Vibration Feature Extraction for Smart Sensors

The Pennsylvania State University

The Graduate School

College of Engineering

Vibration Feature Extraction for Smart Sensors

by

Kenneth P. Maynard

© 2001 Kenneth P. Maynard

Submitted in Partial Fulfillment of the Requirements

for the Degree of

Master of Engineering

November 2001

I grant The Pennsylvania State University the nonexclusive right to use this work for the University’s own purposes and to make single copies of the work available to the public on a not-for-profit basis if copies are not otherwise available.

__________________________________________

Kenneth P. Maynard

We approve the research report of Kenneth P. Maynard.

Date of Signature ___________________________________________ ______________ Dr. Martin W. Trethewey Professor of Mechanical Engineering Advisor ___________________________________________ ______________ Dr. Karl M. Reichard Research Associate/ Assistant Professor of Acoustics Co-Thesis Advisor ___________________________________________ ______________ Dr. Anthony A. Atchley Professor of Acoustics Chair, Graduate Program in Acoustics

iii

Abstract

Condition-based maintenance systems monitor the operation of

mechanical equipment to provide an accurate assessment of the system's

current condition and to facilitate prediction of problem evolution. Vibration

analysis for condition assessment and fault diagnostics has a long history of

application to power and mechanical equipment. The interpretation and

correlation of this data is often cumbersome, even for the most experienced

personnel. As a result, automated processing and analysis methods are often

sought. To facilitate automation, smart sensor systems are being implemented

for advanced diagnostics and prognostics. In conjunction with these smart

systems, advanced features are commonly used to provide a measure of the

vibration level that can be correlated to a fault condition. Many such feature

vectors have been developed over the years and are well documented in the

literature.

This paper introduces concepts related to feature extraction for smart

sensors for improved diagnostics within condition-based maintenance (CBM).

Novel data tools are introduced by examples that identify diagnostic and

prognostic features for transitional data from mechanical systems. These tools

facilitate the establishment of effective methodologies for CBM researchers and

practitioners, and promote environments in which the new methodologies can be

easily and systematically characterized and evaluated. The capability of different

features to identify and track failure modes are treated primarily using gearbox

run-to-failure accelerometer data acquired on the Mechanical Diagnostics Test

Bed (MDTB) at the Pennsylvania State University Applied Research Laboratory.

iv

Table of Contents

LIST OF TABLES ................................................................................................ v

LIST OF FIGURES:............................................................................................. vi

ACKNOWLEDGEMENTS: ................................................................................... 1

CHAPTER - 1 INTRODUCTION........................................................................... 2 1.1 Smart Sensors .......................................................................................................................3 1.2 Why Feature Extraction? ....................................................................................................10

CHAPTER - 2 FEATURE EXTRACTION EXAMPLES ...................................... 11 2.1 Preprocessing for Gear Fault Detection ...........................................................................11 2.2 Preprocessing Steps...........................................................................................................12

2.2.1 Interstitial Preprocessing..........................................................................................12 2.2.2 Asynchronous Demodulation Preprocessing...........................................................13

2.3 Feature Extraction...............................................................................................................14 2.3.1 Statistical Features ..................................................................................................14

2.3.1.1 Root Mean Square (RMS) Feature...................................................................15 2.3.1.2 Skew .................................................................................................................15 2.3.1.3 Kurtosis.............................................................................................................16

2.3.2 Envelope Spectral Peak Feature .............................................................................17

CHAPTER - 3 EXPERIMENTAL AND ANALYTICAL RESULTS...................... 21 3.1 Transitional Gear Failure Data ...........................................................................................21 3.2 Gearbox Features................................................................................................................23

3.2.1 Interstitial RMS.........................................................................................................23 3.2.2 Interstitial Kurtosis....................................................................................................25 3.2.3 Interstitial Envelope Spectral Peak ..........................................................................29

3.3 Bearing Feature: Skew........................................................................................................31

CHAPTER - 4 EVALUATION OF GEARBOX FEATURES................................ 35 4.1 High-Pass Filtering Comparison........................................................................................35 4.2 Comparison with Traditional Gearbox Features ..............................................................37 4.3 Feature Fusion.....................................................................................................................40 4.4 Model-Based Feature Identification...................................................................................41

CHAPTER - 5 CONCLUSION............................................................................ 48

v

List of Tables: TABLE 1: SUMMARY OF INTERSTITIAL PARAMETER EFFECTIVENESS .....................................................40

vi

List of Figures: FIGURE 1: MOORE'S LAW AS APPLIED TO INTEL PROCESSORS...............................................................5 FIGURE 2: ANALOGOUS APPLICATION OF MOORE'S LAW TO PROCESSOR SPEED ....................................5 FIGURE 3: TYPICAL INSTRUMENTATION COSTS .....................................................................................6 FIGURE 4: BLUETOOTH OEM MODULE (CIRCA 2001)............................................................................7 FIGURE 5: IDEALIZED SMART ACCELEROMETER ....................................................................................8 FIGURE 6: SMART SENSOR ARCHITECTURE EXAMPLE FOR A PUMP.........................................................8 FIGURE 7: CURRENTLY AVAILABLE FORMS OF THE SMART SENSOR OR INTELLIGENT NODE ......................9 FIGURE 8: SCHEMATIC OF INTERSTITIAL PROCESSING METHOD ...........................................................11 FIGURE 9: TYPICAL RAW AND FILTERED DATA FROM MDTB RUN .........................................................13 FIGURE 10: SKEW: MEASURE OF SYMMETRY OF THE PROBABILITY DENSITY FUNCTION .........................15 FIGURE 11: COMPARISON OF PDFS HAVING THE SAME STANDARD DEVIATION BUT DIFFERENT

KURTOSIS ................................................................................................................................16 FIGURE 12: SINE WAVE AT 200 HZ WITH AMPLITUDE MODULATION AT 5.5 HZ.......................................17 FIGURE 13: RECTIFIED SINE WAVE AT 200 HZ, AMPLITUDE MODULATION AT 5.5 HZ ..............................18 FIGURE 14: RECTIFIED SINE WAVE AT 200 HZ, AMPLITUDE MODULATION AT 5.5 HZ ..............................18 FIGURE 15: 200 & 126 HZ SINE WAVE WITH AMPLITUDE MODULATION AT 5.5 HZ (A) WAVEFORM; (B)

