, with each case having differing
amplitudes and phases, but same frequency components so that the comparison
between spectra and coherences can be made. Initially, the CSD and their
ordinary coherences were analyzed, and it was observed that the ordinary
coherence provides linearity relation at each frequency between 2 signals,
irrespective of the amplitude and phase at each frequency in the signals. A similar
behavior was also observed when HOS and HOCs were compared. This simply
indicates that HOCs are not amplitude normalization of HOS. Hence HOCs cannot
be used to represent a real system, due to their lack of sensitivity to amplitude and
phase changes, as well as their dependence on noise levels. On the other hand,
HOS components responded adequately to changes in amplitude and phases,
which is a highly desirable characteristic for many applications and diagnosis, so
as to distinguish the different states of signals. It can therefore be concluded that
HOS provide better representation of features at each combination of frequency
components in a signal than HOCs, which make HOS more useful for different
applications including health monitoring and diagnosis technique for structures and
rotating machines.
Combined Bispectrum and Trispectrum for Faults Diagnosis in Rotating Machines
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Akilu Yunusa-Kaltungo 158
PhD in Mechanical Engineering (2015) University of Manchester (UK)
6 Chapter 6 COMBINED BISPECTRUM AND TRISPECTRUM FOR FAULTS DIAGNOSIS
IN ROTATING MACHINES ----------------------------------------------------------------------------------------------
Reformatted version of the following papers:
Paper 1 title: Combined bispectrum and trispectrum for faults diagnosis in
rotating machines
Authors: A. Yunusa-Kaltungo and J.K. Sinha
Published in: Proceedings of the Institution of Mechanical Engineers, Part O:
Journal of Risk and Reliability, Volume 228, Issue 4, February 2014, Pages 419-
428
Paper 2 title: HOS analysis of measured vibration data on rotating machines
with different simulated faults
Authors: A. Yunusa-Kaltungo, J.K. Sinha and K. Elbhbah
Published in: Proceedings of 3rd International Conference on Condition Monitoring
of Machinery in Non-Stationary Operations (CMMNO 2013), Ferrara/Italy, May 8-
10 2013
Series title: Lecture Notes in Mechanical Engineering
DOI: 10.1007/978-3-642-39348-8
Combined Bispectrum and Trispectrum for Faults Diagnosis in Rotating Machines
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Akilu Yunusa-Kaltungo 159
PhD in Mechanical Engineering (2015) University of Manchester (UK)
Publisher: Springer-Verlag Berlin Heidelberg
Abstract
Over the years, condition monitoring (CM) of rotating machines has been
extensively applied for enhancing equipment reliability and maintenance cost
effectiveness, through the early detection and reliable diagnosis of incipient
machine faults. Earlier studies suggest that bispectrum analysis is a good tool for
detecting and distinguishing rotor related faults in rotating machines, with a
significantly reduced number of vibration sensors. Now, the trispectrum analysis is
also applied to the measured vibration data, so as to explore the usefulness of this
analysis in the diagnosis. It is observed that the trispectrum further improves the
reliability of rotating machine faults diagnosis. This paper presents the results and
observations related to the bispectrum and trispectrum analysis for fault(s)
diagnosis, through an experimental rig with different faults simulation.
Keywords: Machine reliability, rotating machines, condition monitoring, higher
order spectrum, bispectrum, trispectrum
6.1 Introduction
Rotating machines form the heart of most industrial activities, which makes the
reliability of this class of machines imperative to any organisation. In the past,
some failures associated with rotating machines have had devastating effects on
personnel, environment, finance, etc [187]. Hence, the development of a reliable
and cost effective fault diagnosis approach that will enhance the planning and
scheduling of maintenance activities, through the provision of reasonable lead
times to failure is always desirable. Vibration-based condition monitoring (VCM) is
a well-known technique for the diagnosis of faults related to rotating machines [8],
through the installation of various numbers of vibration transducers at individual
bearing pedestals of the monitored machine. The present efforts are aimed at
Combined Bispectrum and Trispectrum for Faults Diagnosis in Rotating Machines
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Akilu Yunusa-Kaltungo 160
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minimising the transducer requirements for VCM, through the use of higher order
spectra (HOS), namely bispectrum and trispectrum [98], [103], [157]–[160]. This is
because HOS have the capability to combine different frequency components in a
signal (as opposed to the conventional spectrum analysis that only provides
insights of the amplitudes of individual frequency components [188]), and hence
the relationships that exist amongst the different harmonics and sub-harmonics of
the machine’s rotational speed in the vibration responses from the machine can be
used for the diagnosis of rotor related fault(s). Earlier studies have explored the
possibilities of fault diagnosis by mainly applying the bispectrum [107], [129], while
very limited research study related to the trispectrum [189] was done. It has been
observed that the bispectrum analysis [107], [129] provides a much better feature
for the diagnosis of different faults simulated on an experimental rig, when
compared to the spectrum analysis alone, without the phase and orbit analysis.
Earlier studies by McCormick and Nandi [190], as well as Li et al. [191] have
significantly identified the potentials of using HOS for the diagnosis of machine
faults. However, the former study [190] was solely based on fault diagnosis of
rolling element bearings, while the latter study [191] on the other hand focused on
the detection of incipient gear faults using a combination of bispectrum and
artificial neural networks (ANN). Sinha [106] also applied HOS for detection of
crack and misalignment on a rotating machine with a rotor supported by just two
bearings. However, a significant number of rotating machines are more complex in
structure, with several bearings and couplings. In the present study, a combination
of the newly introduced trispectrum analysis and the earlier bispectrum analysis
[107], [129] are jointly applied to the measured vibration acceleration data for 4
different experimentally simulated cases (healthy, shaft misalignment, cracked
shaft and shaft rub) on an experimental rig supported by 4 anti-friction ball
bearings, so as to enhance the reliability of the diagnosis feature for each fault.
The observations from the earlier studies [107], [129] based on bispectrum
analysis clearly suggested that bispectrum analysis performs extremely well in
detecting and differentiating between all the simulated cases at certain speeds.
However, the incorporation of trispectrum analysis in the current study further
enhances the possibilities of developing a more robust set of condition monitoring
Combined Bispectrum and Trispectrum for Faults Diagnosis in Rotating Machines
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Akilu Yunusa-Kaltungo 161
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indicators (CMI) that will be applicable to various operating conditions of a
machine. Furthermore, a comparison of HOS with the conventional and widely
applied spectrum analysis, which is based on power spectrum density (PSD) for
measured vibration data is also presented here, so as to clearly show the
advantages of HOS analysis. Experiments were carried out at 2 different rotating
speeds – 2400RPM (34Hz) and 3000RPM (50Hz), and the results observed from
both bispectrum and trispectrum analyses at these two speeds are also discussed.
6.2 PSD and HOS Computations
The PSD of a time domain signal can be computed as;
=
(6.1)
where =
N denotes the number of data points
for discrete Fourier transform (DFT) analysis; represents the sampling
frequency; is the frequency resolution; is the number of segments with size
N; and respectively denote the DFT and its complex conjugate at
frequency for the rth segment of the considered time domain signal ,
having a time length of t, with sufficient amount of overlap.
The HOS offers insight on the relationship existing amongst the frequency
components present in a time domain signal , as they entail amplitudes as well
as phases [98], [157]–[159]. In similar definitions, the bispectrum of a time domain
signal , represents a combination of two frequencies (each having amplitude
and phase), and with a third frequency which is equivalent to the sum
of the initial two, and was computed as [157]–[159];
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(6.2)
Similarly, the trispectrum of a time domain signal , involves the combination of
three frequencies (each having amplitude and phase) , and with a fourth
frequency that is equivalent to the sum of the initial three, and was
computed as [98], [159], [188];
(6.3)
In the current paper, the HOS (bispectrum and trispectrum) have been computed
by dividing the measured vibration data into a number of overlapping segments
( ). The DFT for each of the segments is then computed, and the products of the
spectral coefficients generate the HOS, which are eventually averaged across the
segments [98]. Each of the bispectrum components amplitude is a function of two
frequencies, usually plotted in the xyz orthogonal axes, with axes x and y
respectively representing frequencies, while the amplitude of the bispectrum is
plotted on the z axis. On the other hand, each trispectrum component is a function
of three frequencies, requiring a 4-dimensional plot. Therefore, the spherical plot
method earlier suggested by Collis et al. [98] is adopted here, where the
appearance of individual spheres at certain locations signifies the coupling that
exists between the frequencies at that location and the sizes of the spheres relate
to the amplitudes of the trispectrum components for individual cases.
6.3 Experimental Setup
The photographic and schematic representations of the experimental rig are
shown on Figures 6.1and 6.2 respectively, which is situated in the Dynamics
Laboratory of the University of Manchester. The rig principally consists of two
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rigidly coupled steel shafts of uniform diameters (20mm) but varying lengths
(1000mm and 500mm respectively), which were supported by 4 anti-friction ball
bearings mounted on relatively stiff pedestals (just as indicated by Figure 6.1). The
1000mm shaft is connected to the electric motor via a flexible coupling. The motor
speed is regulated through the aid of a PC-based speed controller (NEWTON
TESLA CL750 and FR Configurator SW3), so as to accommodate the selection of
preferred shaft speeds during the experiment. There are 3 balance steel discs of
dimensions 125mm (OD) x 15mm (thickness), with 2 of the discs fitted on the long
shaft (first disc is 300mm from the drive motor and the second is 190mm from the
second bearing) and the third on the shorter shaft (210mm from both bearings 3
and 4) as shown on Figure 6.1. Further details about the experimental setup are
available in Elbhbah and Sinha [107].
Figure 6.1 Photographic representation of the experimental rig
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Figure 6.2 Schematic representation of the experimental rig
6.4 Simulation of Faults
The following four cases (healthy, misalignment, cracked shaft and shaft rub) have
been simulated on the experimental rig (Figure 6.1), and vibration data were
collected at 2 different rotational speeds of 2040RPM (34Hz), which corresponds
to half of the first natural frequency of the rig and at 3000RPM (50Hz). For all 4
cases, only 4 accelerometers (1 at each bearing pedestal, in the horizontal
direction) were used for the collection of the vibration responses. All vibration data
were recorded on to a PC, through the aid of a 16-channel, 16-bits Data
Acquisition Card (NI 6229), for subsequent analysis using a MATLAB code.
Further details about the simulated faults are also available in Elbhbah and Sinha
[107].
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6.5 Data Analysis
The measured vibration data from the 4 bearings, at rotational speeds of
2040RPM (34Hz) and 3000RPM (50Hz) have been analysed using spectrum,
bispectrum and trispectrum, which were computed as per Equations (6.1)-(6.3), in
Section 6.2. The vibration data were analysed using an 80% overlap, frequency
resolution ( of 0.6104Hz at a sampling frequency (fs) of 5000Hz, and a number
of data points, N = 8192. The observations and results are hereby discussed
accordingly.
6.5.1 Spectrum analysis
As extensively analysed in earlier studies [128], the amplitude spectra at 34Hz for
bearing 1 (Figure 6.3), displayed significantly low peaks at 1x and its higher
harmonics for the healthy case (Figure 6.3(a)). The shaft misalignment case
(Figure 6.3(b)) contained similar harmonic components as the healthy case, but
with much higher amplitudes. The cracked shaft case presented additional 4x and
5x harmonic components to the 1x and 2x components in the earlier cases (i.e.
healthy and shaft misalignment), while shaft rub case (Figure 6.3(d)) showed sub-
harmonic components (0.5x and 1.5x). At 50Hz (Figure 6.4) however, the
amplitude spectra at bearing 1 still possessed 1x and 2x peaks with relatively low
amplitudes for the healthy case (Figure 6.4(a)). On the other hand, the features for
misalignment (Figure 6.4(b)), cracked shaft (Figure 6.4(c)) and rub (Figure 6.4(d))
cases have completely changed at 50Hz (mainly due to the fact that 34Hz is
exactly half of the first natural frequency of the machine, which governed the
excitation of 1x), with misalignment showing 1x, 2x, 4x and 6x peaks, while the
cracked shaft case displayed very prominent peaks at 1x and 2x only. The sub-
harmonic components in the rub case disappeared at 50Hz, leaving the presence
of only 1x and 2x peaks with very low amplitudes. Furthermore, a plot of the
normalised amplitudes (i.e. the normalisation of the amplitudes of the higher
harmonics, mainly 2x, 3x, 4x, with the amplitude of 1x) at both 34Hz and 50Hz for
bearing 1 is shown on Figure 6.5, where it can be clearly seen that virtually no
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separation exists amongst the different cases (significant overlap amongst all
cases). This however explains why it is difficult to adequately differentiate between
the various operational states of a machine, using spectrum analysis alone.
Figure 6.3 Typical amplitude spectra at 34Hz for bearing 1
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Figure 6.4 Typical amplitude spectra at 50Hz for bearing 1
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Figure 6.5 Typical normalised amplitude spectrum components at 34Hz ((a)-(b))
and at 50Hz ((c)-(d)) for all the simulated cases
6.5.2 Bispectrum analysis
The findings from the earlier studies [107], [129] already suggested that
bispectrum analysis provided better diagnosis for the different faults. This is
however briefly discussed here, so that the usefulness of trispectrum for a robust
fault(s) diagnosis can be brought out. The amplitude bispectra plots at the two
rotational speeds (34Hz and 50Hz) are shown in Figures 6.6-6.7 [107], [129]
respectively.
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Figure 6.6 Typical amplitude bispectra plots at 34Hz (a) healthy (b) misalignment
(c) cracked shaft (d) shaft rub
Figure 6.7 Typical amplitude bispectra plots at 50Hz (a) healthy (b) misalignment
(c) cracked shaft (d) shaft rub
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As explained in Section 6.2, the bispectrum indicates the relation between 2
frequencies, and with their sum ( ) in a time domain signal . Also, in
Figures 6.6-6.7, the different bispectrum components indicate the relationship
between the different frequencies in the measured vibration signal. For instance,
indicates the relation between one times (twice) and two times the rotational
frequency of the machine, where and in Equation (6.2) are equal to the
rotational frequency of the machine, and is two times the rotational
frequency of the machine. Similarly, , indicates the relation between one times,
two times and their sum (i.e. three times) the rotational frequency of the machine;
relates one times, three times and four times the rotational frequency of the
machine; while relates two times (twice) and four times the rotational
frequency of the machine in the measured vibration signal. The sub-harmonic
bispectrum component indicates the relation between fractions of the rotational
frequency of the machine (twice) and their sum (i.e. and are respectively
fractions of the rotational frequency of the machine, while equals their sum).
On the other hand, the sub-harmonic bispectrum component indicates the
relation between a fraction of the rotational frequency of the machine, one times
the rotational frequency and their sum. Using the current set-up as illustration, the
bispectrum component at 34Hz is respectively the product of the amplitudes
and phases of 1x twice (i.e. the combination of the amplitude and phase at
machine speed of 34Hz twice) and 2x (68Hz). Also, component is respectively
the product of the amplitudes and phases of 1x (34Hz), 2x (68Hz) and 3x (102Hz),
etc. However, the bispectra responses for all simulated cases were quite
consistent at both speeds (34Hz and 50Hz) and at all bearings, except for the
shaft rub case (Figure 6.7(d)). Hence, a summary of the observations from the
experiment are explained here.
At both rotational speeds, the healthy case (Figures 6.6(a) & 6.7(a)) contained
generally small and negligible and (= bispectrum components. For
misalignment, all the bispectrum components slightly went higher in amplitudes,
when compared with the healthy case. In the crack case, all the bispectrum
components significantly went higher in amplitudes (with an order of as much as
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ten times, when compared to the misalignment case). The rub case at 34Hz
(Figure 6.6(d)) displayed an entirely different feature from the other 3 cases, owing
to the fact that most of the rotor’s unbalance energy have been converted to sub-
harmonic responses, which was responsible for the cluster of peaks around
and (= ). At 50Hz however, the rub case displayed a response that looked
identical to the healthy case, due to inadequate shaft deflection (which created a
“touch and go effect” as opposed to the substantial rub experienced at 34Hz)
[107], [129].
6.5.3 Trispectrum analysis
Figures 6.8-6.9 show the amplitude trispectra plots, where signifies the
relation between one times (thrice) and three times the rotational frequency
components; = = signifies the relation between one times (twice),
two times and four times the rotational frequency components; signifies the
relation between fractions of the rotational frequency (thrice) and their sum; =
= signifies the relation between fractions of the rotational frequency
(twice), one times and two times the rotational frequency. As explained for the
bispectrum analysis in Section 6.5.2, trispectrum component in the current
set-up at 34Hz machine speed represents a combination of the amplitudes and
phases of 1x (34Hz) twice, 2x (68Hz) and 4x (136Hz).
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Figure 6.8 Typical amplitude trispectra plots at 34Hz for bearings 1 (a-d) and 3 (e-
h); (a and e) healthy, (b and f) misalignment, (c and g) cracked shaft, (d and h)
shaft rub
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Figure 6.9 Typical amplitude trispectra at 50Hz (a) healthy (b) misalignment (c)
cracked shaft (d) shaft rub
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Table 6.1 Summary of the diagnostic features for bispectrum and trispectrum
Case(s) Bispectrum Trispectrum Remark(s)
Healthy Small B11 and negligible B12=B21 components
T111 only On all bearings and same at both rotational speeds
Misalignment Peaks at B11, B12=B21 and B22 (Higher than healthy)
Prominent peak at T111 but small T121=T211=T112 at Bearing 1 Consistent observations for
trispectrum, but bispectrum components are speed dependent.