SPECTRUM; (C) ENVELOPE SPECTRUM AFTER 50 HZ LOW-PASS FILTER .......................................19 FIGURE 16: RANDOM DATA WITH AMPLITUDE MODULATION AT 5.5 HZ (A) WAVEFORM; (B) SPECTRUM;

(C) ENVELOPE SPECTRUM (NO FILTERING) .................................................................................20 FIGURE 17: MECHANICAL DIAGNOSTIC TEST BED (MDTB) .................................................................22 FIGURE 18: CLOSE-UP OF THE GEARBOX SHOWING ACCELEROMETER LOCATIONS................................23 FIGURE 19: INTERSTITIAL RMS AS A FUNCTION OF TIME OVER THE ENTIRE TEST (RUN 14) ...................24 FIGURE 20: INTERSTITIAL RMS AS A FUNCTION OF TIME WHILE LOADED AT 3X RATED LOAD .................25 FIGURE 21: SAMPLE HISTOGRAMS OF MDTB GEARBOX DATA .............................................................26 FIGURE 22: DATA OF FIGURE 21 RESCALED TO COMPARE TAILS..........................................................26 FIGURE 23: CONTRIBUTION TO KURTOSIS Z4M ...................................................................................27 FIGURE 24: INTERSTITIAL KURTOSIS AS A FUNCTION OF TIME OVER THE ENTIRE TEST (RUN 14)............28 FIGURE 25: INTERSTITIAL KURTOSIS WHILE LOADED AT 3X RATED LOAD ..............................................29 FIGURE 26: INTERSTITIAL ENVELOPE SPECTRAL PEAK.........................................................................30 FIGURE 27: INTERSTITIAL ENVELOPE SPECTRAL PEAK.........................................................................31 FIGURE 28: (A) TYPICAL INSTALLATION OF PROXIMITY PROBE ON FLUID-FILM BEARING

(BENTLY-NEVADA); (B) RESULTING ORBIT .................................................................................32 FIGURE 29: SYNTHESIZED ORBIT WITH RUB AND NOISE .......................................................................33 FIGURE 30: HISTOGRAM OF ONE CHANNEL WITH 10% RUB, 28% NOISE .............................................34 FIGURE 31: SKEW AS A FUNCTION OF PERCENT FLATTENED ...............................................................34 FIGURE 32: COMPARISON OF RMS USING HIGH-PASS AND INTERSTITIAL FILTERING .............................36 FIGURE 33: COMPARISON OF KURTOSIS USING HIGH-PASS FILTERING (3000 HZ AND 5000 HZ) AND

INTERSTITIAL FILTERING (ACCELEROMETER 2) ...........................................................................36 FIGURE 34: COMPARISON OF ENVELOPING USING HIGH-PASS FILTERING (3000 HZ AND 5000 HZ)

AND INTERSTITIAL FILTERING (ACCELEROMETER 2) ....................................................................37 FIGURE 35: COMPARISON OF INTERSTITIAL KURTOSIS WITH NA4 AND FM4 .........................................38 FIGURE 36: COMPARISON OF INTERSTITIAL KURTOSIS WITH NA4 AND FM4 (NOT NORMALIZED) ............39

vii

FIGURE 37: GEAR COMPONENT HEALTH VECTOR BASED ON KURTOSIS AND RMS.................................41 FIGURE 38: FINITE ELEMENT MODEL OF MDTB GEAR TEETH (WITH CONTACT) .....................................42 FIGURE 39: DETAIL OF TOOTH MODEL: A) SHOWING ELEMENTS; B) SHOWING CRACK LOCATION .............42 FIGURE 40: CONTACT MODEL OF GEAR WITH NO CRACKS....................................................................43 FIGURE 41: CONTACT MODEL OF GEAR WITH CRACKED TOOTH............................................................43 FIGURE 42: EFFECTIVE TORSIONAL STIFFNESS PROFILE OF A CRACKED AND UNCRACKED TOOTH..........44 FIGURE 43: FINITE ELEMENT MODEL OF MDTB ROTOR (BEAM MODEL) ................................................45 FIGURE 44: CLOSE UP OF MDTB ROTOR BEAM MODEL SHOWING SCHEMATICALLY THE LOCATION OF

THE VARIABLE SPRING STIFFNESS ASSOCIATED WITH MESH ........................................................45 FIGURE 45: RESULTS OF COMPARISON OF FM4 FROM MDTB TEST AND FINITE ELEMENT MODEL

RESULTS .................................................................................................................................46

1

Acknowledgements:

This work was primarily supported by Multidisciplinary University

Research Initiative (MURI) for Integrated Predictive Diagnostics (Grant Number

N00014-95-1-0461) sponsored by the Office of Naval Research.

Personal gratitude goes to the Condition Based Maintenance (CBM)

department of the Applied Research Lab (ARL) of Penn State for their aid and

support in this research.

2

Chapter - 1 Introduction Vibration measurements have been used as the flagship of condition

monitoring of machinery health for almost a century. During the first half of the

twentieth century, most of the vibration information used involved overall

vibration (peak or RMS) from the time waveform. With the advent of advanced

filtering techniques during the last half-century, much work was been done to

identify vibration at specific frequencies and then correlate it with certain

maintenance issues, such as imbalance and misalignment, whirl, etc. With the

introduction of the Fast Fourier Transform (FFT)1 and the availability of fast

processing, spectrum-based diagnostic techniques enjoyed growth in attention

and importance. With the advent of other advanced technologies, such as oil

analysis, acoustic emissions, infrared thermography, ultrasonics, etc., the fleet of

condition monitoring technologies has grown, but vibration has still retained its

flagship status.

However, in the last few decades, new ways of looking at vibration have

emerged. Much of the information contained in the vibration is not visible in a

time waveform or a simple spectrum. Rather, it is hidden, encrypted in the signal

waveform. Various communication signal processing techniques used to encrypt

and decipher signals have found their way into the machinery condition-

monitoring arena, and new types of information and information portrayal have

been developed. These techniques include various types of demodulation

(asynchronous, AM, FM, phase), wavelets, time synchronous averaging, short-

time Fourier transforms (STFT), etc. By combining several of these techniques,

it has been found that features of the vibration waveform may be extracted and,

often empirically, correlated with various condition or damage states of

machinery components. The techniques employed in the extraction of these

features are varied; however, they generally employ three processing steps: (1)

preprocessing, such as filtering (high-pass, band-pass, low-pass), time

synchronous averaging, demodulation, etc.; (2) feature extraction, using

3

statistical properties, spectral properties, etc.; and (3) feature fusion, combining

the information obtained from several features. The appropriate preprocessing

techniques are most often empirically determined, where investigators may try

different techniques on the data until they find something that makes sense.

However, more and more system modeling is being used to help understand the

physics of the vibration, thereby making the feature selection more physics-

based.

The proliferation of smart sensors makes feature extraction more and

more essential. In smart sensors, we have moved high-speed processing power

close to the machine. However, the thought of transmitting high bandwidth data

for large numbers of signal channels, and then interpreting these signals as well,

is overwhelming. Feature extraction allows us to process the data and transmit

very low bandwidth information about the health of the system or component.

Such information can aid the decision-maker by providing interpretation along

with the data.

The purpose of this paper is to show by example some of the ways that

features may be extracted and correlated with machinery damage states. It is

hoped that the reader will gain insight into the process, and that some of the

features that are commonly used (such as kurtosis) will be demystified as a result

of studying the example process streams.

1.1 Smart Sensors A smart sensor is a system that includes a sensor element and various

other components, which facilitate the diagnostic and prognostic evaluation of

machinery components. The smart sensor is characterized by the following

attributes2:

• Smart sensor systems adapt to the environment by optimizing their sensor

detection performance, power consumption, and communication activity.

• Smart sensor systems record raw data and extract information.

4

• Smart sensor systems have some degree of self-awareness using built-in

calibration, internal process control checking and re-booting, and

measures of “normal” and “abnormal” operation of its internal processes.

• Smart sensor systems are completely re-programmable through their

communications port, allowing access to raw data, program variables, and

the processed data.

• In addition to pattern recognition ability, smart sensor systems are capable

of predicting pattern future states and providing meaningful confidence

metrics for these predictions.

These basic characteristics represent the starting point for defining the smart

sensor node on a network integrating many sensors into a smart system. In

addition, the smart system architecture must be expandable: it must account for

generation gap between sensor hardware and software and the machinery being

monitored.

Gordon Moore (co-founder of Intel) predicted in 1965 that the transistor

density of semiconductor chips would double roughly every 18 months3. Figure 1

and Figure 2 show how Moore’s Law plays out in the realm of personal

computers. This exponential growth is to be compared to “...digging ditches —

the machines that do that don't improve at Moore's Law-type rates. They improve

about three percent a year.”4 This not so flattering description applies to most

mechanical machinery. One task of the smart sensor is to integrate these

technologies, permitting the growth of the smart sensor at a rapid rate on

machines that change at extremely slow rates.

5

Figure 1: Moore's Law as applied to Intel processors

Figure 2: Analogous application of Moore's Law to processor speed

The smart sensor must also allow for newly identified failure modes. As

our understanding of a machine matures, new algorithms may be developed to

assess the condition of the machine. The smart sensor must permit the

incorporation of this new understanding into its architecture.

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Intel Data

Linear Fit (Logarithmic)

Linear fit corresponds to doubling every 2.15 years

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Twenty-five year history

Linear fit of twenty-five year history

Linear fit of first decade

Linear fit of last decade

Last ten years:Doubling every 1.58 years

First ten years:Doubling every 1.87

years

Twenty-five year History:Doubling every 1.96 years

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Twenty-five year history

Linear fit of twenty-five year history

Linear fit of first decade

Linear fit of last decade

Last ten years:Doubling every 1.58 years

First ten years:Doubling every 1.87

years

Twenty-five year History:Doubling every 1.96 years

6

The smart sensor certainly must also be digital. No significant processing

of the sensor data can take place without first digitizing the data. In addition, the

sensor should incorporate current standards, such as IEEE 14515, which defines

the smart sensor interface; Open System Architecture for Condition-Based

Maintenance (OSA-CBM)6, which facilitates integration and interchangeability of

various hardware and software components in a smart sensor system for CBM

from a variety of sources; and Machinery Information Management Open

Systems Alliance (MIMOSA)7, a standard equipment database architecture.

Finally, for most

applications, the smart sensor

must be wireless. A wired

system greatly restricts the

expansion of the system. In

addition, it will often put smart

sensors in a position of being too

expensive. Figure 3 shows the

estimated cost of installing a

sensor onboard a ship. For

some industries, such as the

nuclear power industry, it is essentially impossible to add wires to equipment due

to the lack of penetrations for wires in the building. Finally, a wireless system

makes it possible for the maintenance worker or operator to simply walk out to a

machine, place a wireless sensor, and return to a workstation to reconfigure the

wireless network to include the new sensor.

Figure 3: Typical instrumentation costs 8

66%

17%

17%WiringInstallation

Sensor

Wire

7

On the basis of the current trends

in wireless data communication, several

sensor manufacturers have chosen the

Bluetooth wireless protocol9 for their

smart sensors. This protocol, originally

targeting wireless telephones,

handhelds, and PCs, was founded by a

special interest group (SIG) consisting

of Ericsson, IBM Corporation, Intel

Corporation, Nokia and Toshiba

Corporation, and has since been joined by such players as 3Com Corporation,

Lucent Technologies, Microsoft Corporation and Motorola Inc. to form the

promoter group of the Bluetooth SIG. Most recently, a Working Group for

Industrial Automation was formed, and includes many sensor manufacturers.

Some additional characteristics are desirable in the ideal smart sensor,

including full integration of electronics, signal processing, and power generation

in a small package. Figure 5 shows such an idealized transducer for measuring

vibration acceleration. Perhaps the most difficult attribute to achieve is self-

powering. Work is ongoing to attempt to power such a smart accelerometer

using ambient vibration, ambient thermal gradients, and ambient light.