Prominent peak at T222 and small T122=T212=T221 peak at remaining bearings
Cracked shaft Prominent peaks at B11 , B13=B31, B12=B21 and B22 and much higher amplitude compared to Misalignment
Small T111 Consistent observations at both rotational speeds Large T121=T112=T211
Shaft rub B11, Bss, B1s=Bs1, B12=B21, etc. T111, Tsss, T1ss=Ts1s=Tss1, etc.
Consistent observations for both bispectrum and trispectrum analyses except at 3000RPM for bispectrum analysis due to “touch and go” kind of rub.
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The healthy cases at both rotational speeds (34Hz and 50Hz) only possessed the
component (Figures 6.8(a), 6.8(e) and 6.9(a)), which was as a result of the
residual misalignment between bearings 2 and 3. The misalignment case
possessed components = = which were small and equal in size, and
a large component. At 34Hz [12], misalignment at bearing 3 showed small
= = and a large , which also corresponded to the observation at
50Hz. The crack case possessed a response that was somewhat a reverse of the
misalignment case in size, but similar in components (i.e. = were
large and the was small). Just as in the case of the bispectrum at 34Hz, the
rub case displayed several sub-harmonics ( ). These
observations also conformed to the findings of Sinha [106], except for the
misalignment response at bearing 3 (at 34Hz speed), which possessed
= = and components. This variation is due to the fact that the initial
experiment [106] involved the use of just 2 bearings and a single coupling, as
opposed to the present work that had four bearings and 2 couplings (one flexible
and one rigid). However, the appearance of the = = and
components (at 34Hz speed) is due to the fact that bearing 3 is located next to the
rigid coupling, while bearing 1 is located near the flexible coupling, and therefore
some of the energy generated by the misalignment at bearing 1 are absorbed by
the flexible coupling [192]. The current study showed a strong consistency in the
responses at all 4 bearings for all 4 cases and at both speeds, except for the
misalignment case which had responses at bearings 2, 3 and 4 being similar, but
different from the response at bearing 1 (which is due to the fact that the
misalignment is at bearing 1, which is also the flexible coupling location [192]).
Although earlier studies [107], [129] have shown the advantages of bispectrum
among the different cases (healthy, misalignment, cracked shaft and shaft rub),
however, the trispectrum gave an even better, clearer and very consistent
distinction amongst all the experimentally simulated cases and at both rotational
speeds. While the bispectrum analysis for rub case provided a plot that was very
similar to the healthy case (absence of sub-harmonic components) at 50Hz, due to
the partial rub action, the trispectrum was able to maintain its consistency at both
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rotational speeds (e.g. the presence of sub-harmonic components
at both 34Hz and 50Hz), which is explained more
illustratively in Section 6.5.4.
6.5.4 Diagnostic Features
The observations of both bispectrum and trispectrum analyses have been
summarised in Table 6.1, so as to bring out the indicative diagnostic features for
each of the experimentally simulated cases at both rotational speeds. In the
amplitude bispectra plots shown in Figure 6.6, the appearance of relatively small
B11 and B12 peaks for the healthy case at 34Hz is related to the combination of the
amplitudes and phases of the 1x (34Hz) and 2x (68Hz) frequency components
seen in the amplitude spectrum (Figure 6.3(a)), which is due to some residual
misalignment in the machine set-up. Similarly, the appearance of additional B22
component in the misalignment case (Figure 6.6(b)) is an indication of the coupling
that exists between 2x and 4x components in the amplitude spectrum (Figure
6.3(b)). Although the 4x component is not quite visible in the amplitude spectrum
(Figure 6.3(b)), due to the relative dominance of the 1x component (i.e. half the 1st
natural frequency). However, the relationship between the 2x and 4x components
is clearly highlighted in the amplitude bispectrum (Figure 6.6(b)), since it involves
both amplitude and phase information. In the cracked shaft case (Figure 6.6(c)),
the appearance of multiple bispectrum components (B11, B12, B13 and B22) again
relates to the presence and relationships between the 1x, 2x, 3x, 4x, etc.,
components in the amplitude spectrum (Figure 6.3(c)), while the Bss and B1s in the
rub case (Figure 6.6(d)) are respectively the combination of the sub-harmonic
components 0.5x (visible as the humps in Figure 6.3(d)) twice and the 1x
component. At 50Hz machine speed (Figure 6.7), although the bispectrum
components for the healthy, misalignment and cracked shaft cases are same,
however, the magnitudes of the B11 component has significantly reduced in
comparison to the 34Hz speed (mainly because 50Hz is far from any of the natural
frequencies and their multiples). In the shaft rub case at 50Hz (Figure 6.7(d)), the
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sub-harmonic components have disappeared, due to the inability of the shaft to
deflect enough to cause a continuous rub (i.e. “a touch and go” rub action was
observed).
As similarly explained for the amplitude bispectra, the healthy case at 34Hz for
bearing 1 (Figure 6.8(a)) is characterised by T111 trispectrum component, which
signifies the combination of amplitudes and phases of 1x (34Hz) thrice and 3x
(102Hz) frequency components. In the misalignment case (Figure 6.8(b)), the
massive T111 component as well as the T112=T121=T211 (which signifies the
relationship between twice 1x (34Hz), 2x (68Hz) and 4x (136Hz)) components are
governed by the combinations of the amplitudes and phases of 1x, 2x and 4x
frequency components. The lack of visibility of the 4x (136Hz) component in the
amplitude spectrum (Figure 6.3(b)) is also due to the dominance of the 1x
frequency component (half of the first natural frequency of the machine). Although
the cracked shaft case (Figure 6.8(c)) contains similar trispectrum components as
the misalignment case (Figure 6.8(b)), however, the significant changes observed
in the magnitudes of the components (a significant increase in T112=T121=T211
magnitude and a corresponding reduction in T111 magnitude) also conforms with
the presence of higher harmonic components (2x, 4x, 5x, etc.) in the amplitude
spectrum (Figure 6.3(c)). The rub case at 34Hz (Figure 6.8(d)) contains sub-
harmonic trispectrum components Tsss (representing a combination of the
amplitude and phase at 17Hz thrice and at 51Hz), Tss1=Ts1s=T1ss (combination of
amplitude and phase at 17Hz twice, 34Hz and 68Hz), as well as T111 component.
The sub-harmonic trispectrum components in the rub case can be confidently
related to the sub-harmonic humps visible in the amplitude spectrum on Figure
6.3(d). As the machine speed changed from 34Hz to 50Hz (i.e. away from the
natural frequency of the machine), the trispectrum components for each case
remained consistent for all the simulated cases, except that the T111 component
has been transformed to T222, which corresponds to the appearance of significant
2x, 4x and 6x components in the amplitude spectrum (Figure 6.4(b)). As discussed
in the preceding Sections (6.1, 6.2 & 6.5), the advantages of HOS lies in the fact
that they integrate different frequency components in a signal, which makes the
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development of unique features for different cases at different speeds possible
(which is unachievable through the use of spectrum analysis alone, as it only
involves the amplitudes at individual frequencies).
6.6 Summary
Bispectrum and trispectrum analyses have been applied to an experimental rig,
with different simulated faults at different machine speeds, so as to enhance the
reliability of fault diagnosis in rotating machines. Only 1 accelerometer per bearing
pedestal was used, with the aim of reducing the number of often used sensors to a
fewer number. The observations indicate that the faults identification and their
characterisation, using bispectrum and trispectrum analyses is possible. This is
due to the fact that both bispectrum and trispectrum give the combined relation
between the different harmonics of the machine speed in their vibration responses.
The appearance of different harmonics in vibration response is related to the
different faults in the machine, which is expected to be unique in terms of
amplitudes and phases at each harmonic component for every fault. While earlier
studies have shown the potentials of bispectrum analysis for machine operational
states distinction, the current work has however shown that bispectrum analysis
alone could be limited in its capability to differentiate between certain faulty and
healthy conditions (such as intermittent shaft rubs at certain machine speeds).
However, the trispectrum analysis was able to effectively and consistently capture
all the changes in the machine operational states. Hence, the present study shows
the possibilities of enhancing fault diagnosis and maintenance cost effectiveness,
through a combination of bispectrum and trispectrum analyses. However, more
experiments are planned in the future, so as to further establish the findings in the
present study.
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7 Chapter 7 USE OF COMPOSITE HIGHER
ORDER SPECTRA FOR FAULTS DIAGNOSIS OF ROTATING MACHINES
WITH DIFFERENT FOUNDATION FLEXIBILITIES
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Reformatted version of the following papers:
Paper 1 title: Use of composite higher order spectra for faults diagnosis of
rotating machines with different foundation flexibilities
Authors: A. Yunusa-Kaltungo, J.K. Sinha and A.D. Nembhard
Published in: Measurement 70 (2015) 47-61
Paper 2 title: Coherent composite HOS analysis of rotating machines with
different support flexibilities
Authors: A. Yunusa-Kaltungo and J.K. Sinha
Published in: Proceedings of 10th International Conference on Vibration
Engineering Technology of Machinery (VETOMAC X 2014), Manchester/United
Kingdom, September 9-11 2014
Series title: Mechanisms and Machine Science
Series volume: 23
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DOI: 10.1007/978-3-319-09918-7
Publisher: Springer International Publishing
Abstract
It is commonly observed in practise that rotating machines installed at different
plant locations often exhibit different dynamic behaviours, due to variations in the
flexibilities of their supports, which often affects fault diagnosis. In the current
study, a similar scenario has been experimentally simulated on a rotating rig with
different foundation flexibilities. Also, different faults were experimentally simulated
at different machine speeds so as to develop a reliable diagnosis technique that
will be suitable for different machine foundations. Recently developed data fusion
methods for constructing composite spectrum (CS) and composite bispectrum
(CB) for a machine are again applied for faults diagnosis here. In addition, the
present study introduces the composite trispectrum (CT) as a new feature for
diagnosis. The paper hereby presents the computational concepts of all composite
spectra, rig details, data analysis and diagnosis.
Keywords
Rotating machines, flexible foundation, faults diagnosis, data fusion, composite
bispectrum, composite trispectrum
7.1 Introduction
The dynamic behaviours of ‘as installed’ rotating machines at different locations in
a plant and/or in different plants is observed to be significantly different in many
cases [193], [194]. This is mainly due to different flexibility of the foundation at
different places. For instance, two large turbo-generator sets may exhibit different
dynamic behaviours as a result of the differences in their foundations [195]. To
further enhance clarity, an abstract representation of machine and foundation is
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shown in Figure 7.1, where machines can be identical (for example pump and
motor units, identical turbines, etc.), but may have different foundations. It is also
important to state that the term rotating machine in Figure 7.1 solely refers to the
rotor-bearing-motor assembly (including other integral components such as
couplings, discs, etc.), that may have been acquired with such a machine from the
original equipment manufacturer (OEM), which can be identical for several rotating
machines. The foundation on the other hand refers to all machine installations
onsite, including structural connections (e.g. piping, bracing, etc.) that can have an
influence on the ‘as installed’ machine dynamics.
Since rotating machines are sometimes subjected to a wide range of operating
conditions, which often leads to the emergence of faults that require early and
effective diagnosis that will avoid compromising personnel and equipment safety
[187]. These factors make the fault diagnosis process complex. This however
explains why good prior understanding of the modal parameters and dynamic
behaviours of rotating machines play a very vital role in vibration-based fault
diagnosis. Perhaps, model-based diagnosis approach [32], [65], [66], [196]–[199]
may prove useful for such cases where foundation dynamics is generally taken
into account. However, some of the popular techniques highlighted in research
articles [19], [200]–[202] summarising various fault diagnostics and prognostics
techniques may or may not be directly applicable for reliable diagnosis when
dealing with rotating machines installed on different foundations.
Within the past few decades [159], appreciable research contributions on the
application of higher order signal processing techniques for fault diagnosis in
rotating machines have been made. This was based on the premise that fault
diagnosis using conventional and well-known linear spectral analysis techniques
such as power spectrum density (PSD) alone is unable to establish the
interactions that exist between frequency components of measured vibration
signals when faults occur, due to its lack of phase information [159]. However,
these studies have been dominated by the application of the normalised forms of
the higher order spectra (HOS), known as the higher order coherences (HOCs)
[99]–[105], [203]. Sinha [106] experimentally and theoretically explored the
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application of HOS (bispectrum and trispectrum) for fault detection on a very
simple rotating rig, supported by just two bearings. However, a significant number
of industrial rotating machines often posses a more complicated configuration, with
more bearings. This therefore triggered further investigation of HOS for the
diagnosis of more rotor-related faults on a relatively rigid rotating machine
supported by four bearings, at a single [189] and multiple machine speeds
respectively [204]. In the latter study [204] it was shown that bispectrum could not
adequately distinguish between certain machine conditions (intermittent rotor rubs
and healthy conditions) at certain machine speeds, which led to the combination of
bispectrum and trispectrum features for a more robust diagnosis. Despite the
significant contributions on HOS and HOCs, as well as considering the fact that a
significant number of industrial rotating machines are mounted on flexible
foundations, none of the earlier studies has been geared towards diagnosing faults
associated with ‘as installed’ identical rotating machines with different foundations.
Hence, the current paper aims to simulate an industrial scenario through an
experimental rig with different flexible foundations. The impacts of the different
foundations on the rig have also been confirmed by conducting modal tests to
obtain the modal parameters [205]. Different faults have been experimentally
simulated and the observed dynamic behaviours for each fault have been found to
be different for the different foundations, and hence the diagnosis features. In this
study, the recently developed data fusion technique for computing composite
spectra (CS) [128] and composite bispectra (CB) [127] for a machine is used on
the present experimental data. Furthermore, the concept of composite trispectrum
(CT) for a machine has also been introduced as an additional diagnosis feature, so
as to significantly enhance the ability of the proposed technique to discriminate
between different machine conditions, owing to the fact that the CT component
expresses the relationships between more frequency components in the measured
vibration data. The current research effort is based on the development of a
reliable and simplified fault diagnosis approach that will be applicable to rotating
machines with different foundation flexibilities. The developed method can utilise
the diagnosis features for identical rotating machines with different foundations.
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Several sets of measured vibration data from the rig with different foundations
under various experimentally simulated faults at different machine speeds are
analysed using all composite higher order spectra. Hence, the paper provides
details of signal processing, rigs, experiments and faults diagnosis using
composite higher order spectra.
Figure 7.1 Abstract representation of rotating machine and foundation
7.2 Composite Spectra Computations
Earlier studies by Elbhbah et al. [128] and Sinha et al. [127] have respectively
provided the concepts of CS and CB. The computational concepts are again
presented here.
Let’s consider a rotating machine with “b” number of bearings from which vibration
data were measured, and the measured vibration data were divided into “ns”
number of equal segments, then the CS for the entire rotating machine was
computed as [127], [128];
(7.1)
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where = (k-1) ; k = 1, 2, ...., N/2; = fs/N; N denotes the number of data
points for Fourier transformation (FT); and
respectively denote
the coherent composite FT and its complex conjugate for the rth segment of the
measured vibration data collected from “b” number of bearings at frequency, .
Hence, is thus computed as [128];
(7.2)
In Equation (7.2),
, ....,
respectively denote the coherence [127]
derived between vibration signals recorded at bearing locations 1-2, 2-3, …, (b-1)-
b. Also,
,
, ....,
respectively denote the
coherent cross-power spectrum between bearings 1-2, 2-3, …, (b-1)-b, which was
computed as [128];
(7.3)
The CS [128] computed as per Equation (7.1) contains no phase information,
which therefore limits its analysis to just amplitudes at individual harmonic
components. In practise however, rotating machines often produce several
harmonic components due to faults, and the inter-relations that exist between
these harmonic components are expected to be different for different faults.
Hence, the introduction of CB and CT, which express the relation between few
harmonic components, may become desirable.
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The CB [127] is thus computed as;
(7.4)
Based on the premise that the CT provides information about the inter-relation that
exists between more frequency components, an additional CT component is also
proposed on a similar concept as the CB [127], so as to further understand the
usefulness of data fusion in rotating machine fault diagnosis and resultant machine
vibration behaviour. It is also important to note that the bispectrum [103], [157],
[158], [190], [191] is a representation of the combination of 2 frequencies (each
containing amplitude and phase information), and with a third frequency
which is equivalent to the sum of the initial 2 for a signal. Similarly, the
trispectrum [98], [106], [159], [189], [204] is a representation of the combination of
3 frequencies (each containing amplitude and phase information), , and
with a fourth frequency which is equivalent to the sum of the initial 3
for a signal. Hence, the CT for “b” number of signals can be computed as;
(5)
7.3 Experimental Rig with Different Foundations
The experimental rig with different foundations (FS1 and FS2), i.e. slightly different
support flexibilities have been simulated for this study. In FS1 (Figures 7.2-7.3),
two mild steel shafts (1000mm and 500mm lengths respectively) of 20mm
diameters are rigidly coupled together, while the 1000mm shaft is coupled to an
electric motor through the aid of a flexible coupling. Two mild steel balance discs
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of dimensions 125mm (outside diameter) x 20mm (internal diameter) x 15mm
(thickness) were mounted on the 1000mm shaft at distances of 300mm from the
flexible coupling and 190mm from bearing 2 respectively. A third similarly
dimensioned balance disc was also mounted on the 500mm shaft at an equal
distance of 210mm from both bearings 3 and 4. The entire assembly is however
supported by 4 flange-mounted anti-friction ball bearings.
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Figure 7.2 Photograph of the experimental rig
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Figure 7.3 Schematic of the experimental rig
FS2 is similarly configured as FS1 in terms of machine size, capacity, components
and the respective location of each component. However, both experimental rigs
slightly differ in their support flexibilities (Figure 7.4), owing to the fact that the
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bearings on each rig were mounted with threaded bars of different thicknesses.
FS1 bearings were mounted on 10mm threaded bars, while FS2 bearings were
mounted on 6mm threaded bars (Figure 7.4). In Figure 7.3, components (a)-(m)
respectively represent accelerometer (a), rigid coupling (b), shaft (c), balance disc
(d), bearing flange (e), threaded bar (f), flange mounted anti-friction ball bearing
(g), flexible coupling (h), tachometer (i), electric motor (j), electric motor base
mount (k), lathe bed (l) and neoprene rubber pad (m). Figure 7.3 also shows the
schematic representation of vibration data collection in which the data from
accelerometers are collected into the PC, through the conditioner unit and the
analogue-to-digital device. It is also important to note that the accelerometers were
stud mounted at 45° from both vertical and horizontal directions, so that the
accelerometers can measure the vibration from both directions. Accelerometer
installation is typically shown in Figure 7.4.
Figure 7.4 Different rig supports (a) FS1 (b) FS2
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7.3.1 Modal tests and data analysis
In order to better understand the dynamic characteristics of both experimental rigs,
experimental impulse response [21] method of modal analysis was conducted
using instrumented hammer and accelerometer. Hence, Table 7.1 shows the first
few natural frequencies (by appearance) identified for FS1 and FS2 respectively.
Table 7.1 Experimentally identified natural frequencies for FS1 and FS2
Experimental Set-up Natural Frequencies (Hz)
1st
2nd
3rd
4th
FS1 50.66 56.76 59.2 127.6
FS2 47 55.54 57.98 127
7.4 Experiments
A total of six cases were experimentally simulated on both rigs and at 3 machines
speeds (1200RPM, 1800RPM and 2400RPM). Since it is generally difficult to
achieve a perfect alignment on the rigs, a healthy case associated with some
residual misalignment (HRM) has been considered as a healthy (HRM) reference
case. In addition to the HRM case, 5 other cases, namely; bent shaft (BS), shaft
crack (SC), loose bearing (LB), shaft misalignment (SM) and shaft rub (SR) were
also simulated on both rigs and at all speeds. The BS case was simulated by
creating a 3.4mm centre line run-out on the 1000mm shaft, using a fly press. The
SC case (Figure 7.5(a)) was studied by creating a 4mm (depth) x 0.25mm (width)
breathing crack on the 1000mm shaft at a distance of 160mm from bearing 1,
using the wire electric discharge machining (EDM) process. The LB case (Figure
7.5(b)) was however simulated by loosening some of the threaded bar nuts on
bearing 3. A slight misalignment (using a 0.4mm mild steel shim) in the vertical
direction beneath bearing 1 support block was used to simulate the SM case
(Figure 7.5(c)). Finally, the SR case (Figure 7.5(d)) was simulated by placing 2
Perspex blades (at top and bottom dead centres respectively) at a distance of
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275mm from bearing 1. For the purpose of simplification and clarity, each of the
experimentally simulated cases, the fault locations on the rig and abbreviated
names have been summarised in Table 7.2. Several sets of vibration
measurements were then collected through the aid of 4 (i.e. 1 per bearing)
diagonal stud mounted accelerometers (Figure 7.4) for further signal processing. It
is important to note that for each case (e.g. HRM, FS1, 1800RPM), 20 sets of
measured vibration data were collected.
Figure 7.5 Experimentally simulated cases (a) SC (b) LB (c) SM (d) SR
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Table 7.2 Summary of cases, locations and abbreviations
S/No. Case(s) Fault Location Abbreviation
1 Healthy with some residual misalignment
Possible residual misalignment at couplings HRM
2 Bent shaft Centre of 1000mm shaft BS
3 Shaft crack 160mm from bearing 1 on the 1000mm shaft SC
4 Loose bearing Bearing 3 threaded bar nuts LB
5 Shaft misalignment Bearing 1 support block in vertical direction SM
6 Shaft rub 275mm from bearing 1 on the 1000mm shaft SR
7.5 Data Analysis
A computational code has been developed in MatLab for computing CS, CB and
CT as per Equations (7.1)-(7.5). The 20 sets of measured vibration data for each
of the simulated cases at each machine speed have been analysed using; 95%
overlap, frequency resolution ( ) = 0.6104 Hz, sampling frequency (fs) = 10000
Hz, number of data points (N) = 16384 and 148 number of averages. Figures 7.6,
7.7 and 7.10 show typical CS, CB and CT plots of the measured vibration data for
HRM and LB cases for the rig with FS1 and FS2 at 1200RPM.
7.6 CS Analysis and Observations
In Figure 7.6, the composite spectra (CS) for HRM and LB cases (Table 7.2) for
the rig with FS1 and FS2 at 1200RPM have been used to illustrate the ability of
CS to differentiate between various rotating machine conditions. On both FS1 and
FS2 foundations, the HRM case (Figures 7.6(a)-(b)) were characterised by
prominent 1x components and negligible 3x components (which is due to the
residual misalignment in the case). On the contrary, the LB cases (Figures 7.6(c)-
(d)) for the rig with both foundations (FS1 and FS2) were characterised by 1x
components of significantly larger amplitudes than in the HRM case, plus the
appearance of several higher harmonic components (3x, 4x, 5x, etc.) of notable
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amplitudes. This observation was however consistent for all the cases simulated
on the rig with both foundations and at all speeds.
Figure 7.6 Typical composite spectra at 1200RPM (a) HRM for FS1 (b) HRM for
FS2 (c) LB for FS1 (d) LB for FS2
7.7 CB Analysis and Observations
The composite bispectra (CB) in Figure 7.7 clearly show distinct features for the
HRM and LB cases for both foundations (FS1 and FS2) at 1200RPM, and these
observations were also fairly consistent for all cases at all speeds. The CB plots in
Figure 7.7 are plotted in x, y and z axes, where x and y axes relate to the
frequencies and z represents the amplitude related to the frequency components
in the x and y axes. The amplitude peaks (Table 7.3) are denoted by B11, B12, B13,
etc. For instance, B11 CB component represents the relation between 1x (twice)
and 2x frequency components, while B12=B21 represents the relation between 1x,
2x and 3x frequency components, and so on. Figures 7.7(a)-(b) respectively
denote the HRM case for both foundations, which only contain relatively small B11
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and B12 = B21 CB components, which is again due to the residual misalignment
associated with this case.
Although the LB case for both foundations (Figures 7.7(c)-(d)) also contained B11
and B12 = B21 CB components, their magnitudes were significantly larger than
observed in the HRM case. In addition, the LB case also contained prominent
B13=B31, B33 and B23=B32 CB components peaks. It is important to note that each
of the CB components in Figure 7.7 contains amplitude and phase information.
Also, individual CB components amplitudes and phase have been investigated for
FS1 and FS2 at all measured speeds. Figures 7.8-7.9 show that even the
individual CB components such as B11 (amplitude and phase) provides a
possibility of distinction for all cases.
Figure 7.7 Typical coherent composite bispectra (CB) at 1200RPM (a) HRM for
FS1 (b) HRM for FS2 (c) LB for FS1 (d) LB for FS2
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Table 7.3 CB components for HRM and LB cases (FS1 and FS2) at 1200RPM
CB Components FS1 at 1200 RPM FS2 at 1200 RPM
HRM LB HRM LB
B11 3.78E-03 7.42E-03 1.21E-03 4.67E-03
B12=B21 8.36E-04 2.18E-03 4.29E-04 2.51E-03
B13=B31 - - 7.63E-03 - - 1.07E-02
B23=B32 - - 1.13E-03 - - 9.07E-02
B33 - - 6.44E-04 - - 4.84E-03
Although each case in the CB plots shown in Figure 7.7 appears different with
respect to the amplitudes of each component (Table 7.3), however, diagnosis may
not be straightforward based on visual inspection. Hence it is good to compare
either different CB components or both amplitude and phase for a particular
component for each case. Amplitude and phase for a number of CB components
are analyzed to understand their usefulness in fault diagnosis. Figures 7.8-7.9
show typical amplitude and phase plots for B11 and B12 for all the 20 sets of data
collected for each case (i.e. a total of 120 sets of data at each machine speed for
each foundation), at all machine speeds with both foundations. It is obvious from
the figures that each of the cases appears in different regions (separated from
each other). Hence, a combination of the amplitude and phase of a single CB
component also offers appreciable fault diagnosis potentials.
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Figure 7.8 Typical B11 CB component magnitude and phase (a) FS1 (1200RPM)
(b) FS2 (1200RPM) (c) FS1 (1800RPM) (d) FS2 (1800RPM) (e) FS1 (2400RPM)
(f) FS2 (2400RPM)
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Figure 7.9 Typical B12 CB component magnitude and phase (a) FS1 (1200RPM)
(b) FS2 (1200RPM) (c) FS1 (1800RPM) (d) FS2 (1800RPM) (e) FS1 (2400RPM)
(f) FS2 (2400RPM)
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7.8 CT Analysis and Observations
The composite trispectra (CT) in Figure 7.10 clearly display different features for
the HRM and LB cases for both foundations. Unlike the CB, each CT component
(containing amplitude and phase information) is a function of 3 frequencies
(plotted in x, y and z axes), usually represented by spheres [98]. The appearance
of each sphere at a particular location generally represents the relation between
the frequencies at that particular location, while the sizes of the spheres represent
the amplitudes related to the frequency components in the x, y and z axes. The CT
components are generally denoted by T111, T112=T121=T211, T113=T131=T311, etc.
T111 signifies the relation between 1x (thrice) and 3x frequency components; while
T112=T121=T211 signifies the relation between 1x (twice), 2x and 4x frequency
components; and so on. The HRM cases for both foundations (Figures 7.10(a)-(b))
only contain T111 CT component probably due to some residual misalignment. The
LB cases for both FS1 and FS2 (Figures 7.10(c)-(d)) were characterized by T111
(which was significantly larger than in the HRM cases) and T113=T131=T311 CT
components.
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Figure 7.10 Typical coherent composite trispectra (CT) at 1200RPM (a) HRM for
FS1 (b) HRM for FS2 (c) LB for FS1 (d) LB for FS2
Table 7.4 CT components for HRM and LB cases (FS1 and FS2) at 1200RPM
Case(s) FS1 at 1200 RPM FS2 at 1200 RPM
T111 T113=T131=T311 T111 T113=T131=T311
HRM 2.44E-03 - - 4.47E-04 - -
LB 1.29E-02 6.67E-03 8.09E-03 3.01E-03
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Although, the CT plots for both FS1 and FS2 appear similar in components;
however, the components differ in amplitudes as can be clearly seen from Table
7.4. Similarly, a combination of several CT components’ amplitudes and phase for
the 20 sets of data collected for each case (i.e. a total of 120 sets of data at each
machine speed for each foundation) at all machine speeds with both foundations
was also investigated for further fault diagnosis. It can be observed from Figures
7.11-7.12 that the combination of amplitudes and phase of CT components such
as T111 and T112 offered good distinction between the different cases for all
foundation flexibilities and at all machine speeds considered.
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Figure 7.11 Typical T111 CT component magnitude and phase (a) FS1 (1200RPM)
(b) FS2 (1200RPM) (c) FS1 (1800RPM) (d) FS2 (1800RPM) (e) FS1 (2400RPM)
(f) FS2 (2400RPM)
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Figure 7.12 Typical T112 CT component magnitude and phase (a) FS1 (1200RPM)
(b) FS2 (1200RPM) (c) FS1 (1800RPM) (d) FS2 (1800RPM) (e) FS1 (2400RPM)
(f) FS2 (2400RPM)
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7.9 Combined Diagnostic Features
Although individual CB and CT components such as B11 and T111 provided
appreciable separation between the different cases, however, the combinations of
several CB and CT components amplitudes and phase has also been investigated
for further enhancement of the fault diagnosis. Many combinations provided very
good separations at all measured speeds for the different foundations. Typically,
just a combination of B11 and T111 CB and CT components amplitudes shown in
Figure 7.13 was observed to provide the required result for all cases at all speeds,
which significantly reduces the computational load that may be associated with the
use of higher harmonic components.
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Figure 7.13 Typical combined magnitudes of B11 CB and T111 CT components
(a) FS1 (1200RPM) (b) FS2 (1200RPM) (c) FS1 (1800RPM) (d) FS2 (1800RPM)
(e) FS1 (2400RPM) (f) FS2 (2400RPM)
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7.9.1 Sensitivity analysis
The sensitivity of the proposed technique to various scenarios (Table 7.5) of signal
processing parameters was also examined, so as to further ascertain the
robustness of the technique. Hence, using the typical plots of combined CB (B11)
and CT (T111) components’ magnitudes for FS2 foundation at 1200 RPM shown in
Figure 7.14 for illustration, it was observed that variations in signal processing
parameters had insignificant effects on the earlier separation of the different faults
shown in Figure 7.13. It is also important to note that the measured vibration data
are generally contaminated by noise, which is often the case with most real life
vibration data recorded from rotating machines. Hence, the proposed method
seems to be robust and reliable, even with measurement noise and changing
signal processing parameters.
Table 7.5 Different scenarios of signal processing parameters
Signal Processing Parameters
Scenarios
1 2 3 4
Number of data points (N) 8192 8192 16384 16384
Frequency Resolution (df), Hz 1.2207 1.2207 0.6104 0.6104
Number of averages 220 220 11 11
Segments Overlap 98% 98% 85% 85%
Window None Hanning None Hanning
Sampling Frequency (fs), Hz 10000
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Figure 7.14 Typical combined magnitudes of B11 CB and T111 CT components at
1200RPM for FS2 foundation (a) scenario 1 (b) scenario 2 (c) scenario (d)
scenario 4
7.9.2 Practical application
The proposed method clearly indicates the separation of other faults from the
healthy condition. Hence, the emergence of any faulty condition in a typical
rotating machine will definitely trigger the classification of such a machine as one
with fault. Also, once the historical data describing the operations of typical rotating
machines are available for reference, then onward classification of the machines
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when faults emerge becomes possible. However, it is important to note that the
task of accurately differentiating a faulty machine from a healthy one in itself is
vital for fault diagnosis, especially considering the complexities often associated
with the fault diagnosis process of rotating machines with multiple bearings, for
instance, steam turbo generator sets. Hence, the proposed method of data fusion
for computing a single CB and CT from all bearings data simplifies the fault
diagnosis process.
7.10 Summary
The paper introduces the concept of CT for fault diagnosis in combination with the
earlier CB. It is experimentally observed that the combination of a single CB and
CT component provides a much better separation and diagnosis for each fault.
The proposed method is tested on a rig with 2 different flexible foundations (FS1
and FS2). Hence, the potentials of the method to diagnose different faults
associated with ‘as installed’ rotating machines with different foundation flexibilities
and operating at different speeds was clearly highlighted, which is a very vital
consideration for a significant number of plants. It is planned to apply the proposed
method to different experimental rigs with different foundations and possibly on
industrial rotating machines with different foundations, so as to further enhance the
confidence level of the proposed diagnosis method. Also, further analysis on the
sensitivity of the proposed technique to different faults severities are scheduled for
future studies.
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8 Chapter 8 AN IMPROVED DATA FUSION
TECHNIQUE FOR FAULTS DIAGNOSIS OF ROTATING MACHINES
----------------------------------------------------------------------------------------------
Reformatted version of the following paper:
Paper title: An improved data fusion technique for faults diagnosis of rotating
machines
Authors: A. Yunusa-Kaltungo, J.K. Sinha and K. Elbhbah
Published in: Measurement 58 (2014) 27-32
Abstract
The composite spectrum (CS) data fusion technique has been shown to simplify
rotating machine fault diagnosis by earlier studies. Fault diagnosis with the earlier
CS relied solely on the amplitudes of several harmonics of the machine speed,
owing to the loss of phase information leading to its computation. The proposed
improved CS applies the concept of cross power spectrum density for computing a
poly-Coherent Composite Spectrum (pCCS) of a machine, which retains amplitude
and phase information at all measurement locations. The present study compares
the proposed pCCS method with the earlier CS method for faults diagnosis in
rotating machines, using experimental data from a rotating rig. Results and
observations show that the proposed pCCS offered a much better representation
of the machine dynamics when compared to the earlier CS method and hence
better fault diagnosis.
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Key words Vibration-based condition monitoring, rotating machine, fault
diagnosis, data fusion, composite spectrum, poly-Coherent Composite Spectrum
8.1 Introduction
Measured vibration data at individual bearing pedestals of a rotating machine have
been successfully analysed with several vibration-based condition monitoring
(VCM) techniques such as; spectrum analysis [55], higher order spectra analysis
[98], [106], [159], [189], [190], [204], [206], wavelet analysis [207]–[213], artificial
intelligence-based diagnosis [214]–[219], model-based identification [197], etc.
However, large and complex rotating machines with multi-shafts are often
associated with numerous bearings, which imply that several vibration data
measured from each bearing location, will have to be separately analysed during
fault diagnosis. Therefore, the development of a VCM technique that will
significantly simplify the fault diagnosis process in rotating machines is highly
desirable. Earlier studies by Elbhbah and Sinha [128] proposed the use of reduced
sensors (i.e. a single accelerometer per bearing pedestal) for vibration
measurements in rotating machines. The study [128] also proposed the use of a
single composite spectrum (CS) for the representation of the entire machine
dynamics, which offered some useful fault diagnosis features in rotating machines.
In the earlier CS technique however [128], the concept of cross power spectral
density (CSD) [146] was used for fusing the vibration data measured at all bearing
pedestals, which did not utilize phase information from the measured vibration
data at the different measurement locations.
The current study however proposes the use of a poly-Coherent Composite
Spectrum (pCCS) of a machine, which is also based on the concept of CSD, but
has been extended to involve a number of signals. Hence, amplitude and phase
information are retained for all measured vibration data, which is further explained
in Sections 8.2 and 8.3. The computational approaches and observations from
both techniques are hereby discussed in this paper. Furthermore, the present
study compares the proposed pCCS method with the earlier CS method for fault
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diagnosis in rotating machines, using experimental data from a rotating rig.