The smart sensor occupies the lowest level in the smart system

architecture. The smart sensor architecture includes the sensing element and

intelligent node, which together comprise the smart sensor (they may or may not

be physically integrated into one unit), an area reasoner, which collects health

information from the intelligent nodes, and the operator/maintainer local area

network, by which the information is communicated to the operator/maintainer.

Figure 6 shows a typical architecture for a smart pump. Note that the area

reasoner may reside at the platform level, and integrate the information from

intelligent bearing nodes, intelligent motor nodes, and intelligent lubrication

system nodes, etc., to arrive at a health vector for the pump system.

Figure 4: Bluetooth OEM module (circa 2001)

8

Figure 5: Idealized smart accelerometer

Figure 6: Smart sensor architecture example for a pump

1”

1”

Communications

Diagnostic Processor (ASIC)

General Purpose Processor

Digital Signal Processing

Signal Conditioning/ADC

Power interface/Generation

Sensing Element

Self Calibration/Active Cancellation

1”

1”

Communications

Diagnostic Processor (ASIC)

General Purpose Processor

Digital Signal Processing

Signal Conditioning/ADC

Power interface/Generation

Sensing Element

Self Calibration/Active Cancellation

The Worldvia Internet

™

LAN

Area Reasoner Operator/Maintainer

™

Intelligent Node

Intelligent Node

The Worldvia Internet

™

LAN

Area Reasoner Operator/Maintainer

™

Intelligent Node

Intelligent Node

9

Examples of commercially available versions of the smart sensor or

intelligent node are shown in Figure 7. Note that some, such as the Wilcoxon

device, integrate the sensing element (in this case, an accelerometer) with the

electronics, digitizer, radio, etc., and some, such as the Oceana device and the

PC104, would have wired or wireless connection to the sensing element, and

may provide intelligence for several sensing elements. For example, an

intelligent node for a bearing might have two or more accelerometers, two or

more proximity probes, and a temperature-sensing element all attached to one

unit, which then wirelessly communicates information to the area reasoner.

Figure 7: Currently available forms of the smart sensor or intelligent node

Wilcoxonhttp://www.wilcoxonlabs.com

Oceana Sensorshttp://www.oceanasensor.com

Rockwellhttp://www.rsc.rockwell.com

PC104 (PSU, others)http://www.arl.psu.edu

10

1.2 Why Feature Extraction? Usually, raw data cannot provide information about the vibration without

feature extraction. Generally, humans understand data by feature extraction.

For example, one might look at a vibration time waveform, intuit that the peak

amplitude is important, and extract a visual estimate of that feature. Or, one

might examine a spectrum and recognize features, such as vibration at one times

and two times operating speed. Since only a few features associated with a time

waveform or spectrum might be of real interest, transmitting the large amounts of

data associated with vibration time waveforms and spectra is a waste of precious

bandwidth. Additionally, it may lead to data overload in the transmitting network

or information overload at the receiver. Often, this overload at the receiver tends

to lead to ignoring the data. So, rather than recording and transmitting large

amounts of data, features are extracted and information is sent to the

operator/maintainer. Finally, feature extraction facilitates automated reasoning

and information fusion to aid the user/maintainer in the decision-making process.

It is the intention of the author that the reader will glean from this paper an

understanding of the overall feature extraction methodology and how it fits into a

smart sensor architecture. In addition, it is hoped that the reader will gain some

insights into specific methods of preprocessing as well as feature extraction that

will enable experimentation with feature development and evaluation. The

specific objectives of this paper are:

• Review the process of feature extraction by showing typical examples.

• Test gear tooth failure feature examples using transition-to-failure data

from the Mechanical Diagnostic Test Bed (MDTB) at the Penn State

Applied Research Laboratory.

• Compare feature effectiveness using different preprocessing schemes.

• Compare features described herein to gear tooth failure feature

algorithms currently in use for helicopter gearboxes.

• Demonstrate a data fusion method for gear tooth diagnostics.

• Present example of model-based feature extraction for tooth failure.

11

Chapter - 2 Feature Extraction Examples To demonstrate the methodology employed in feature extraction, four

statistical features (second, third, and fourth moment) and one envelope spectral

peak feature are investigated for the detection of gear tooth cracking. Note that

the third moment was not found to be useful for gear fault detection. For all of

the gearbox features, an interstitial filtering preprocessing (a high-frequency

filtering technique) step is performed before feature extraction. For the envelope

spectral peak feature, an additional preprocessing step (asynchronous

demodulation, or envelope detection) is also employed. A diversion to a fluid-film

bearing diagnostic feature is made for a demonstration of a suitable application

for skew. This chapter summarizes the preprocessing and feature extraction

steps. The process for feature extraction for gearbox faults is shown

schematically in Figure 8.

Figure 8: Schematic of interstitial processing method

2.1 Preprocessing for Gear Fault Detection Various high-frequency techniques have been used for gear fault

detection for some years10. Enveloping has been used extensively for the

AccelerometerData

Bandpass FilterBetween

Higher GMF

RectifyLowpass

FilterDFT

AnalysisPeak

Search

RMS1

3Kurtosis2

12

detection of rolling contact bearing faults in rotating machinery10, 11. High-pass

filtering prior to enveloping has often been used to enhance the ability of the

envelope detection techniques to identify faults in rolling contact bearings10.

Bandpass filtering has also been used for bearing diagnostics in systems with

significant mechanical energy in higher frequency bands, such as geared

systems12. Analogous filtering is used in some of the kurtosis-based gear figures

of merit, such as NA413 and FM414.

2.2 Preprocessing Steps

2.2.1 Interstitial Preprocessing

The preprocessing technique associated with the example feature

extraction is designed to isolate a region in the gearbox acceleration spectra that

is relatively free from the dominant periodic signals associated with gear meshing

and its sidebands. This allows the identification of enveloping signals and the

use of kurtosis for impact detection in a “quiet” region of the spectrum, where the

acceleration distribution approaches Gaussian.

The most obvious area in the spectrum that would have Gaussian

distribution is at or near the noise floor of the data. The assumption is that when

impact-like events occur which are associated with gear tooth fracture, the

broadband effects will be evident in the bandpass region. After some

experimentation with the data, it was found that the region between the third and

fourth multiple of the gear mesh frequency produced good results. To isolate this

region, a bandpass filter was employed. The filter was a forward and reverse

FIR (finite-duration impulse response) filter using a Blackman window and 501

coefficients. Figure 9 shows typical spectra of the raw and bandpass filtered

data.