Results and observations indicate that the proposed pCCS offered a much better
representation of the machine’s dynamics when compared to the earlier CS
method and hence better fault diagnosis.
8.2 Earlier Composite Spectrum
Assuming that vibration measurements were collected from “b” number of bearing
locations of a rotating machine, and the measured data have been divided into a
number of equal segments (ns), then the CS for the entire machine was computed
as [128];
(8.1)
where and
respectively denote the coherent composite Fourier
Transformation (FT) and its complex conjugate for the rth segment of the
measured time domain vibration data from “b” bearing locations at frequency, .
was thus computed as [128];
(8.2)
where
and
respectively denote the coherence [156] between
bearings1-2, 2-3, …, (b-1)-b (where b = 1, 2, ..., b). Also,
.....
respectively denote the coherent cross-power spectrum
between bearings 1-2, 2-3, …, (b-1)-b, which was computed as [128];
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(8.3)
It can be clearly seen from Equations (8.2)-(8.3) that all the phase information at
the intermediate measurement locations will be lost due to the CSD approach
adopted for the data fusion. For example, the multiplication of the FT of the rth
segment of the measured time domain vibration data at frequency at bearing 2
(i.e. ) in the second term (
) of Equation (8.2) by its complex
conjugate (i.e.
) in the first term (
) of the same equation
automatically produces a real number, thereby signifying a loss of phase
information between the two measurement locations (i.e. bearings 2 and 3) and so
on. Similarly, Equation (8.1) shows that the final CS has lost all of its phase
information, due to the multiplication of the coherent composite FT by its complex
conjugate.
8.3 Proposed poly-Coherent Composite Spectrum (pCCS)
It has been clearly shown in Section 8.2 that all phase information at the
intermediate vibration measurement locations is lost during the computation of CS
using the earlier method. Therefore, an improved CS that provides a better
representation of the entire machine dynamics is required. Hence, the improved
CS is defined as;
=
(8.4)
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where, ,
, ,
, ...., and
respectively denote
the FT of the rth segment at frequency of the time domain vibration data at
bearings 1, 2, 3, 4, ...., (b-1) and b. Similarly, ,
, , ....,
respectively
denote the coherence between bearings 1-2, 2-3, 3-4, …, (b-1)-b, while
is the poly-Coherent Composite Spectrum (pCCS) at frequency, . The
computation of the proposed pCCS shown in Equation (8.4) is also based on the
concept of CSD. However, it has been extended to a number of signals instead of
just 2 signals used in CSD, so that amplitude and phase information of signals are
retained for better representation of the machine dynamics.
8.4 Experiments and Observations
As conducted in the earlier study [128], 4 different conditions (healthy,
misalignment, crack and rub) were simulated at 2 separate speeds (2040RPM and
3000RPM) on an experimental rig (Figure 8.1). The healthy case contained some
residual unbalance and possibly little misalignment. A 2mm misalignment (in both
vertical and horizontal directions) was introduced near bearing 1 for the
misalignment case. In the crack case, a crack of 0.25mm (width) by 4mm (depth),
with a 0.22mm steel shim insert was used to simulate a shaft with a breathing
crack. A Perspex sheet with a 21mm hole was used to simulate shaft rub near
bearing 1. The rig consists of 2 rigidly coupled shafts (1000m and 500m lengths)
of similar diameter (20mm). The 1000mm shaft is flexibly connected to an electric
motor, while the entire shaft assembly is supported by 4 anti-friction ball bearings
as shown in Figure 8.1 [128].
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Figure 8.1 Photograph of experimental rig [128]
Vibration data were collected from all bearing pedestals for all the experimentally
simulated cases (healthy, misalignment, crack and rub) at both speeds (2040RPM
and 3000RPM). Hence, the averaged spectra for all cases have been computed
using a sampling frequency (fs ) = 5000Hz, number of data points (N) = 8192,
frequency resolution ( ) = 0.6104Hz, 80% overlap with Hanning window and 146
number of averages. Figures 8.2-8.3 respectively show typical pCCS and phase
plots for 2 cases (healthy and crack), at 2040RPM and 3000RPM. The healthy
cases at both machine speeds (Figures 8.2(a) & 8.3(a)) show no visible peaks,
while the crack cases (Figures 8.2(c) & 8.3(c)) are characterized by conspicuous
peaks at several harmonics (e.g. 1x, 2x, 4x, etc.). Similarly, the phase plots
(Figures 8.2(b), 8.2(d), 8.3(b) & 8.3(d)) are different for each of the experimentally
simulated cases at both machine speeds.
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Figure 8.2 Typical pCCS and phase plots at 2040RPM (a)-(b) Healthy and (c)-(d)
crack
Figure 8.3 Typical pCCS and phase plots at 3000RPM (a)-(b) Healthy and (c)-(d)
crack
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8.4.1 Diagnosis features
The pCCS amplitudes and phases of several vibration measurements for each of
the experimentally simulated cases at both machine speeds have been computed.
Figures 8.4-8.5 show a combination of the amplitude and phase of the first 2
harmonics (i.e. 1x and 2x) of the machine speed, where it can been seen that
there is a clear separation between each of the experimentally simulated cases, at
both 2040RPM and 3000RPM speeds.
Figure 8.4 Typical 1x and 2x pCCS amplitudes and phases for all four cases at
2040RPM
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Figure 8.5 Typical 1x and 2x pCCS amplitudes and phases for all four cases at
3000RPM
8.5 Diagnosis with Earlier Composite Spectrum Method
Although the earlier method of CS [128] provided some meaningful diagnosis
features, however, its lack of phase information leads to a strong reliance on the
amplitudes at the different harmonics during fault diagnosis. Hence, fault diagnosis
with the earlier data fusion method of the CS could entail the use of several
harmonic amplitudes as can be seen from Figures 8.6-8.7.
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Figure 8.6 Typical normalised CS amplitudes for all four cases at 2040RPM
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Figure 8.7 Typical normalised CS amplitudes for all four cases at 3000RPM
8.6 Summary
The poly-Coherent Composite Spectrum (pCCS) has now been defined, which is
an improved version of the earlier composite spectrum (CS) data fusion. In the
present pCCS, a combined information of amplitude and phase from all
measurement locations is achieved, which is expected to provide a more accurate
representation of the entire machine dynamics. The proposed method has also
been applied for fault diagnosis on an experimental rig, where it was observed that
the amplitude and phase information of pCCS at the operating speed or any
harmonic can provide a much better diagnosis, when compared to the earlier
method (which relied on several harmonics of the machine speed for fault
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diagnosis). Future fault diagnosis using pCCS is planned on different rotating
machines with more faults.
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9 Chapter 9 A NOVEL FAULTS DIAGNOSIS
TECHNIQUE FOR ENHANCING MAINTENANCE AND RELIABILITY OF
ROTATING MACHINES ----------------------------------------------------------------------------------------------
Reformatted version of the following paper:
Paper title: A novel faults diagnosis technique for enhancing maintenance
and reliability of rotating machines
Authors: A. Yunusa-Kaltungo, J.K. Sinha and A.D. Nembhard
Submitted to: Structural Health Monitoring Journal (in press)
Abstract
Equipment standardisation as a cost-effective means of rationalising maintenance
spares has significantly increased the existence of several identical (similar
components and configurations) ‘as installed’ machines in most industrial sites.
However, the dynamic behaviours of such identical machines usually differ due to
variations in their foundation flexibilities, which is perhaps why separate analysis is
often required for each machine during fault diagnosis. In practise, the fault
diagnosis process is even further complicated by the fact that analysis is often
conducted at individual measurement locations for the different speeds, since a
significant number of rotating machines operate at various speeds. Hence, through
the experimental simulation of a similar practical scenario of 2 identically
configured ‘as installed’ rotating machines with different foundation flexibilities, the
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present study proposes a simplified vibration-based fault diagnosis (FD) technique
that may be valuable for fault detection irrespective of foundation flexibilities or
operating speeds. On both experimental rigs with different foundation flexibilities,
several common rotor-related faults were independently simulated. Data
combination method was then used for computing composite higher order spectra
(composite bispectrum and composite trispectrum), after which principal
component analysis is used for fault separation and diagnosis of the grouped data.
Hence, the current paper highlights the usefulness of the proposed FD approach
for enhancing the reliability of identical ‘as installed’ rotating machines, irrespective
of the rotating speeds and foundation flexibilities.
Key words Reliability, condition based maintenance, data fusion, composite
spectra, principal component analysis, multiple speeds, multiple foundations
9.1 Introduction
Faults always occur in rotating machines due to the vast and severe conditions
under which they operate across several industries. The lack of early detection of
such faults often leads to depleted machine reliability, which could have
catastrophic consequences on the safety and profitability of any organisation
[187]. A maintenance activity (which has evolved over time) has always been
applied for the detection and elimination of these faults. Maintenance can be
described as the combination as well as synchronisation of all technical,
administrative and managerial tasks directed towards ensuring that a machine
adequately performs the functions for which it was acquired [220]–[222]. Initially,
maintenance interventions (mainly repair and replace) are only conducted to
restore already failed machines back to operating condition. This type of
maintenance strategy ultimately required huge investments in spares,
incorporation of high levels of redundancies in plant designs, and a significantly
large maintenance team. The capital intensiveness and high equipment failure
levels associated with breakdown maintenance (BM) triggered the shift towards a
periodic or planned preventive maintenance (PPM) philosophy that entailed the
repair of machines over a predefined time period, irrespective of machines’
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conditions. Although the planned preventive maintenance approach significantly
reduced plant interruptions, however, the cost associated with this practise was
also high. Based on this premise, maintenance experts have continuously sorted
after a more effective maintenance philosophy that will only be triggered by the
presence of symptomatic changes in a machine’s operating conditions due to
faults, such as condition-based maintenance (CBM).
In an adequately implemented and managed CBM system, the decision to repair
or replace a machine is often guided by the results obtained from the analysis of
measured machine operations data (e.g. vibration, temperature, sound, etc.). The
reviews by Jardine et al. [19], Lee et al. [90], Heng et al. [223] and Lee et al. [200]
offered extensive details and trends of commonly applied CBM diagnostic and
prognostic techniques for machines. In these reviews [19], [90], [200], [223], it was
also highlighted that vibration-based fault diagnosis (VFD) techniques [224]–[228]
are amongst the most popular, owing to the fact that different components in a
machine assembly often exhibit peculiar vibration characteristics due to faults.
Machinery vibration signals have been processed using time [25], [229], frequency
or time-frequency [29], [230] domain techniques. The frequency domain signal
analysis, based on Fourier transformation (FT) is one of the most conventionally
applied VFD signal processing techniques in practise, since it provides the
opportunity to easily identify frequency components of interest [19]. Some of the
frequency domain vibration signal processing techniques used for fault diagnosis
in rotating machines include power spectrum [55], higher order spectra [98], [106],
[159], [189], [190], [204], holospectrum [231], cepstrum [232], composite spectrum
[128], composite bispectrum [127], etc.
Despite the maturity of spectrum-based techniques, the quest for more profound
understanding of the dynamic characteristics of vibrating systems has led to the
application of model-based approaches [233] for rotating machines’ fault
diagnosis. These model-based approaches [233] usually involve the development
and application of explicit mathematical models for simulating the behaviour of an
‘as installed’ machine. The emergence of very powerful computers has
significantly reduced the complexity and time required to perform model-based
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fault diagnosis. Such technological advancements have also enhanced the ease
with which researchers can reliably analyse and predict future behaviours of
vibrating systems. Kerschen et al. [234] provided extensive reviews on model-
based analysis of vibrating systems. Other researchers have also applied model-
based approaches for analysing rotating machine faults such as unbalance and
misalignment [32], rotor crack [66], [198], [235], etc. Although model-based
analysis can offer more descriptive results if a precise model is built, however, it is
sometimes near impossible to achieve the required precision when dealing with
very complex structures [19].
In order to reduce dependence on human interference and experience, some
researchers have adopted artificial intelligence (AI) techniques such as artificial
neural networks (ANN) [77]–[84], support vector machine (SVM) [86], [87], [236]–
[238], and fuzzy logic [239]. ANN is basically a computational model that contains
simple processing elements that are linked via a complex layer structure, thereby
imitating the formation of the human brain [19]. A comprehensive review on more
than a decade-long applicability of artificial neural networks in the industry was
compiled by Meireless et al. [77]. Other studies have also shown the capabilities of
ANN in classifying rotating machine conditions [78], detection of rotor loading
conditions [79], gear faults identification [80]–[82], fan blade faults detection [83]
as well as diagnosis of rolling element bearing faults [84]. Although AI-based
techniques possess the potentials to automate VFD processes, however, studies
[19], [223] have also highlighted the difficulties associated with providing physical
interpretations of the trained model as well as the complexity of the training
process. SVM is another popularly used AI-based technique that has proven
capable of providing accurate decision results in some cases, mainly due to its
augmented decision boundary and real time analysis capability [86], [87]. Although
SVM has been used to detect faults related to rotors [236], bearings [237], gears
[80], pump valves [238], etc., however, studies [90] have also shown that there is
still a lack of standard technique for selecting its key process (i.e. Kernel process)
function. Other efforts aimed at further simplifying rotating machine fault diagnosis
using pattern recognition tools such as principal components analysis (PCA) has
also been explored by some researchers [93]. The application of PCA for fault
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diagnosis is particularly strengthened by its ability to compress large multi-
dimensional input data sets into lower dimensional but representative data sets
[90]. Nembhard et al. [240] recently applied PCA for detecting and classifying
rotor-related faults such as misalignment, crack and shaft rub. In this study [240],
the combination of measured vibration and temperature features was explored.
PCA has also been used for identifying faults related to rolling element bearings
[95], [241] and gears [91], [94], [96].
As valuable and significant as the contributions from these earlier studies are, they
have been predominantly used to diagnose faults associated with rotating
machines on single foundations and at single machine speeds. In practice
however, 2 or more identical (similar components and configurations) rotating
machines installed at different plant locations may exhibit different dynamic
characteristics, due to variations in their foundation flexibilities. These differences
in dynamic characteristics often require that separate analysis is conducted for
each machine at the different operating speeds, which may complicate the fault
diagnosis process. Hence, the development of a unified VFD technique that will be
capable of detecting and differentiating rotating machine faults, irrespective of
foundation flexibility and machine speed is highly desirable. In the present study,
the earlier [127], [128] and improved [242] composite higher order spectra (i.e.
composite bispectrum and composite trispectrum) data combination (in the
frequency domain) techniques have been respectively used to compute fault
diagnosis features for 2 identical flexibly supported rotating machines, operating
under different faults and speeds. Through the application of a PCA-based fault
diagnosis algorithm, a unified fault diagnosis technique capable of fault detection
and classification, irrespective of machine speed or foundation is proposed. The
proposed technique is expected to reduce the complexity and subjectivity
associated with fault diagnosis at individual machine speed and foundation, which
is often characterised by the appearance of several features. The study also
compares the results of the diagnosis features computed using the earlier and
improved composite higher order spectra approaches. Hence, detailed
descriptions of the composite spectra computations, experimental rigs, vibration
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experiments with different faults, signal processing and the results of the proposed
unified PCA-based fault diagnosis technique are presented here.
9.2 Composite Spectra Computations
The computational approaches for the composite spectra based on both the earlier
[127], [128] and the proposed improved [242] methods are also described here.
9.2.1 Earlier method
The earlier proposed method for computing the composite spectrum (CS) of a
rotating machine from which vibration measurements were collected from “b”
number of bearing locations is [128];
(9.1)
where and
are respectively the coherent composite Fourier
Transformation (FT) and its complex conjugate for the rth segment of the
measured vibration data from “b” bearing locations at frequency, . ns represents
the number of equal segments used for FT computation. Hence, is thus
computed as [128];
(9.2)
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In Equation (9.2),
, ...,
respectively denote the coherence [156]
between bearings1-2, 2-3, …, (b-1)-b (where b = 1, 2, ..., b). Also,
.....
respectively denote the coherent cross-power
spectrum between bearings 1-2, 2-3, …, (b-1)-b, which was computed as [128];
(9.3)
where q = 1, 2, ..., (b-1).
It is evident from Equations (9.2)-(9.3) that in the earlier method of CS
computation, all the phase information at the intermediate measurement locations
will be lost. This is due to the cross power spectrum density (CSD) approach
adopted for the earlier data combination process.
The composite bispectrum (CB) is computed as [127], [243], [244];
(9.4)
Through the application of a similar computational concept as the CB [127], the
composite trispectrum (CT) [243], [244] can be computed as;
(9.5)
Where each bispectrum [157], [158], [191] component represents the combination
of 2 frequencies (with each possessing amplitude and phase information), and
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with a third frequency which equals the sum of the first 2 for a signal.
Also, each trispectrum [98], [106], [159], [189], [190], [204] component represents
the combination of 3 frequencies (with each possessing amplitude and phase
information), , and with a fourth frequency that equals the sum
of the first 3 for a signal. It is also vital to note that if the frequencies , and
are equivalent to the th, th and th harmonics of the vibration response at the
rotor RPM (1x), then the CB and CT components defined in Equations (9.4)-(9.5)
can also be referred to as and .
9.2.2 Improved method
The improved CS is also based on CSD, but has been extended to several signals
(instead of just 2 signals applied in the earlier method), called the poly-Coherent
Composite Spectrum (pCCS). Unlike the earlier method of data combination
described in Section 9.2.1, the improved computational approach (i.e. pCCS)
retains both amplitude and phase information. It is therefore anticipated that this
feature (amplitude and phase) retention capability of pCCS will lead to better
representation of the entire machine dynamics. Hence, the improved CS is defined
as [242];
(9.6)
where, ,
, ,
, ...., and
respectively denote
the FT of the rth segment at frequency of the vibration responses at bearings 1,
2, 3, 4, ...., (b-1) and b. Similarly, ,
, , ....,
respectively denote the
coherence [156] between bearings 1-2, 2-3, 3-4, …, (b-1)-b. is the poly-
Coherent Composite Spectrum (pCCS) at frequency, .
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The CB and CT have also been introduced based on the improved CS [242], and
are respectively defined as;
(9.7)
(9.8)
In Equations (9.7)-(9.8), is the poly Coherent Composite Fourier
Transformation (FT) for the rth segment of the measured vibration data from “b”
bearing locations at frequency, , which was computed as [242];
(9.9)
9.3 Proposed Fault Diagnosis Method
The large number of data usually generated from the computation of CB and CT
sometimes makes visual diagnosis very difficult and subjective. The analysis
becomes even more complicated when dealing with multiple identical (similar
components and configurations) rotating machines with slightly different dynamic
characteristics (due to variations in their foundation flexibilities) and operating at
different speeds. This perhaps explains why some researchers have explored
other avenues for simplifying rotating machines FD, through the application of
pattern classification tools such as PCA. As previously highlighted in Section 9.1,
PCA [240] is a well-known statistical analysis technique, capable of significantly
reducing the dimensionality associated with originally measured data sets through
the definition of new variables, often referred to as the principal components
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(PCs). The first few of the computed PCs usually offer the maximum
representation of the variability that exists in the originally measured data [91].
Similarly, the current study proposes a simplified and unified PCA-based FD
technique, that will be capable of identifying changes in the operating conditions of
several identical ‘as installed’ rotating machines, irrespective of the variations in
their foundation flexibilities and/or operating speeds. Hence, the proposed PCA-
based FD technique could eliminate the need for conducting individual analysis
(which is often the case in practise) for several identical ‘as installed’ rotating
machines with different foundation flexibilities and speeds. Figure 9.1 provides a
flowchart that illustrates the different steps of the proposed FD technique. The
concept of PCA is briefly discussed in Section 9.3.1, while Section 9.3.2 provides
details of the computational approach for the proposed FD technique.
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Figure 9.1 Proposed faults diagnosis process flow chart
9.3.1 Concept of PCA
PCA is a multivariate statistical analysis technique that is capable of reducing
large interrelated data sets to smaller numbers of variables, without necessarily
compromising the variance that exists in the original data set. The fundamental
concept of PCA revolves around the projection of data sets onto a subspace of
lower dimensionality [91]. PCA explains the variance that exists within an original
data matrix that is characterised by n1 observations (e.g. number of vibration
measurements recorded from a typical rotating machine as part of continuous
condition monitoring activities) and n2 variables (e.g. CB and CT fault diagnosis
components) in terms of an entirely new set of variables, the PCs.
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The concept of PCA has existed for decades, with the initial proposal of the
technique dating back to 1933 by Hotelling [245], where it was used for analysing
problems related to the statistical dependency between variables in multivariate
statistical data obtained from examination scores [91], [245]. From then onwards,
the relevance and applications of PCA has significantly grown across various
disciplines including process monitoring, statistical analysis and faults diagnosis
[91], [245]–[248]. Kresta et al. [249] provides a comprehensive introduction as well
as a review of the applications of PCA in process systems engineering, while the
studies by Morison [250] and Jackson [245] respectively offered information on the
complete treatment of the PCA algorithm. Hence, for the purpose of this study, it
suffices to just highlight that PCA was performed and the original data set is
eventually expressed as a linear combination of orthogonal vectors along the
directions of the PCs.
Let’s consider that n1 number of independent samples (also referred to as
observations) of n2 random variables (also referred to as features) which can be
represented by an n1 x n2 matrix, F. The computation of the PCs of F reduces to
the solution of an eigenvalue-eigenvector problem [91], [92],
(9.10)
In Equation (9.10), is the covariance matrix of F. A is the orthogonal matrix
whose mth column is equivalent to the mth eigenvector of corresponding to the
mth largest eigenvalue of . is a diagonal matrix, whose mth diagonal element is
the mth largest eigenvalue of . In general, as many as n2 PCs can be computed.
However, it is expected that the vast majority of variation in F will be accounted for
by t PCs, where .
In the current study, PCA is applied for examining the relationship between
several experimentally simulated rotating machine conditions. The features used
are comprised of computed vibration-based condition monitoring indicators for
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rotating machines under different states of health. Diagnosis through the
application of many condition monitoring (CM) features can be complex and
tedious. Hence, for implementing a simplified diagnosis approach, reduction in
data dimensionality while retaining correlation among them becomes useful.
Therefore PCA is used to achieve this objective.
9.3.2 Computational approach of the proposed FD technique
Assuming that vibration data were collected from a rotating machine at various
speeds, then the PCA feature matrix F related to Equation (9.10) can be
mathematically expressed as;
(9.11)
F is a feature matrix including feature matrices at different speeds, ,
, ..., ,
where , ,....., are the different rotor speeds in RPM.
Let’s now consider a typical rotating machine, from which sets of vibration data
were separately collected under a number of different operating conditions, say “r”
and at a particular rotor speed, . Then the feature matrix can be similarly
defined as;
(9.12)
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where ,
,....., are matrices for each of the experimentally simulated
cases, , , ..., at rotor speed .
If “p” number of vibration data sets were collected from a rotating machine under a
particular machine operating condition (case), , and at a particular rotor speed
. Then, the feature matrix is computed as;
(9.13)
where X1, X2, X3, ...., Xq are individual features for “p” number of observations
under a particular machine operating condition (case) and at a rotor speed .
To further enhance clarity of the PCA feature matrix shown in Equation (9.13),
consider that , , and respectively represent CB and CT
components that have been computed using Equations (9.7)-(9.8) for a particular
machine operating condition ( ), for “p” number of measured data sets at rotor
speed . Hence, the PCA feature matrix can be similarly written as;
(9.14)
Now, let’s further assume that fault diagnosis is to be conducted on a particular
rotating machine with “B” number of flexible support (FS) at rotor speeds , then
Equation (9.12) can be modified thus;
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(9.15)
Hence, if the vibration data were then collected at several machine speeds ( , ,
..., ) for the same rotating machine with “B” flexible foundation (FS), then;
(9.16)
Finally, if several identical rotating machines with different flexible foundations ,
, ..., exists, and vibration measurements were conducted on each of them at
rotor speeds , ,....., . Then the multiple speeds and multiple foundations
PCA feature matrix can be written as;
(9.17)
Once matrix F in Equation (9.11) is constructed, then PCA is carried out as
described in Section 9.3.1.
9.4 Experimental Example
It is often noticed in practice that the dynamic characteristics of “as installed”
identical rotating machines in different locations may slightly vary, owing to
differences in the flexibilities of their foundations. Hence, the current study
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attempts to experimentally simulate a similar example, through the aid of 2 rotating
rigs with identical components and configurations (Figure 9.2), but differ in
foundations (FS1 and FS2). FS1 bearings are mounted with 10mm thick bright
mild steel threaded bars, while FS2 bearings are mounted using 6mm thick bright
mild steel threaded bars (Figure 9.3). A full description of the experimental rig and
faults simulation is provided in Section 9.4.1.
Figure 9.2 Experimental rig
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Figure 9.3 Different rig supports (a) FS1 (b) FS2
9.4.1 Rig and faults simulation
Since both experimental rigs (FS1 and FS2) [244] are identical, only FS1 is
illustrated here (Figure 9.2). In FS1, two 20mm diameter mild steel shafts of
lengths 1000mm and 500mm respectively are rigidly coupled together, while the
1000mm shaft is flexibly coupled to an electric motor. 3 mild steel balance discs of
dimensions 125mm (external diameter) x 20mm (internal diameter) x 15mm
(thickness) were evenly mounted across the entire length of the rig. 2 balance
discs were mounted on the long shaft at 300mm from the flexible coupling and
190mm from bearing 2 respectively. The third balance disc was then mounted on
the short shaft at an equal distance of 210mm from both bearings 3 and 4. The
complete assembly (rotor, balance discs, couplings, etc.) is supported by 4 flange-
mounted anti-friction ball bearings.
A total of 6 cases were experimentally simulated on both FS1 and FS2, at 3
machine speeds (1200RPM, 1800RPM and 2400RPM). The reference case is a
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healthy case that is associated with some residual misalignment (HRM), as it was
very difficult to obtain a perfectly aligned rig. In addition to the HRM case, bent
shaft (BS), shaft crack (SC), loose bearing (LB), shaft misalignment (SM) and
shaft rub (SR) cases were also simulated on both rigs at all the considered
machine speeds. The BS case was simulated by using a fly press to create an
axial run-out of 3.4mm at the centre of the 1000mm shaft. To study the SC case
(Figure 9.4(a)), a crack of 4mm (depth) and 0.25mm (width) was created on the
1000mm shaft using the wire electric discharge machining (EDM) process. As it
was very unlikely for the created crack to breath, a 0.23mm mild steel shim was
inserted in the crack to cause breathing. The LB case (Figure 9.4(b)) was
simulated by loosening the threaded bar fixation nuts on bearing 3. A slight
misalignment of 0.4mm in the vertical direction near bearing 1 was used to
simulate the SM case (Figure 9.4(c)). For the SR case (Figure 9.4(d)), 2 Perspex
blades (i.e. 1 at the top and the other at the bottom of the 1000mm shaft
respectively) were mounted at a distance of 275mm from bearing 1.
On both FS1 and FS2 rigs, vibration data were measured under 36 scenarios (i.e.
18 scenarios of 6 cases at 3 speeds each for FS1 and FS2 respectively), where
each scenario corresponds to specific rig/case/speed combinations (e.g.
FS1/HRM/1200RPM). In order to enhance understanding, details of all the
considered scenarios are provided in Table 9.2. Furthermore, 20 sets of measured
vibration data (a total of 120 sets of measured vibration data per experimental rig)
were collected through the aid of 4 diagonally mounted PCB accelerometers (1 at
each bearing location) for further processing through a computational code
developed in MATLAB.
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Figure 9.4 Experimentally simulated cases (a) SC (b) LB (c) SM (d) SR
9.4.2 Experimental modal analysis
Experimental modal analysis is a widely accepted technique for design
improvements and useful life enhancement of ‘as installed’ rotating machines and
structures [145], [146]. The knowledge of the modal properties of a machine
significantly enhances the understanding of the dynamic behaviour of that
machine. Similarly, the first few natural frequencies (by appearance) of both FS1
and FS2 rigs have been experimentally identified using the impact-response
method. During the experiment, both FS1 and FS2 were excited at 2 locations with
an instrumented hammer (PCB) in both vertical and horizontal directions. The first
excitation location was at 209mm from both balance discs 1 and 2 (i.e. exactly
midpoint of the 1000mm shaft), while the second excitation location was at 44mm
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from bearing 3 and disc 3 (Figure 9.5). During the excitation of FS1 and FS2, the
dynamic responses were measured with a PCB accelerometer installed on bearing
2. Table 9.1 provides a summary of the identified natural frequencies, while
Figures 9.6-9.7 show the frequency response function (FRF) amplitude and phase
for FS1 and FS2 in both vertical and horizontal directions.
Figure 9.5 Experimental setup for modal test
Table 9.1 Experimentally identified natural frequencies for FS1 and FS2
Experimental Set-up Natural Frequencies (Hz)
1st
2nd
3rd
4th
FS1 50.66 56.76 59.2 127.6
FS2 47 55.54 57.98 127
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Figure 9.6 Typical FRF amplitude and phase plots for FS1, measured at bearing 2
(a) vertical direction (b) horizontal direction
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Figure 9.7 Typical FRF amplitude and phase plots for FS2, measured at bearing 2
(a) vertical direction (b) horizontal direction
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9.4.3 Signal processing
The CB and CT (computed as per Equations (9.7)-(9.8)) of the 20 sets of
measured vibration data for each of the 36 scenarios (Table 9.2) have been post-
processed with a MATLAB code using 95% overlap, frequency resolution (df) =
0.6104Hz, sampling frequency (fs) = 10000Hz, number of FT data points (N) =
16384 and 148 number of averages. Typical CB and CT plots of measured
vibration data for 4 scenarios (i.e. scenarios 1, 10, 19 and 28 in Table 9.2) are
shown in Figures 9.8-9.9. It can be observed that a distinction exists between the
reference (scenarios 1 and 19) and fault (scenarios 10 and 28) scenarios, and this
observation was fairly consistent for all other scenarios. In the CB plots (Figure
9.8), the reference scenarios (Figures 9.8(a)-(b)) only contained relatively small
B11 and B12=B21 CB components, due to inherent residual misalignments. On the
contrary, the fault scenarios (Figures 9.8(c)-(d)) were associated with several CB
components (e.g. B11, B12=B21, B13=B31, B33, etc.) of significantly higher amplitudes
than observed in the reference scenarios.
Table 9.2 Experimental scenarios for FS1 and FS2
Rig Speed
Scenarios
FS1 FS2
HRM BS SC LB SM SR HRM BS SC LB SM SR
20 Hz 1 4 7 10 13 16 19 22 25 28 31 34
30 Hz 2 5 8 11 14 17 20 23 26 29 32 35
40 Hz 3 6 9 12 15 18 21 24 27 30 33 36
It is vital to note that the amplitude of each CB peak in Figure 9.8 is a function of 2
frequency components, usually plotted in the xyz orthogonal axes, with axes x and
y respectively representing frequencies, while the amplitude of the CB component
is plotted on the z axis. For instance, the appearance of a B11 CB peak indicates
that the pCCS frequency components and (plotted on both x and y
orthogonal axes) shown in Equation (9.7) are both equal to the machine speed
(also known as 1x). Therefore, the B11 CB peak is a representation of the relation
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between (1x), (1x) and (2x). Similarly, each B12=B21 CB peak indicates
that the pCCS frequency components and shown in Equation (9.7) are
respectively equal to 1x machine speed and its second harmonic (2x) or vice
versa, while is equivalent to their sum (3x). Hence, each B12=B21 CB peak
shows the relation between 1x, 2x and 3x frequency components. Similarly, the
CT plots (Figure 9.9) for the reference (scenarios 1 and 19) and fault (scenarios 10
and 28) scenarios are different. The reference scenarios contain only T111 CT
component (due to some residual misalignment associated with the scenario),
while the fault scenarios contained T111, T113=T131=T311, etc. This observation was
also consistent for all the 36 experimentally simulated scenarios.
Figure 9.8 Typical CB plots for FS1 and FS2 at 1200RPM (a) HRM (FS1), (b)
HRM (FS2), (c) LB (FS1), (d) LB (FS2)
Unlike the CB, each CT component is a function of 3 pCCS frequency
components, therefore requiring a 4-dimensional plot. In this study, the spherical
plot method earlier suggested by Collis et al. [98] is adopted. In this method, the
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appearance of individual spheres at certain locations signifies the coupling that
exists between the pCCS frequency components at that location. Furthermore, the
size of each sphere is a representation of the amplitude of that particular CT
component. Hence, T111 CT component in Figures 9.9(a)-(b) is a representation of
the relation between (1x), (1x), (1x) and (3x). Also, each
T113=T131=T311 CT component in Figures 9.9(c)-(d) indicates that the pCCS
frequency components , and shown in Equation (9.8) are respectively equal
to 1x, 1x and 3x (third harmonic of the machine speed) or vice versa, while
is equivalent to their sum (5x).
Figure 9.9 Typical CT plots for FS1 and FS2 at 1200RPM (a) HRM (FS1), (b) HRM
(FS2), (c) LB (FS1), (d) LB (FS2)
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9.5 Faults Diagnosis
It is clear from Figures 9.8-9.9 that the CB and CT plots provided distinct features
for each of the experimentally simulated scenarios. However, faults diagnosis
based on visual observation of the CB and CT plots alone can be extremely
difficult and sometimes subjective. This is due to the appearance of several
components in the plots. Hence, the core of the current study is focussed on
eliminating or significantly reducing such subjectivities, through the application of
the proposed unified fault diagnosis technique described in Section 9.3.
9.5.1 Data preparation
The proposed fault diagnosis process was simplified by preparing the feature
matrix in stages. Firstly, a matrix was constructed for a particular flexible
foundation at a single machine speed, for instance . The 20 sets of
vibration measurements for each scenario in Table 9.2 were classified as
observations (i.e. rows). Each observation was then used to compute 2 CB (B11
and B12) and 2 CT (T111 and T112) components amplitudes as per Equations (9.7)-
(9.8). The computed CB and CT components then represented the features of the
matrix (columns). Hence, a matrix containing 4 features (B11, B12, T111 and T112)
and 120 observations (20 observations per scenario) was obtained, as detailed by
Equation (9.18). The second stage is concerned with fault diagnosis under multiple
machine speeds for a single setup (e.g. ), where the
feature matrix is characterised by 12 features (i.e. 2 CB and 2 CT features at each
machine speed) and 120 observations. The third and final stage of the data
preparation involves the harmonisation of all the features obtained from the
second stage for each machine setup. At this stage, a feature matrix containing
120 observations and 24 features (i.e. 12 features each for FS1 and FS2) is
constructed. During each of the stages, the constructed feature matrix is
eventually fed into a PCA algorithm that computes the PCs. Since maximum
representation can be obtained from the first few PCs, a graphical plot of the first
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and second PCs (Figure 9.10) is then used for classification of the different
scenarios.