13

Figure 9: Typical raw and filtered data from MDTB run

2.2.2 Asynchronous Demodulation Preprocessing

Envelope detection, or asynchronous demodulation15, of a waveform may

be used to identify low-frequency impact events that modulate high frequency

data. The process is shown schematically in Process 3 in Figure 8. The

envelope of the bandpass filtered waveform is extracted by first rectifying, then

low-pass filtering the data. The low-pass filter used in this final step was a 25-

pole Butterworth filter. The resulting waveform is then transformed using a

discrete Fourier transform (DFT). Finally, the resulting spectrum is searched for

peaks near the two gear shaft speed frequencies, and the values at these peaks

are recorded.

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14

2.3 Feature Extraction Two basic statistical features (Interstitial Kurtosis and Interstitial RMS)16

and one advance feature (Interstitial Envelope Spectral Peak) are extracted from

the gearbox acceleration data, and one statistical feature (skew) is extracted

from simulated bearing data to demonstrate feature extraction methodology.

2.3.1 Statistical Features

The features considered here are the statistical moments. The first

moment, or mean, is assumed to be zero. Often some preprocessing is required

to enforce this assumption (subtracting the average from a block of data). The

statistical moments considered are shown below. Note that the formulation of

the second, third, and fourth moments shown below assumes zero-mean data.

Further, the third and fourth moments are normalized by the square root of the

variance to the third and fourth power, respectively, which facilitates comparison

from data set to data set.

Mean = µ = N

xN

ii∑

=1 = 0 (1)

Variance = σ2 = N

xN

ii∑

=1

2

(2)

Skew = S = 3

1

3

σN

xN

ii∑

= (3)

Kurtosis = k = 4

1

4

σN

xN

ii∑

= (4)

15

2.3.1.1 Root Mean Square (RMS) Feature

The first statistical feature is obtained from the second moment (see

Equation 2). This feature is a traditional vibration feature form, root mean square

(RMS), which, for zero-mean data, is simply the square root of the second

moment (variance).

2.3.1.2 Skew

The second feature is the normalized third moment, or skew (Equation 3).

This is a measure of the symmetry of the probability distribution function (PDF).

If the median is smaller than the mean, then the distribution is said to have a

"positive" skew. If the median is larger than the mean, then the distribution is said

to have a "negative" skew. Figure 10 shows a normal (Gaussian) distribution

and both positive and negative skewed distributions. Skew is useful in identifying

un-symmetric phenomena in machinery, such as rub or impacting.

Figure 10: Skew: measure of symmetry of the probability density function

0

0.1

0.2

0.3

0.4

0.5

-5 -4 -3 -2 -1 0 1 2 3 4 5

σ

PD

F

Skew = 0 (Gaussian Distribution)Skew = +0.686Skew = -0.686

16

2.3.1.3 Kurtosis

Kurtosis, like skew, is a measure of the shape of the PDF. It is defined as

the fourth moment normalized by the square root of the variance to the fourth

power (Equation 4). Kurtosis provides a measure of the size of the tails of a

distribution, or the “peakedness” of the data. Kurtosis is a measure of whether

the data is peaked or flat relative to a normal distribution. Data with high kurtosis

tend to have a distinct peak near the mean, decline rather rapidly, and have

heavy tails. Data sets with low kurtosis tend to be flat near the mean. A uniform

distribution would be the extreme case of low kurtosis17. Figure 11 shows the

shapes for mesokurtic (labeled “normal” in the figure), leptokurtic (kurtosis >3.0),

and platykurtic (kurtosis < 3.0) probability distribution functions. Note that there

exists some differences in the way that kurtosis is defined. Some would define

kurtosis (as herein) such that the kurtosis of a Gaussian distribution is 3. Others

define kurtosis by subtracting three from the normalized fourth moment of

Equation 4. Still others term such a value, “excess kurtosis”.

Figure 11: Comparison of PDFs having the same standard deviation but different kurtosis18

One significant advantage of using a kurtosis-based feature is the fact

that, for a Gaussian (or normal) distribution, kurtosis may be shown to equal 3.0

(for a sine wave, k=1.5; for a square wave, k= 1.0). Thus, if one could find a

region in which the signal is Gaussian when there is no mechanical fault, but

non-Gaussian when there is a fault, we could have a figure of merit, which does

17

not require the establishment of a baseline, e.g., one could know whether there is

a fault without knowing the details of history of the machine.

2.3.2 Envelope Spectral Peak Feature

Envelope detection, or asynchronous demodulation19, of a waveform may

be used to identify low-frequency impact events that modulate high frequency

data. The envelope of the bandpass filtered waveform is extracted by first

rectifying, then low-pass filtering the data. The resulting waveform is then

transformed using a discrete Fourier transform (DFT). Finally, the resulting

spectrum is searched for peaks near gear shaft speed frequencies, and the

values at these peaks are recorded.

Envelope detection is best understood by first examining amplitude

modulation. Figure 12a shows a sine wave at 200 Hz modulated by a sine wave

at 5.5 Hz. The spectrum of Figure 12b shows a peak at 200 Hz, but no peak at

5.5. Rather, the 5.5 Hz modulating frequency manifests itself as sidebands of

the 200 Hz peak.

(a) (b)

Figure 12: Sine wave at 200 Hz with amplitude modulation at 5.5 Hz (a) waveform; (b) spectrum

The envelope detection process described above is then applied to the

waveform. First, the waveform is rectified by taking the absolute value. Figure

13 shows the resulting waveform and the associated spectrum. Note that the

spectrum now contains a peak at 5.5 Hz in addition to the 200 Hz peak and its

sidebands.

-1.5

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18

(a) (b)

Figure 13: Rectified sine wave at 200 Hz, amplitude modulation at 5.5 Hz (a) waveform; (b) spectrum

The final step is to pass the rectified waveform through a low-pass filter (3

dB point at 50 Hz) to remove the carrier and its sidebands. Figure 14 shows the

resulting waveform and its spectrum. The 5.5 Hz modulating frequency is all that

remains.

(a) (b)

Figure 14: Rectified sine wave at 200 Hz, amplitude modulation at 5.5 Hz After low-pass filtering (a) waveform; (b) spectrum

The above example represents the amplitude demodulation of a signal

where there is a single carrier frequency (200 Hz). To extend the example

further, we apply the same techniques to the modulation of the sum of two sine

waves of different frequencies. Figure 15a shows two sine waves, one at 200 Hz

and one at 126 Hz, modulated by a 5.5 Hz sin wave. Once again, the spectrum

(Figure 15b) shows no peak at 5.5 Hz, but both of the peaks (200 and 126 Hz)

-1.4

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19

have sidebands at 5.5 Hz. The demodulation process is applied, and the

resulting spectrum shows only the 5.5 Hz modulating frequency.

(a) (b)

(c) Figure 15: 200 & 126 Hz sine wave with amplitude modulation at 5.5 Hz (a) waveform; (b) spectrum; (c) envelope spectrum after 50 Hz low-pass filter

Finally, asynchronous modulation, or enveloping, occurs when every

frequency is modulated, implying the there would be sidebands on every spectral

line. This makes interpretation in the time domain or the raw spectrum near to

impossible. Figure 16a shows random data modulated by 5.5 Hz, and Figure

16b its spectrum. As expected, there is no discernable peak at 5.5 Hz.

However, once the demodulation process is applied, the spectrum of Figure 16c

shows the 5.5 Hz modulating frequency. Note that, when the “carrier” is random,

low-pass filtering becomes optional, since there are no discrete carrier

frequencies to remove.

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20

(a) (b)

(c) Figure 16: Random data with amplitude modulation at 5.5 Hz (a) waveform;

(b) spectrum; (c) envelope spectrum (no filtering)

This type of broadband, asynchronous modulation (or enveloping) is

known to occur in signals associated with rotating assemblies. It has proven to

be particularly useful in the diagnosis of bearing faults19, and will be shown to be

useful for gear faults herein (see Chapter 3).

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21

Chapter - 3 Experimental and Analytical Results The feature extraction techniques described in Chapter 2 are applied to

experimental accelerometer data from a gearbox test bed (Interstitial RMS,

Interstitial Kurtosis, and Interstitial Envelope Spectrum Peak features), and to

analytically synthesized fluid-film bearing data (skew feature). Interstitial RMS,

Interstitial Kurtosis, and Interstitial Envelope Spectrum Peak were found to be

good indicators of imminent damage for all runs in which gear tooth fracture

occurred. During the early runs, damage assessment was performed only at the

end of the run by post-mortem inspection, so that the actual time of tooth fracture

could only be surmised from the data. However, in the later runs, periodic optical

inspection via borescope was introduced, so that we have a much better

opportunity for correlation of features with damage. In this paper, only the results

from one of the runs (Run 14) with borescopic inspection will be reviewed.

3.1 Transitional Gear Failure Data The availability of high fidelity data associated with fault development in a

gearbox has been facilitated by the development of the Mechanical Diagnostics

Test Bed, in which off-the-shelf industrial gearboxes are run to failure. This has

created a unique opportunity to develop and tune diagnostic algorithms aimed at

the region of transition-to-failure, rather than at the failure itself, as has been

done previously for data from gearboxes with seeded faults. Such a focus may

provide earlier and better data to fuel accurate prognostic models.

The test platform used to generate the transitional data was the

Mechanical Diagnostics Test Bed (MDTB)20 (see Figure 17). This motor-driven

platform employs two digital vector drive motor motors: a 30 HP drive motor, and

a 75 HP load (absorption) motor. The MDTB has been used to date to run

commercial single-reduction gearboxes to failure by loading by a factor of two or

three over the manufacturer’s rated load. Most of the failures to date involve

22

gear tooth failures on the output gear, and a few of the gearboxes have

experience shaft failure.

Figure 17: Mechanical Diagnostic Test Bed (MDTB)

The overall test plan and operation of the MDTB are detailed in Reference

20. Basically, the MDTB is operated at normal, rated loading conditions for four

days as a “break-in” period. Then, the loading is increased by a factor of two or

three, and the gearbox is operated at that level until preset vibration levels have

been exceeded. For all the tests, postmortem examination indicated that these

levels were observed after significant damage to the gearbox had occurred.

Most of the damage was associated with gear tooth fracture, but there have been

several shaft failures as well. A close-up of the gearbox showing some of the

installed instrumentation is found in Figure 18.

23

Figure 18: Close-up of the gearbox showing accelerometer locations

3.2 Gearbox Features

3.2.1 Interstitial RMS

Interstitial RMS refers to a feature that includes the interstitial

preprocessing (bandpass filtering) of Section 2.2.1 followed by the statistical

feature extraction of RMS (Section 2.3.1.1 ). Figure 19 shows the normalized

results of the Interstitial RMS feature (12:00 on 3/18/98 in Figure 19). Note that

the gearbox was operated at its rated load for about four days for break-in. Then

the load was increased to three times its rated load to accelerate damage. It is

evident that Interstitial RMS increased significantly not only when damage

occurred, but also due to the load change.

24

Figure 19: Interstitial RMS as a function of time over the entire test (Run 14)

Figure 20 shows the same RMS acceleration after increasing load to 3X

rated load. Periodic borescopic inspection revealed no damage at 2:00 AM on

March 20, 1998. As seen in the figure, except for accelerometer 5, there is about

factor of two increase in the amplitude just prior to the onset of macroscopic

(e.g., visible via borescope) damage, which occurred between 2 and 3:00 AM on

March 20, 1998. At 3:00 AM, the first visible evidence of damage was noted in

the borescopic photographs: one tooth was broken and one showed signs of

cracking. By 5:00 AM, the second tooth had broken off, and by 8:15 AM, there

were 8-9 broken teeth. The value of the Interstitial RMS continued to rise as the

damage increased.

0

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Nor

mal

ized

RM

SAccelerometer 2Accelerometer 3Accelerometer 4Accelerometer 5Start 3X Load

25

Figure 20: Interstitial RMS as a function of time while loaded at 3X rated load

3.2.2 Interstitial Kurtosis

Interstitial Kurtosis refers to a feature that includes the interstitial

preprocessing (bandpass filtering) of Section 2.2.1 and the statistical feature

extraction of kurtosis (Section 2.3.1.3 ). Figure 21 shows the histograms of

normal (break-in) MDTB data and data at the point of highest kurtosis in a run.