(9.18)
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9.5.2 Results and discussions
Results of the proposed fault diagnosis method for multiple speeds on FS1 and
FS2 rigs are respectively shown in Figures 9.10(a)-(b). With the exception of the
slight overlap between the scenarios associated with HRM and SM machine
conditions (cases), there was a good separation between all the experimentally
simulated cases. However, this overlap was adjudged to be due to the low severity
of induced misalignment (i.e. 0.4mm) as well as the presence of residual
misalignment in the HRM case. However, the results of the multiple speeds and
multiple foundations diagnosis shown in Figure 9.10(c) provided an even better
separation for all scenarios, although a relatively small amount of overlap is still
evident between the scenarios associated with HRM and SM cases. Hence, the
proposed fault diagnosis technique may be useful for significantly reducing the
rigour associated with conducting separate analysis for each machine, and at
different speeds.
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Figure 9.10 Proposed faults diagnosis (a) multiple speeds – FS1 setup (b) multiple speeds – FS2 foundation (c) multiple speeds
and multiple foundations
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9.5.3 Comparison with Earlier Method
Figure 9.11 shows the results of similar analyses conducted using CB and CT
components amplitudes that were computed based on the earlier method
(Equations (9.4)-(9.5)). Although appreciable separation was also achieved using
the earlier method, however, significantly better results were obtained with the
improved method.
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Figure 9.11 Faults diagnosis with earlier CB and CT method (a) multiple speeds – FS1 setup (b) multiple speeds – FS2 setup (c)
multiple speeds and multiple foundations
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9.6 Practical application of the proposed FD technique
In practice, VFD of rotating machines often involves the analysis of measured
vibration data that represent the state(s) of a particular machine or group of
machines. These measured vibration data are often acquired after pre-defined
machine operation periods (also referred to as condition monitoring interval), so as
to determine whether a change in machine health has occurred. In order to
examine the ability of the proposed technique to diagnose machine faults on a
continuous basis, 3 additional fault diagnosis scenarios (FDS) were considered.
The first 2 fault diagnosis scenarios (FDS1 and FDS2) consider that additional
vibration measurements were collected from FS1 and FS2 rotating machines with
cracked shafts at 1800RPM machine speed (i.e. scenarios 8 and 26 in Table 9.2).
The newly acquired vibration data were then used to compute CB (B11 and B12)
and CT (T111 and T112) components as per Equations (9.7)-(9.8) for FDS1 and
FDS2. The computed CB and CT components were then added to the already
existing PCA feature matrices described in Equation (9.13). A combination of the
above additional scenarios (FDS1 and FDS2) is also considered for the combined
approach (multiple speeds and multiple foundations). The predictions are once
again consistent as shown in Figure 9.12.
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Figure 9.12 Continuous faults diagnosis, (a) Multiple speeds - FS1 setup (b) Multiple speeds - FS2 foundation (c) Multiple speeds
and multiple foundations
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9.7 Summary
The chapter proposes a novel vibration-based fault diagnosis (VFD) technique for
detecting and distinguishing common rotor-related faults in rotating machines,
which is independent of the machine foundation flexibility and operating speed.
The proposed technique aims to significantly minimise the rigour and complexities
associated with the common practise of performing separate vibration-based
analysis for identically configured ‘as installed’ rotating machines on industrial sites
(owing to variations in the flexibilities of foundations and operating speeds). In this
study, several sets of vibration data were collected from 2 identical rotating rigs
with different foundation flexibilities and at various machine speeds, through the
aid of only 4 vibration sensors (1 per bearing location). For each of the
experimental rigs, the measured vibration data under each machine operating
condition and speed were then used to independently compute composite
bispectrum (CB) and composite trispectrum (CT) components. The computed CB
and CT components were then used as the features of a principal component
analysis (PCA) based algorithm, so as to develop the multiple-speeds and
multiple-foundations faults diagnosis technique. The current research presents an
integrated VFD method for rotating machines, and further emphasizes the
relevance of data combination approaches in the minimisation of the level of
subjectivity and human judgements associated with popular techniques such as
ordinary amplitude spectra. Hence, the proposed VFD technique presents the
potential to significantly enhance maintenance and overall reliability of industrial
rotating machines through these summarised advantages:
Usefulness: with the proposed VFD technique, diagnosis results from 1
rotating machine are directly applicable to another identically configured
rotating machine despite variations in foundation flexibilities and
operating speeds. This approach aims to eliminate the common practise
of conducting separate analysis for individual rotating machine at
different speeds. Hence, historical data and diagnosis results from 1
rotating machine could be used for fault detection on an identical ‘as
installed’ rotating machine.
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Computational time: in condition monitoring, the computational duration
of any chosen technique is very vital, as it may significantly influence the
ability to prevent the occurrence of catastrophic machine failures. The
proposed VFD technique applies CB and CT components as features in
a PCA-based algorithm, which implies that a single composite spectrum
is adequate for describing the entire machine dynamics. This significantly
reduces the computational rigour and time, when compared to the
common practise of computing different spectra at individual vibration
measurement locations.
Interpretation: interpretation of the results obtained from the proposed
VFD technique is quite simple and does not require the services of an
expert, since the classification of different machine conditions are very
visible.
Practical application: for any new machine fault diagnosis, the computed
features from measured vibration data must be fed into the PCA
database. Upon the introduction of the new data, analysis will then be
performed to observe the classification of new machine state (healthy or
faulty). This diagnosis approach is already demonstrated in the present
study.
Furthermore, a comparison of the diagnosis results from CB and CT components
computed using the earlier CS method and the improved poly coherent composite
spectra (pCCS) was also conducted, and it was clearly observed that CB and CT
components derived from the pCCS method offered better discrimination between
the different experimentally simulated scenarios. In general, the proposed VFD
technique is versatile, non-intrusive and computationally efficient, which therefore
enhances its potential for usage in industries. However, in order to further confirm
the robustness and reliability of the technique, the investigation of more faults with
different severities are planned for the near future.
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10 Chapter 10 SENSITIVITY ANALYSIS OF
HIGHER ORDER COHERENT SPECTRA IN MACHINE FAULTS DIAGNOSIS
----------------------------------------------------------------------------------------------
Reformatted version of the following paper:
Paper title: Sensitivity analysis of higher order coherent spectra in machine
faults diagnosis
Authors: A. Yunusa-Kaltungo and J.K. Sinha
Submitted to: Structural Health Monitoring Journal
Abstract
In an earlier study, the poly coherent composite higher order spectra (i.e. poly
coherent composite bispectrum and trispectrum) frequency domain data fusion
technique was proposed to detect different rotor related faults. All earlier vibration-
based faults detection (VFD) involving the application of poly coherent composite
bispectrum (pCCB) and trispectrum (pCCT) have been solely based on the notion
that the measured vibration data from all measurement locations on a rotating
machine are always available and intact. However, practical industrial scenarios
sometimes deviate from this notion, owing to faults and/or damages associated
with vibration sensors or their accessories (e.g. connecting cables). Sensitivity
analysis of the method to various scenarios of measured vibration data availability
(i.e. complete data from all measurement locations and missing/erroneous data
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from certain measurement locations) is also examined through experimental and
industrial cases, so as to bring out the robustness of the method.
Keywords
Rotating machines, induced draft fan, data fusion, poly coherent composite
bispectrum, poly coherent composite trispectrum, sensitivity analysis
10.1 Introduction
In recent years, several research efforts have been invested into the development
of simplified but yet robust vibration-based fault detection (VFD) techniques. One
of such VFD approaches is the recently developed poly coherent composite higher
order spectra frequency domain data fusion method [251], whereby the dynamic
behaviour of a typical rotating machine can be described using a single poly
coherent composite bispectrum (pCCB) and/or trispectrum (pCCT), irrespective of
the number of vibration data measurement locations on the monitored machine.
Based on the results obtained from initially conducted experimental investigations,
pCCB and pCCT showed that it was possible to significantly reduce the rigour
often associated with the computation and analysis of separate higher order
spectra (mainly bispectrum and trispectrum) for vibration data collected from
individual measurement locations, which can be significant for large industrial
rotating machines supported by several bearings (e.g. large industrial turbines or
multi-shaft drive assemblies).
Besides the noteworthy ability of using a single pCCB or pCCT to effectively
distinguish different rotating machine conditions, the recent study conducted by
Yunusa-Kaltungo et al. [251] further highlighted the possibilities of developing a
hybrid data fusion (i.e. data fusion at both sensor and feature levels) method that
can detect and classify different operating conditions in identically configured
rotating machines irrespective of their foundation flexibilities and speeds, which
may foster the sharing of measured vibration data between identical ‘as installed’
rotating machines. While it is commendable that enormous research and practical
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efforts are continuously aimed at improving VFD of rotating machines, it is also
well-known that the successful operation of any VFD system is a direct function of
the proper integration of its 3 fundamental stages, namely; data collection, signal
processing and fault diagnosis. The data collection stage of a typical VFD system
provides the vibration data from which features (e.g. kurtosis, peak-to-peak
amplitude, 1x, 2x, 3x, etc.) are extracted during signal processing, before
eventually matching the various identified features with corresponding machine
conditions during fault diagnosis. The adverse conditions under which most
industrial rotating machines operate as well as the fragility of VFD instruments
sometimes restrict the availability of measured vibration data, which often affects
the effectiveness of the entire VFD system.
Until now however, studies on VFD of rotating machines have been significantly
based on the premise that vibration data from all sensors are intact and available,
irrespective of whether the measured vibration data will be separately analysed for
individual measurement locations with known techniques such as spectrum
analysis [55], [57], [252]–[254], wavelet analysis [208], [209], [255]–[260], higher
order statistical analysis [98], [106], [158], [204], [206], [261], etc., or fused
together for all measurement locations to generate a single but representative poly
coherent composite spectrum [251]. In practise however, the amount of data
available for faults diagnosis of some rotating machines may be limited at certain
instances, owing to faults/damages associated with the sensors or connecting
cables during auxiliary activities in the plant such as machine cleaning or general
maintenance, especially when dealing with critical industrial rotating machines that
are installed in highly remote and/or restricted plant locations (e.g. river gallery
pumps in water generation plants or drilling machines in mines). Hence, such
damages usually lead to the loss of vibration data from certain measurement
locations on these critical rotating machines.
However, owing to the operational demands as well as extremely low tolerances
for equipment downtime in most industrial plants, the VFD analyst may be
sometimes confined to conducting faults diagnosis based on limited measured
vibration data, as it may not be always feasible to recollect the vibration data
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representing the behaviours of such critical industrial rotating machines. Based on
this premise, it will be very useful to develop a VFD technique that possesses the
capability to identify incipient changes in the operating conditions of a rotating
machine due to the emergence of different faults, despite the unavailability of
measured vibration data from certain measurement locations on the machine.
In the current study, the concepts of pCCB and pCCT are applied to 2 examples –
laboratory scale experimental rig and critical cement manufacturing process fan.
Although vibration measurements were obtained from all the 4 bearing locations in
both examples, however, practical instances sometimes arise when some of the
measurements acquired from some sensors may be faulty. However, timely
machine fault diagnosis is often a requirement for all plants, irrespective of the
completeness of the measured data. In the current study however, measured
vibration data under different scenarios of data availability are analysed with the
method so as to understand its sensitivity and robustness in faults classification for
both examples, which generally leads to faults diagnosis. Hence, the current paper
explains;
The computational concepts of pCCB and pCCT.
The experimental and industrial examples considered.
The laboratory experiments conducted as well as on-site measurements in
the cement plant.
The data analysis, especially the sensitivity analysis for faults classification
based on both experimental and industrial examples.
10.2 poly-Coherent Composite Spectra
Equations (10.1)-(10.3) respectively provide the mathematical computations of the
poly Coherent Composite Spectra for an entire rotating machine with “b” number
of vibration measurement locations, which has already been extensively described
in an earlier study by Yunusa-Kaltungo et al. [242], [251].
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(10.1)
(10.2)
(10.3)
In Equation (10.1), ,
, ,
, ...., and
respectively denote the Fourier transformation (FT) of the rth segment at
frequency of the vibration responses at bearings 1, 2, 3, 4, ...., (b-1) and b.
Similarly, ,
, , ....,
respectively denote the coherence [156]
between bearings 1-2, 2-3, 3-4, …, (b-1)-b. is the poly-Coherent
Composite Spectrum (pCCS) at frequency, .
The shown in Equations (10.2)-(10.3) represents the poly coherent
composite FT for a particular segment ‘r’ of the measured vibration data from ‘b’
bearing locations at a particular frequency, , which was also computed as [242];
(10.4)
In order to enhance proper understanding of the current study, a brief re-iteration
of the steps involved in the computations of pCCB and pCCT VFD method are
again illustrated by the flowchart shown in Figure 10.1.
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Figure 10.1 Schematic representation of pCCS computational process
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10.3 Example 1: Laboratory Scale Experimental Rig
The laboratory scale experimental rig consists of two rigidly coupled shafts (S1
and S2) and three identical balance discs (D1, D2 and D3). D1 and D2 are
mounted on S1, while D3 is mounted on S2. S1 was then flexibly coupled (FC) to
an electric motor (EM), and the complete rig assembly is supported by 4 bearings
(B1-B4). Figure 10.2 shows a photograph of the experimental rig, while Table 10.1
provides the specifications of its main components. On this experimental rig [251],
the 5 experimentally simulated cases (C1-C5) detailed in Table 10.2 were studied
at a machine speed of 1800 RPM (30 Hz). Under each case, 20 sets of vibration
measurements were collected through the aid of 4 accelerometers (A1-A4).
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Figure 10.2 Laboratory scale experimental rig
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Table 10.1 Experimental rig components and their specifications
S/No. Rig Component Parameter Specification
1 S1
Material type Mild steel
Length (mm) 1000
Diameter (mm) 20
2 S2
Material type Mild steel
Length (mm) 500
Diameter (mm) 20
3 D1-D3
Material type Mild steel
External diameter (mm) 125
Internal diameter (mm) 20
4 B1-B4 Type Flange mounted ball bearings
Bore (mm) 20
5 EM
Type 3-phase induction motor
Power (kW) 0.75
Speed (RPM) 3000
6 FC
Type Flexible
Length (mm) 55
Internal diameter (mm) 20
External diameter (mm) 50
7 RC
Type Rigid
Length (mm) 65
Internal diameter (mm) 20
External diameter (mm) 42
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Table 10.2 Experimentally simulated cases
S/No. Case Abbreviation Severity and Location
1 Healthy with residual misalignment
C1 Possible residual misalignment at couplings (FC & RC)
2 Bent shaft C2 3.4mm axial run-out was created at the centre of S1
3 Shaft misalignment C3 0.4mm mild steel shim beneath the left-hand-side (LHS) of B1foundation
4 Shaft rub C4 Rub using a brass sleeve of 21mm on S1, near D2
5 Cracked shaft C5 4mm (depth) x 0.25mm (width) crack on S1, at 160mm from B1
10.3.1 Earlier Faults Detection Method [251]
The earlier study conducted by Yunusa-Kaltungo et al. [251] has already provided
significant details about the capabilities of the method to detect several rotor
related faults at different machine speeds. However, it is anticipated that a brief
recap of the earlier observations will significantly buttress the understanding and
relevance of the current study. Using C1 and C2 cases as illustration, the signal
processing parameters in Table 10.3 were used to compute pCCB and pCCT for a
set of measured vibration data. It is clearly visible from Figure 10.3 that the pCCB
features for both cases are significantly different. For instance, the C1 case
(Figure 10.3(a)) contained a slightly prominent B11 pCCB peak and very negligible
B12=B21 and B22 peaks while the C2 (Figure 10.3(b)) case contained several pCCB
components (B11, B12=B21, B22, B13=B31 and B23=B32) with significantly larger
amplitudes. Similarly, the computed pCCT features (Figure 10.4) for C1 and C2
cases are very different. The C1 case (Figure 10.4(a)) contains only T111 pCCT
component. As observed with pCCB (Figure 10.3), the C2 case (Figure 10.4(b))
contained several pCCT components (T112=T121=T211, T122=T212=T221, T222,
T113=T131=T311 and T333).
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Figure 10.3 Typical pCCB plots (a) C1 (b) C2
Figure 10.4 Typical pCCT plots (a) C1 (b) C2
Figures 10.3-10.4 clearly indicate the capabilities of pCCB and pCCT plots to
provide distinctions between different machine conditions. However, the earlier
study by Yunusa-Kaltungo et al. [251] proposed the combination of the amplitudes
of pCCB and pCCT, owing to the rigour and subjectivities associated with limiting
faults detection to visual inspection of numerous and sometimes highly diverse
pCCB and pCCT components that emerge as a result of continuous measurement
and analysis of vibration data during routine condition monitoring (CM) activities.
Hence, Figure 10.5 again shows the benefits of such a combined approach based
using 20 sets of measured vibration data for each experimentally simulated case.
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It is visible from Figure 10.5 that data related to each case are clustered together
and separated from the clusters of other cases.