Note that Figure 22 shows the broad tails of the high kurtosis data.

0

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RM

SAccelerometer 2Accelerometer 3Accelerometer 4Accelerometer 5Start 3X Load

2:00 AM: No visible damage

3:00 AM: One broken tooth, one cracked

8:15 AM: 8 teeth missing

5:00 AM: Two broken teeth

26

Figure 21: Sample histograms of MDTB gearbox data

Figure 22: Data of Figure 21 rescaled to compare tails

0

2000

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6000

8000

10000

12000

-12.0 -10.0 -8.0 -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0z (standard deviations)

M (c

ount

)Data Set 136 (k=3.07)Data Set 307 (k=22.39)

0

20

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M (c

ount

)

Data Set 136 (k=3.07)

Data Set 307 (k=22.39)

27

Figure 23 is the more intuitive plot of the product zi

4Mi, where zi is the

number of standard deviations from the mean of bin i and Mi is the number of

samples in ith bin (of I total) of the histogram. Now, kurtosis becomes simply:

∑=

=I

iii Mzk

1

4 (5)

The figure dramatically demonstrates the effects of the quartic weighting of the

distribution tails.

Figure 23: Contribution to kurtosis z4M

Figure 24 shows the Interstitial Kurtosis feature as a function of time

during Run 14. Note that the value of this feature remains at about 3.0 before

the onset of damage, and there is little sensitivity to the load increase to three

times rated load.

0.00

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0.45


Kur

tosi

s C

ontri

butio

n, z

4 M

Data Set 136 (k=3.07)Data Set 307 (k=22.39)

∑=

=I

iii Mzk

1

4

28

Figure 24: Interstitial kurtosis as a function of time over the entire test (Run 14)

Figure 25 shows the data of Figure 24 during the overload period. As with

the Interstitial RMS, the Interstitial Kurtosis performs well, and gives an indication

of a fault before macroscopic damage is observable via borescope. Periodic

borescopic inspection revealed no damage at 2:00 AM on March 20, 1998.

However, except for accelerometer 5, kurtosis already indicates a significant

change in the distribution before the damage is visible. At 3:00 AM, the first

visible evidence of damage was noted in the borescopic photographs: one tooth

was broken and one showed signs of cracking. By 5:00 AM, the second tooth

had broken off, and by 8:15 AM, there were 8-9 broken teeth. Note that kurtosis

maximized at about 4:00 AM, implying that kurtosis, although an excellent

indicator of the onset of tooth impact, may not always be a good measure of the

extent of the damage. Barkov and Barkova noted that, for rolling contact

bearings, “peaks may rise more slowly and may even decrease as impact

0

3

6

9

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15

18

21

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Date/Time

Kur

tosi

s

Accelerometer 2Accelerometer 3Accelerometer 4Accelerometer 5Start 3X Load

29

producing discontinuities are worn away”21. In fact, in other kurtosis features

kurtosis has been observed to decrease as damage increases on other gearbox

tests13,14.

Figure 25: Interstitial kurtosis while loaded at 3X rated load

3.2.3 Interstitial Envelope Spectral Peak

Figure 26 and Figure 27 show the normalized amplitude of the envelope

spectral peak at the output gear shaft speed. Note that the parameter is best

viewed using logarithmic scaling due to the significant increases in its value.

Figure 26 shows that there is about an order of magnitude increase in the

amplitude when the load is increased to three times rated load.

0

3

6

9

12

15

18

21

3/19/9812:00

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Date/Time

Kur

tosi

s


2:00 No visible damage

3:00 One broken tooth, one cracked

8:15 am: 8 teeth missing

5:00 Two broken teeth

30

Figure 26: Interstitial envelope spectral peak at output gear speed as a function of time

Figure 27 shows the normalized values of the spectral peak during the

loading at 3X rated load only. As seen in the figure, except for accelerometer 5,

there is about an order of magnitude increase in the amplitude just prior to the

onset of visible damage, which occurred between 2:00 AM and 3:00 AM on

March 20, 1998. The value of the parameter continued to rise as the damage

increased.

0.000001

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1

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31

Figure 27: Interstitial envelope spectral peak at output gear speed as a function of time while loaded at 3X rated load

3.3 Bearing Feature: Skew It was found that the skew feature did not provide meaningful information

when applied to gearbox accelerometer data during gear tooth failure. To

demonstrate the potential application of this feature, a fluid film bearing is

considered during shaft-to-bearing rub. Such rub leads to premature bearing

wear and, sometimes, catastrophic damage to the rotating equipment. Figure 28

shows a typical installation of proximity probes on a fluid film bearing22. The

resulting data from the orthogonally mounted proximity probes may be displayed

as an orbit by synchronously plotting one channel versus the other channel.

Often, diagnostics for rub are performed by visually inspecting the orbit to look for

“flat spots” associated with rub. We will examine some synthetic data to

investigate the application of skew to bearing rub diagnostics.

0.00001

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plitu

deAccelerometer 2Accelerometer 3Accelerometer 4Accelerometer 5Start 3X Load


3:00 AM:One broken tooth, one cracked



32

(a) (b)

Figure 28: (a) Typical installation of proximity probe on fluid-film bearing (Bently-Nevada)22; (b) Resulting orbit

Figure 29 shows some synthesized data with and without rub. Note that a

value of 10% is displayed to allow visualization. Actual incipient rub would be

significantly less than 10 %. To explore the sensitivity of skew to noise, we have

injected various amount of random noise to the synthesized signal, as seen in

Figure 29(b) and (c). Clearly, even with exaggerated values of rub, noise can

obscure visual interpretation of the orbit.

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-1

-0.5

0

0.5

1

1.5

33

(a) (b)

(c) (d) Figure 29: Synthesized orbit with rub and noise

Figure 30 shows a typical histogram of the synthesized data. Note that

the “double hump” distribution underlying this data is associated with sinusoidal

data. Although there is significant rub (10%) for the data associated with this

histogram, the skew is not visibly obvious.