Figure 10.5 Typical combined magnitudes of B11 pCCB and T111 pCCT
components for all cases under ideal laboratory scenario (LS0) of complete data
10.4 Sensitivity Analysis Based on Experimental Data
In Figure 10.5, the faults classification based on the combination of the computed
B11 pCCB and T111 pCCT components for all 100 sets (i.e. 20 sets of data per
case) of measured vibration data for C1-C5 cases solely assumes an ideal
laboratory scenario (LS0), where the data from all 4 measurement locations are
available and intact. However, this scenario may not always be practicable in “real
life” industrial machines, owing to the possibilities of damages to sensors or their
accessories at certain instances. Therefore, in order to ascertain the robustness
and sensitivity of this technique under changing conditions of measured vibration
data availability, the 4 additional scenarios (LS1-LS4) described in Table 10.4 have
been considered. In all 4 scenarios, vibration data from only 3 measurement
locations were used to compute the pCCB and pCCT components that produced
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the faults classifications shown in Figure 10.6. Based on the current experimental
rig and cases simulated, the omission of measured vibration data from certain
measurement locations did not have any significant effect on the faults
classification patterns. In fact, Figure 10.6 shows that data corresponding to each
of the 5 experimentally simulated cases consistently remained clustered together
and separated from the clusters of other cases under all scenarios of data
availability. For all scenarios, the C2 cluster consistently occupied the highest
position owing to its possession of significantly greater B11 pCCB and T111 pCCT
components amplitudes. Although C1, C4 and C5 cases for all scenarios
possessed relatively similar T111 pCCT components amplitudes, however, the
variations in their B11 pCCB components amplitudes still enabled appreciable
separations between them which further highlight the benefits of faults detection
based on the combination of pCCB and pCCT components. Similarly, the cluster
comprising of data related to the C3 case was positioned at the bottom left corner
of the plots for all scenarios due to its lower B11 pCCB and T111 pCCT components
amplitudes.
Table 10.3 Signal processing parameters for experimental data
Table 10.4 Description of laboratory scenarios
Scenario(s) Abbreviation Accelerometers Missing Data Location
1 LS1 123 Bearing 4
2 LS2 234 Bearing 1
3 LS3 124 Bearing 3
4 LS4 134 Bearing 2
S/No. Signal Processing Parameter(s)
1 Sampling frequency 10000 Hz
2 Number of data points (N) 8192
3 Frequency resolution (df) 1.2207 Hz
4 Number of averages 88
5 Segment overlap 95%
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Figure 10.6 Typical combined magnitudes of B11 pCCB and T111 pCCT
components for all cases under different laboratory scenarios of missing data (a)
LS1 (b) LS2 (c) LS3 (d) LS4
In order to perform a more detailed examination of the consistency of the
clustering for individual cases under all the scenarios described in Table 10.4, B11
pCCB and T111 pCCT components amplitudes were then separately combined for
each experimentally simulated case for all scenarios (for example C1 for LS0-LS5
and so on). The results of the various combinations are shown in Figure 10.7,
where it was again observed that the clusters for individual cases for all the
considered scenarios appear around the same region. For instance, Figure
10.7(a)-(e) respectively show the clustering together of C1-C5 cases for scenarios
LS0-LS4. It is also interesting to note that the patterns and relative locations of the
clusters for the four scenarios representing missing data (i.e. LS1-LS4) cannot be
distinguished from that of the ideal scenario (LS0). Therefore, based on the current
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experimental data and scenarios considered, the combined pCCB and pCCT VFD
technique is robust enough to classify rotating machine faults despite the
unavailability of data from certain measurement locations.
Figure 10.7 Typical combined magnitudes of B11 pCCB and T111 pCCT
components for individual cases for all scenarios (a) C1 (b) C2 (c) C3 (d) C4 (e)
C5
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10.5 Example 2: Industrial Fan
A fundamental rationale behind the development of any new rotating machines
VFD technique (or any other technique) is usually to enhance and/or simplify the
currently existing faults detection process in “real life” industrial machines. Based
on this premise, the current study similarly explored the capability and robustness
of pCCB and pCCT [251] in detecting changes in the operating conditions of a
very critical cement process rotary kiln induced draft fan (RKIDF), due to the
emergence of fault(s).
10.5.1 The Case Study (RKIDF)
The case study is a rotary kiln ID fan (RKIDF) for a cement process plant (Figure
10.8), which its main technical specifications are shown in Table 10.5. The RKIDF
is a twin inlet backward curved centrifugal fan that provides air draft across the
cement rotary kiln. The entire fan assembly is supported by 4 bearings, namely;
motor drive end (MDE), motor non-drive end (MNDE), fan drive end (FDE) and fan
non-drive end (FNDE) bearings as shown in Figure 10.8. The motor and fan shafts
are coupled by a very flexible spring-type coupling.
Table 10.5 Technical specifications of RKIDF [262]
S/No. Parameter Specification
1 Fan type 105 type – 12 double inlet
2 Fan serial number VW5/39231-02-01 & 02-02
3 Fan shaft length (m) 4.65
4 Impeller diameter (m) 2.697
5 Fan weight (kg) 5350
6 Number of impeller blades 11
7 Motor speed (RPM) 993
8 Power (kW) 656
9 Voltage (V)/current (A)/frequency (Hz) 690/674/50
10 Fan bearings Cooper self-aligning
11 Motor bearings Cooper self-aligning
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Figure 10.8 Schematic representation of RKIDF assembly [262]
The RKIDF performs 2 very critical functions in the cement manufacturing process.
Firstly, the draft of air needed for fuel combustion during clinker (the main
component of cement) production is provided by the RKIDF. Secondly, the hot kiln
exit gases used for drying and pre-heating fresh kiln feed are also conveyed by the
RKIDF. In order to increase the rotary kiln throughput, there has to be a
corresponding increase in the amount of fuel to be burnt, which is directly
dependent on the RKIDF speed (i.e. higher kiln feed requires more fuel; more fuel
requires more combustion air and more combustion air requires higher RKIDF
speed). Since the performance of cement process plants is most often judged by
the outputs from their rotary kilns (since this stage produces the clinker that is
eventually grinded into cement in the cement mills), hence, the optimum
performance and reliability of the RKIDF is very vital. The criticality of RKIDF to
this cement burning line is further compounded owing to its lack of built-in
redundancy (i.e. no standby available), as illustrated by Figure 10.9.
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Figure 10.9 Schematic representation of the burning line
10.5.2 On-site vibration measurements
During the on-site measurements, a total of 40 sets of vibration data were
collected from the RKIDF assembly at 600RPM (10Hz) fan speed. The first 20 sets
of vibration data were collected during the RKIDF fault condition, while the other
20 sets of vibration data were collected immediately after the conduction of a
corrective maintenance intervention to align the machine and remove heavy
limestone deposits from the impeller blades (Figure 10.10).
Figure 10.10 Limestone deposits on RKIDF impeller and blades [263]
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During these measurements (Figure 10.11), 4 diagonally mounted PCB
accelerometers (i.e. 1 per bearing) were used for collecting vibration data at a
sampling frequency (fs) of 10000Hz onto a PC, through the aid of a 16 channels
16-bit analogue-to-digital converter (ADC), as shown in Figure 10.11. In Figure
10.11, PC, ADC and A1-A4 respectively denote personal computer, analogue-to-
digital converter and accelerometers 1-4.
Figure 10.11 Photograph of on-site vibration measurement setup [263]
10.5.3 Detection and Classification of RKIDF Operating Conditions using
Earlier Method
As performed with the experimentally acquired data, (Section 10.3.1), the earlier
method was also used to analyse one set of vibration data measured on the
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RKIDF under faulty and healthy conditions. As anticipated, Figures 10.12-10.13
respectively display distinct pCCB and pCCT faults diagnosis for both cases. The
faulty case (Figure 10.12(a)) contains a very dominant B11 pCCB peak along with
smaller B12=B21 and B13=B31 pCCB peaks, while the healthy case (Figure 10.12(b))
only contained very negligible B11 and B12=B21 pCCB components. Similarly, the
pCCT components shown in Figure 10.13 are different for both RKIDF cases. The
healthy case (Figure 10.13(b)) contained a single T111 pCCT component, while the
faulty case (Figure 10.13(a)) contained several pCCT components (T112=T121=T211
and T113=T131=T311) in addition to a large T111 pCCT component.
Figure 10.12 Typical pCCB plots (a) faulty (b) healthy
Figure 10.13 Typical pCCT plots (a) faulty (b) healthy
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Similarly, the combined amplitude approach described earlier [251] was also
explored for the classification of 40 sets (i.e. 20 sets for faulty and 20 sets for
healthy cases) of vibration data acquired from the RKIDF, where it is again visible
from Figure 10.14 that all data sets related to the faulty case are grouped in the
same cluster and separated from the cluster comprising of data sets measured
during the healthy RKIDF condition.
Figure 10.14 Typical combined magnitudes of B11 pCCB and T111 pCCT
components for all cases under ideal industrial scenario (IS0) of complete data
10.6 Sensitivity Analysis Based on Industrial Data
The faults classification shown in Figure 10.14 is based on an ideal industrial
scenario (IS0) of total data availability from all measurement locations, which might
not always be the case. However, 4 additional industrial scenarios (IS1-IS4) similar
to those described in Table 10.4 have been considered with the industrial data,
and the result of the faults classification for each scenario is shown in Figures
10.15(a)-(d). As observed in the experimental example (Section 10.4), the healthy
and faulty conditions were separately clustered for all scenarios (Figure 10.15),
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which could be an indication of the industrial applicability of the technique in the
near future.
Figure 10.15 Typical combined magnitudes of B11 pCCB and T111 pCCT
components for all cases under different industrial scenarios of missing data (a)
IS1 (b) IS2 (c) IS3 (d) IS4
Figures 10.16(a)-(b) respectively show the separate combination of all faulty and
healthy data for the different scenarios (IS1-IS4) listed in Table 10.3, including the
ideal scenario of complete measured vibration data from all measurement
locations (IS0). The observations were quite similar and consistent with the
experimental example, with the clusters relating to each of the machine conditions
from all scenarios retaining their unique and respective regions.
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Figure 10.16 Typical combined magnitudes of B11 pCCB and T111 pCCT
components for individual cases for all scenarios (a) all faulty (b) all healthy
10.7 Summary
The quantity of measured vibration data available for classifying an industrial
rotating machine as healthy or faulty could be sometimes hampered by damages
to VFD sensors during routine field activities such as machine cleaning and
general maintenance. The avenues for ensuring the integrity of installed VFD
sensors such as accelerometers prior to each instance of data acquisition is
sometimes restricted by the immense production requirements, especially when
dealing with an on-line condition monitoring system for critical rotating machines
situated in isolated plant locations. Based on this premise, faults classification of
rotating machines (which generally leads to faults diagnosis) may be performed
based on the available vibration data from only certain measurement locations. In
the current study, several sets of measured vibration data from an experimental rig
and a critical induced draft fan of a cement manufacturing company have been
collected under different operating conditions. The results of the faults
classification performed using a combination of the amplitudes of poly coherent
composite bispectrum and trispectrum components for different scenarios of
measured vibration data (i.e. complete and incomplete data), indicated that the
proposed technique is able to separately classify the different cases. This however
shows the robustness and insensitivity of the technique to variations in the
availability of measured vibration data, which may be very useful for faults
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identification in critical industrial rotating machines, especially those installed in
remote and isolated locations, where the frequency of machine inspection is very
low. Future considerations for the current study will be aimed at observing the
impact of varying fault severities and locations on the cluster patterns for different
faults.
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11 Chapter 11 CONCLUDING REMARKS AND
FUTURE RESEARCH ----------------------------------------------------------------------------------------------
11.1 Overall Summary
Rotating machines are indispensable parts of most industrial processes including
power generation turbines, cement manufacturing rotary kilns, water transport
pumps, instrument air compressors, hotel and hospital ventilation fans, etc.
Failures of critical rotating machines can lead to catastrophic outcomes including
significant plant downtimes and fatalities, which makes early fault detection
imperative. Over the years, the reliability and quality of products/services delivered
by these critical machines have always been ensured through maintenance
activities whereby CM has been identified as one of the most efficient strategies.
Amongst the very popular rotating machine CM techniques, VCM is the most pre-
potent. The popularity of VCM in research and practise is largely owed to its ability
to offer the longest lead-time to machine failure as well as the relative
computational simplicity and sensitivity of standard VCM techniques such as
amplitude spectrum and rotor orbit analyses to various machine conditions.
While the advancements recorded through the application of amplitude spectrum
analysis for rotating machine faults detection has been immense, however, the
ability of the technique to provide simple, reliable, consistent and conclusive
results still remains questionable due to 2 main reasons. Firstly, the conventional
spectrum analysis process often entails the acquisition of vibration data from
several orthogonal directions of each measurement location (mostly the bearing
pedestal), which results in the accumulation of large volumes of data sets requiring
processing and interpretation. Secondly, the loss of phase information resulting
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from the computation of the final amplitude spectrum greatly limits its ability to
accurately distinguish certain machine conditions. A combination of these
limitations is a fundamental inducement for applying spectrum analysis in
conjunction with other standard VCM techniques such as rotor orbits analysis.
Although some useful results have been achieved, this amalgamation of
techniques makes the fault diagnosis process very complex, time-consuming,
costly, subjective and solely dependent on the expertise of an experienced
analyst. Besides the complexity of combining various standard VCM techniques
such as amplitude spectrum and rotor orbits analyses during fault diagnosis, it has
been experimentally observed that even rotor orbits for different machine
conditions sometimes appear similar thus making the entire diagnosis process
indeterminate.
By taking advantage of the recent and fast-growing computational advancements,
some researchers have explored other VCM approaches including model-based,
AI, higher order signal processing (mainly HOS and HOC) and data fusion
techniques. Although several studies have shown that it is possible to gain
intricate understanding about the dynamics of rotating machines through model-
based techniques, however, the possibility of generating FE models that would
accurately represent complex industrial rotating machines is still a topic of intense
debates. AI techniques on the other hand have recorded significant strides in an
attempt to reduce subjectivities arising from over-reliance on human experience.
However, popular AI techniques such as ANN and SVM are respectively limited by
lack of clearly defined guidelines for acquiring training data and Kernel function
selection.
Amongst all the emerging techniques currently available in the literature, higher
order signal processing appeared the most likely to overcome all the limitations
associated with the commonly used amplitude spectrum analysis. This is based on
the premise that HOS or its normalised form (i.e. HOC) provides information about
both amplitude and phase relationships that exist between the frequency
components of measured vibration signals. Without necessarily compromising the
fault diagnosis process, the phase and amplitude retaining capabilities of HOS and
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HOC offer the opportunity to reduce the number of sensors required for VCM of
rotating machines, which in turn leads to tangible reductions in the number of
measured data sets to be processed and interpreted. A detailed investigation of
the available literature indicates that right up till this moment, most of the current
efforts involving the application of higher order signal processing tools are
significantly skewed towards HOC, with no clarity on whether the features from
both classes (i.e. HOS and HOC) are exactly the same or whether one class
supersedes the other. Also, the very few studies that have explored fault diagnosis
with HOS are restricted to very simple experimental rigs and limited machine
faults. However, real life machines possess various levels of complexity and are
susceptible to several faults. Hence, there is a need to compare the capabilities of
HOS and HOC, so as to adequately justify the selection of what class to use. Also,
ample opportunities still exist to further examine the robustness of HOS on
different kinds of rotating machines and faults.
Maintenance cost effectiveness in the industry refers to any approach to
maintenance that would sustainably reduce maintenance cost, which includes the
rationalisation of rotating machines’ spares. A popular approach for rationalising
maintenance spares is the standardisation of plant machines, which implies that
there would be several identical rotating machines available in a typical plant.
Despite the similarities in configuration (e.g. components), the natural frequencies
of these rotating machines often differ due to variations in the flexibilities of their
foundations. Currently existing fault detection approaches are restricted to a
particular rotating machine, which means that separate analysis needs to be done
for individual rotating machines. Therefore, the development of a robust data
fusion approach that permits the application of measured vibration data from one
rotating machine on another identical rotating machine is highly warranted by the
industry and academia.
Through several experimental and numerical simulations, the current study
proposes a fault diagnosis approach that is capable of detecting and classifying
rotating machine faults irrespective of the variations in foundation flexibilities and
operating speeds. Based on the experimental results obtained, the current
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approach evades the lack of phase and need for multiple measurement locations
that often complicate the commonly used amplitude spectrum analysis.
11.2 Achieved Objectives
This section provides a description of how each of the 5 objectives defined in the
introductory chapter (Section 1.2) of this thesis were precisely achieved.
1. Compare higher order spectra and higher order coherences in order
to determine the usefulness of either class of signal processing tools.
Several studies have reported the abilities of higher order spectra (HOS)
and their normalised forms, higher order coherences (HOC) to establish the
amplitude and phase relationships that exist between several frequency
components of a measured vibration signal. All the studies currently
available in the literature portray both classes of tools as similar, with no
justifications for the selection of one class ahead of the other. Also, most of
the studies involving higher order signal processing tools have been
centred on HOC (i.e. bicoherence and tricoherence). Therefore, in order to
truly justify the choice of tool to use in the current study, a comparative
study was initially conducted to ascertain the usefulness of HOS and HOC.
In the study, a total of 4 cases were numerically simulated. Although the
frequency components for the 4 cases were same, each case possessed
different amplitudes and phases (representing a typical rotating machine
operating at same speed under different conditions of health). The HOS
and HOC components were then computed for each of the 4 cases under 4
different noise levels, so as to reflect industrial situations where
measurement noise is always an integral part of vibration signals measured
from rotating machines. The comparison showed that HOS components
adequately responded to amplitude and phase changes irrespective of the
measurement noise levels. On the contrary, HOC components varied
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inversely with measurement noise contents. This therefore implies that
HOC components are not only affected by amplitude and phase changes
but by measurement noise which can yield misleading diagnosis results in
practice.
2. Observe the dynamics of different rotating machine faults with
reduced sensors, using higher order spectra.
The capability of HOS (bispectrum and trispectrum) components to respond
to amplitude and phase change has already been established. On a
relatively rigid experimental rig and using significantly reduced sensors (1
accelerometer per bearing pedestal), vibration measurements were
acquired under 4 machine conditions at 2 machine speeds. Although the
computed amplitude bispectrum was relatively distinct for most machine
conditions at the 2 speeds, the healthy and shaft rub conditions at the
higher machine speed were quite similar. On the contrary, the computed
amplitude trispectra were clearly different for all machine conditions at both
speeds. Most importantly, the trispectrum features for each machine
condition were fairly consistent at both machine speeds, which is very
valuable for rotating machine fault diagnosis. It is a widely held view that the
appearance of different harmonics in vibration response is often associated
with the changing state of health of any typical rotating machine, which is
expected to be unique in terms of amplitude and phase at respective
harmonic components for every condition. Hence, these observations
provide clear indications that despite the reduced number of measurement
sensors (which significantly reduces fault diagnosis time and equipment
downtime), fault diagnosis is very possible with HOS. In order to increase
robustness of the fault diagnosis process, a combination of both bispectrum
and trispectrum components are proposed for defining machine health
indicators with the hope that the limitations of bispectrum would be
accounted for by the strengths of trispectrum and vice versa.
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3. Improve the existing frequency domain data fusion technique used for
constructing a single composite spectrum for a rotating machine, so
as to ease and enhance the accuracy of fault diagnosis.
Large and complex industrial rotating machines with multiple shafts are
always associated with numerous bearings. VCM of rotating machines
requires the collection of vibration data from each of the bearing pedestals.
During fault diagnosis, the measured vibration data from each bearing
pedestal is individually analysed for several machine faults and speeds.
This approach can be very demanding, especially when dealing with very
large rotating machines with several bearings. Based on this premise, the
concept of constructing a single composite spectrum (CS) that would be
independent on the number of measurement locations was proposed by
earlier studies. The results obtained from CS frequency domain data fusion
approach were quite encouraging, especially in terms of its ability to ease
fault diagnosis and significantly reduce equipment downtime. However, the
cross-power spectrum density (CSD) approach adopted for fusing the
measured vibration data led to a loss of phase information at intermediate
measurement locations. Also, the final CS is totally phase blind as a result
of the product of the coherent composite Fourier transformation (FT) and its
complex conjugate. As a consequence, fault diagnosis with earlier CS leads
to an extreme reliance on the amplitudes at the different harmonics.
In order to obviate the limitations of CS, an improved poly coherent
composite (pCCS) frequency domain data fusion technique was proposed
to provide a better representation of machine dynamics. Still based on the
concept of CSD, however, it was modified to incorporate all signals as
opposed to just a few signals considered in the earlier CS. The proposed
pCCS therefore guarantees better representation of machine dynamics,
owing to its retention of amplitude and phase information at all
measurement locations. The proposed pCCS was then used to diagnose
faults on an experimental rig where it was observed that the amplitude and
phase information at the operating speed or any higher harmonic can offer
Concluding Remarks and Future Research
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Akilu Yunusa-Kaltungo 285
PhD in Mechanical Engineering (2015) University of Manchester (UK)
better and easier diagnosis, especially when compared to CS that relied on
only the amplitudes of several harmonics of the machine speed.
4. Develop a faults diagnosis method that is independent of machine
speeds and foundation flexibilities, using composite spectra.
Nowadays, a significant number of plants have adopted equipment
standardisation strategies, so that the cost-effectiveness of their operations
can be enhanced. A notable consequence of such strategies is the
existence of several identical (similar components and configurations)
rotating machines on plant sites. Despite the similarities in configurations
and components, it has been observed that these identical rotating
machines often exhibit different natural frequencies, owing to variations in
their foundation flexibilities. Previously, all fault diagnosis efforts involving
identical rotating machines with different foundations requires the
independent collection and analysis of vibration data from each machine.
The complexity of the fault diagnosis process becomes even bigger if the
considered rotating machines operate at various speeds.
Hence, a similar scenario was experimentally simulated using 2 identical
rotating rigs with 2 different foundations. On both experimental rigs, several
sets of vibration data were collected under a wide range of machine health
conditions and at 3 separate speeds. For each of the experimental rigs, the
measured vibration data under each machine operating condition and
speed were then used to independently compute poly coherent composite
bispectrum (pCCB) and poly coherent composite trispectrum (pCCT)
components. The computed pCCB and pCCT components were then used
as the features of a multiple-speeds and multiple-foundations algorithm,
which was able to group data corresponding to the various machine
operating conditions into their respective clusters irrespective of speed or
foundation. The proposed technique therefore presents an integrated VCM
method that minimises the level of subjectivity and human judgements
Concluding Remarks and Future Research
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Akilu Yunusa-Kaltungo 286
PhD in Mechanical Engineering (2015) University of Manchester (UK)
associated with commonly used techniques such as amplitude spectrum
analysis.
5. Determine the sensitivity of composite higher order spectra to various
scenarios of data availability.
Over the years, VCM of rotating machines has always been based on the
premise that measured vibration data from all sensors are intact and
available for processing. In reality though, the quantity of measured
vibration data available for classifying industrial rotating machines as
healthy or faulty is sometimes hampered by damages to VCM sensors
during routine field activities including cleaning, general maintenance and
sabotage. The immense production requirements and extremely low
tolerance for plant downtime sometimes limits the practicability of always
ensuring the integrity of all VCM sensors prior to each instance of vibration
measurement. Consequently, fault detection is sometimes performed using
vibration data available from only certain measurement locations.
In an attempt to examine the abilities of pCCB and pCCT to adequately
classify rotor-related faults despite the unavailability of data from certain
measurement locations, several sets of vibration data were acquired from
an experimental rig and critical cement manufacturing process fan under
different conditions of health. The results showed that a combination of
pCCB and pCCT components is able to consistently classify machine
conditions under all the tested scenarios (complete and incomplete data).
This therefore shows the robustness and insensitivity of the technique to
variations in the availability of measured vibration data, which is valuable for
fault identification in critical industrial rotating machines, especially those
installed in remote and isolated locations, where the frequency of machine
inspection is very low.
Concluding Remarks and Future Research
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Akilu Yunusa-Kaltungo 287
PhD in Mechanical Engineering (2015) University of Manchester (UK)
11.3 Concluding Remarks
In an attempt to enhance the robustness and simplicity of vibration based
condition monitoring (VCM) of rotating machines, the current study proffers a novel
approach that is capable of detecting and classifying a wide range of rotor-related
faults on identical rotating machines with different foundations and operating at
different speeds. The current study showed how the proposed approach is able to
evade the complexities, rigour and over reliance on human experience often
associated with the application of standard VCM techniques such as amplitude
spectrum and rotor orbits analyses by allowing the transfer of measured vibration
data from one rotating machine to another identical rotating machine. Although
most of the findings from the current study are based on experimental
observations gathered from 3 separate rotating rigs with different faults and
speeds, the sensitivity of the proposed technique to different scenarios of data
availability was also validated with vibration data collected from a very critical
industrial rotating machine. Based on these initially observed eminences, the
proffered technique might be a feasible contender for industrial deployment in the
near future.
11.4 Future Research
The current study has clearly shown the potentials and merits of the proposed
VCM technique over the standard techniques such as amplitude spectrum and
rotor orbit analyses. However, the success and sustainability of this technique as
well as any other technique significantly depends on continuous improvement
strategies planned for the future. Therefore, the viability of the proposed approach
would be greatly enhanced by exploring the following research areas in the near
future.
1. All of the measured vibration data analysed using the VCM technique
proposed in the current study were acquired from rotating machines
Concluding Remarks and Future Research
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Akilu Yunusa-Kaltungo 288
PhD in Mechanical Engineering (2015) University of Manchester (UK)
supported by anti-friction ball bearings. However, several industrial rotating
machines are supported by fluid film bearings. Therefore, it will be very
useful to equally conduct similar faults diagnosis activities on vibration data
measured from several identical rotating machines that are supported by
fluid film bearings under different operating conditions.
2. The current study was principally based on detecting the existence of faults
as well as classifying measured vibration data related to certain rotor-
related faults. However, knowledge of faults severities is a very vital aspect
of VCM of rotating machines especially when dealing with very critical
industrial machines with costly downtime implications. Therefore, using the
techniques proposed in the current study to analyse more measured
vibration data acquired from rotating machines under different faults
severities will provide very useful information about the sensitivity of the
proposed technique to different fault severities.
3. Based on the considered experimental test rigs and experimentally
simulated cases considered for the current study, the proposed VCM
techniques successfully detected, differentiated and classified different
rotating machines operating conditions. However, it is strongly believed that
better and more precise theoretical understanding of the dynamic
behaviours of the considered rotating machines in certain ways can be
achieved through the development of mathematical models of the different
rigs as well as the experimentally simulated faults.
4. It well-known that a fundamental objective of academic research is usually
to enhance and/or simplify currently existing industrial processes, so as to
enhance efficiency and overall effectiveness. Based on this premise, it is
anticipated that the confidence level of the VCM approaches proposed in
the current study will be significantly enhanced through its application on
several identical industrial rotating machines with different foundation
flexibilities.
References
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Akilu Yunusa-Kaltungo 289
PhD in Mechanical Engineering (2015) University of Manchester (UK)
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Appendix A
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APPENDIX A
APPENDIX A THEORETICAL BACKGROUND OF SPECTRUM BASED SIGNAL
PROCESSING TOOLS ----------------------------------------------------------------------------------------------
A.1 Overview of Frequency Domain Signal Processing
During faults diagnosis, it is often desired to convert a time domain signal into the
frequency domain so as to observe the various frequency components within such
a signal. This conversion from time into the frequency domain (often achieved
through the Fourier transformation (FT) process) significantly enhances the
understanding of the physical behaviour of the studied system through a plot of the
vibration amplitude against frequency, also known as the spectrum of the signal.
A.2 Power Spectrum
The power spectrum can be arguably regarded as one of the most commonly used
signal processing tool, and this is evident from the huge body of literature
published with regards to its applications [21], [98], [159]. The power spectrum is a
second-order measure of stationary random processes, which can be
mathematically defined as [98];
(A.1)
Appendix A
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where and are respectively the Fourier transformation (FT) and the
complex conjugate of a time domain signal at a particular frequency.
During the computation of the FT for experimentally measured time domain data,
the direct application of Equation (A.1) is often limited by the following reasons
[21]:
Measured time domain data is often associated with noise
Accurate definition of the time period (T) of the signal
Obtaining the digital form of the data with sampling frequency
Therefore, it is often required to artificially define T, compute the frequency
resolution (d =
) and divide the measured time domain data into equal
segments ( for averaging where the segment size is guided by the number of
data points (N). Based on this premise, Equation (A.1) can also be written as:
(A.2)
where =
. Here, N denotes the number of data
points for FT analysis; represents the sampling frequency; is the frequency
resolution; is the number of equal segments with size N; and
respectively remain the FT and its complex conjugate at frequency for the rth
segment of the considered time domain signal , having a time length of t, with
sufficient amount of overlap.
Equations (A.1) and (A.2) clearly show that the power spectrum is a real quantity
owing to the magnitude squared operation (i.e. the product of and ).
Hence the power spectrum contains no phase information which is the reason why
faults diagnosis using power spectrum density is restricted to the comparison of
amplitudes at individual frequencies.
Appendix A
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A.3 Cross-power Spectrum
Equations (A.2) defines the averaged auto-power spectral density, for a
particular time domain signal at frequency . However, practical VCM of
rotating machines often entails the measurement of vibration data from several
machine locations. Therefore, it is sometimes required that the relationship
between 2 separate time domain signals ( and ) at a particular frequency
is established. The cross-power spectrum (which can be mathematically
computed using Equations (A.3)-(A.4)) is known to provide information about such
relationships.
(A.3)
The averaged cross-power spectrum can be similarly computed as:
(A.4)
where and respectively represent the FT and the complex conjugate
of the FT at frequency for the rth segment of the signals and , while
is the averaged cross-power spectrum for number of segments.
A.4 Ordinary Coherence
The vibration responses acquired from rotating machines and structures in general
are known to be contaminated by noises generated by the measurement sensors
and the monitored structures. The coherence between 2 vibration signals, and
at a frequency provides an indication of the linear correlation between
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them. Coherence values are always bounded between 0 and 1. A coherence value
of 0 at a frequency indicates a lack of relation between the 2 signals, while a
coherence value of 1 indicates a perfect relation between them. According to a
study by Suryam et al. [156], the following can be inferred about coherence:
Coherence value increases as the linear correlation between input
excitation and response increases.
Coherence value may decrease with increase in measurement noise
A nonlinear relation between input excitation and response leads to
reduction in the coherence value
Hence, the ordinary coherence between 2 vibration signals, and at a
frequency is defined as [21]:
(A.5)
Similarly, the averaged coherence can be computed as:
(A.6)
A.5 Higher Order Signal Processing Tools
Equation (A.2) has shown that all phase information is lost during the magnitude
squared operation leading to the computation of the power spectrum, which is why
the power spectrum is only capable of comparing the magnitudes at individual
frequencies. However, the outcomes of analysing measured vibration signals
Appendix A
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(especially during VCM of rotating machines) based on the comparisons of
magnitudes at individual frequencies for different operating conditions is
sometimes unreliable, owing to the possibilities of generating identical power
spectral patterns for various machine conditions. Hence, the establishment of the
level of interaction between several frequency components in a time domain signal
through the application of higher order signal processing tools is desirable for
faults diagnosis.
A.5.1 Bispectrum
Just as the power spectrum provides information about the decomposition of the
power of a measured time domain signal, the bispectrum provides information
about the third order moment [98]. Consequently, the bispectrum can be regarded
as a function of 2 frequency components (each containing amplitude and phase),
say and . The bispectrum provides information about the relations that exist
between , and the complex conjugate of their sum , which can be
mathematically represented as:
(A.7)
A.5.2 Trispectrum
Similarly, the trispectrum of a time domain signal , involves the combination of
3 frequencies (each having amplitude and phase) , and with a fourth
frequency that is equivalent to the sum of the initial 3, and was
computed as [98], [159]:
(A.8)
Appendix A
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In contrast to the bispectrum, each trispectrum component is a function of 3
frequencies, requiring a 4-dimensional plot. Therefore, the spherical plot method
earlier suggested by Collis et al. [98] is adopted here, where the appearance of
individual spheres at certain locations signifies the coupling that exists between
the frequencies at that location and the sizes of the spheres relate to the
amplitudes of the trispectrum components for individual cases.
A.6 Normalisation of Higher Order Signal Processing Tools
Another popular class of higher order signal processing tools are the normalised
forms of higher order spectra (HOS), also known as higher order coherences
(HOCs). HOCs represent the amplitude normalisation of HOS between a range of
0 and 1. The 2 most common classes of HOCs are the bicoherence and
tricoherence.
A.6.1 Bicoherence
The bicoherence is the amplitude normalisation of bispectrum, and can be
computed as [98]:
b2 ( , ) =
(A.9)
A.6.2 Tricoherence
Similarly, the tricoherence is the amplitude normalisation of the trispectrum which
can be computed as [98]:
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t2 =
(A.10)
In order to further boost the understanding of HOS and their normalised forms
(HOCs), their mathematical derivations provided in an earlier study by Howard
[159] is again repeated here.
Let’s consider a time domain signal, , where
. By
applying the exponential form of the Fourier series, the coefficients can be
represented by:
(A.11)
In general, m=0, , , , etc. Hence the positive and negative Fourier series
coefficients of m are determined. The expansion of the time domain signal
can be achieved by using Euler’s theorem as follows:
(A.12)
Substituting Equation (A.12) into Equation (A.11), we obtain:
(A.13)
Appendix A
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Substitute
and
into Equation (A.13) to obtain:
(A.14)
Let’s assume a specific case where , Equation (A.13) can be rewritten to
obtain the positive and negative frequency components for ,
and
, then:
(A.15)
This therefore yields
and
for the positive and negative
Fourier series coefficients respectively.
Since vibration data measured from real structures is often a combination of
several periodic waves due faults, let’s then consider other time domain signals
with period T, say:
and
and are respectively equivalent to
and
, where
Appendix A
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By applying the procedure earlier described, the Fourier series coefficients can be
determined as:
,
and
,
Therefore, the averaged normalised bispectrum for a time domain signal with
equal FT segments can be similarly obtained from the positive and negative
Fourier series coefficients as:
(A.16)
where the bispectrum,
During the computation of the bicoherence, it more convenient to separately
compute the numerator and denominator of Equation (A.16).
Solving for the first denominator term, we have:
(A.17)
Appendix A
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Using a similar approach to solve for the second denominator term, we have:
(A.18)
The numerator on the other hand gives:
(A.19)
By expansion of Equation (A.19), we get:
(A.20)
A very similar approach to that shown in Equation (A.16) is adopted for the
averaged tricoherence for a time domain signal with equal FT segments except
that 4 frequency components ( , and ) are involved, with each having
amplitudes ( , , and ) and phases ( , and ). Hence, the
tricoherence can be computed as:
(A.21)
Appendix A
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where the trispectrum,
In the case of bispectrum and bicoherence, , and are the amplitudes of
the signal components at frequencies , and respectively, while , and
( = + ) are the respective random phases of the signal components at
frequencies , and respectively. Although only the positive frequency
components have been used in the above derivations, however, the same would
apply for the negative frequency components.
The outcome of the trispectrum and tricoherence are similar to those of the
bispectrum and bicoherence except that 4 frequency components ( , , and
) with amplitudes , , and and phases , , and ( = +
) are considered. Each of the bispectrum components amplitude is a
function of 2 frequencies, usually plotted in the xyz orthogonal axes, with axes x
and y respectively representing frequencies, while the amplitude of the bispectrum
is plotted on the z axis. On the other hand, each trispectrum component is a
function of three frequencies, requiring a 4-dimensional plot. Therefore, the
spherical plot method suggested by Collis et al. [98] is often adopted, where the
appearance of individual spheres at certain locations signifies the coupling that
exists between the frequencies at that location and the sizes of the spheres relate
to the amplitudes of the trispectrum components.
Vibration-based Condition Monitoring of Rotating Machines
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