-1.5 -1 -0.5 0 0.5 1 1.5-1.5

-1

-0.5

0

0.5

1

1.5

Normal Orbit

-1.5 -1 -0.5 0 0.5 1 1.5-1.5

-1

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0

0.5

1

1.5

Orbit with 10% Rub

-1.5 -1 -0.5 0 0.5 1 1.5-1.5

-1

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0

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1

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Orbit with 10% Rub, 14% Noise

-1.5 -1 -0.5 0 0.5 1 1.5-1.5

-1

-0.5

0

0.5

1

1.5

Orbit with 10% Rub, 28% Noise

34

Figure 30: Histogram of one channel with 10% Rub, 28% Noise

Skew was then extracted from the synthesized data. Figure 31 shows the

results. It is evident that (1) skew is a good measure of the flattening due to rub;

and (2) skew is reasonably immune to noise. Additional research is required to

demonstrate the efficacy of a skew feature in an actual fluid-film bearing system.

Figure 31: Skew as a function of percent flattened

-1.5 -1 -0.5 0 0.5 1 1.50

5

10

15

20

25

30

35

40

45

0.001

0.01

0.1

1

0 2 4 6 8 10 12 14 16 18 20

Percent Flattened

Ske

w

No Noise14% Noise14% Noise14% Noise28% Noise28% Noise28% Noise

35

Chapter - 4 Evaluation of Gearbox Features The three gearbox features (Interstitial RMS, Interstitial Kurtosis, and

Interstitial Envelope Spectral Peak) are evaluated in two ways: first, by

comparing with the more traditional preprocessing step of high-pass filtering; and

second, by comparing the experimental results for these features with the

commonly used gearbox features FM4 and NA4.

4.1 High-Pass Filtering Comparison The interstitial results for a single accelerometer (Accelerometer 2) are

compared with the more traditional high-pass filtering (3000 Hz and 5000 Hz)

results in Figure 32, Figure 33, and Figure 34. For all of the three features, the

interstitial results showed clear indications before there was any visible damage.

The parameters obtained after high-pass filtering did show evidence of damage

after the gear tooth cracking was visible. However, the interstitial parameters are

better prognostic indicators and are more robust.

36

Figure 32: Comparison of RMS using high-pass and interstitial filtering

Figure 33: Comparison of kurtosis using high-pass filtering (3000 Hz and 5000 Hz) and interstitial filtering (Accelerometer 2)

0

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RM

S

Unfiltered3000 Hz HP5000 Hz HPBandpassStart 3X Load





37

Figure 34: Comparison of enveloping using high-pass filtering (3000 Hz and 5000 Hz) and interstitial filtering (Accelerometer 2)

4.2 Comparison with Traditional Gearbox Features Several features have been developed over the years for the detection of

gear tooth failures. Most are based on time synchronous averaging (TSA)

preprocessing schemes, followed by some peak removal, and, finally kurtosis

extraction. A few, such as M6A and M8A23, use higher statistical moments (6th

and 8th respectively). TSA is usually done by interpolating the raw data, aligning

the data corresponding to one revolution at a time, averaging and then

decimating back to the original sampling frequency. It is effective in removing

information not associated with the rotation of the machine. TSA is followed by

various schemes to normalize the kurtosis (or higher moment), such as removing

the gear mesh frequency and its multiples using digital filtering, and sometimes

removing the first and occasionally the second order side bands. Again, the

primary goal of the preprocessing is to force the kurtosis to be 3.0 (corresponding

to Gaussian distribution) when there is no gear damage. It does appear that

different gear systems may require different schemes.

0.00001

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3000 Hz Highpass5000 Hz HighpassBandpassStart 3X Load





38

A number of gearbox features were evaluated on the MDTB24,25, and it

was found that the most consistent and robust were FM414 and NA413. These

two kurtosis-based features are compared to Interstitial Kurtosis in Figure 35.

Figure 35: Comparison of interstitial kurtosis with NA4 and FM4

(Normalized to 1.0)

As seen in the figure, both FM4 and Interstitial Kurtosis provide similar

early warning, and both drop off in value, with FM4 retaining its amplitude longer.

NA4 does not show as clear an early change. Note that normalization was

performed because (1) the values for NA4 were two orders of magnitude larger

than for FM4 and Interstitial Kurtosis; and (2) the values of kurtosis before

damage for NA4 had considerable scatter about the expected value of 3.0. This

is seen in Figure 36, in which normalization was not performed.

0

0.1

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0.5

0.6

0.7

0.8

0.9

1

12:00 14:00 16:00 18:00 20:00 22:00 0:00 2:00 4:00 6:00 8:00 10:00

Time

Nor

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elop

e Sp

ectr

al A

mpl

itude

at O

utpu

t G

ear S

peed

, Nor

mal

ize

RM

S

Start 3X LoadInterstital KurtosisNA4FM4

2:00 AM: No visible



5:00 AM: Two broken

39

Figure 36: Comparison of interstitial kurtosis with NA4 and FM4 (not normalized)

So, Interstitial Kurtosis and FM4 are equally good at identifying a gear

tooth fault without a baseline (due to kurtosis being 3.0 when undamaged). For

this case, NA4 did not yield the expected robust behavior of the other two

kurtosis-based features.

The extraction of Interstitial Kurtosis may be performed without a

tachometer, since the positioning of the interstitial band-pass filter may be

accomplished without a direct measure of speed. However, FM4 and NA4

require a tachometer to perform time-synchronous averaging. An effect of the

time synchronous averaging, however, is that an increase in FM4, for instance,

ensures that the fault is associated with gear meshing. Interstitial kurtosis could

be affected by other faults that manifest themselves in sharp events, such as

rolling element contact bearing flaws.

0

5

10

15

20

25

30

12:00 14:00 16:00 18:00 20:00 22:00 0:00 2:00 4:00 6:00 8:00 10:00

Time

Nor

mal

ized

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elop

e Sp

ectr

al A

mpl

itude

at O

utpu

t G

ear S

peed

, Nor

mal

ize

RM

S

Start 3X LoadInterstital KurtosisNA4FM4

2:00 AM: No visible



5:00 AM: Two broken

40

4.3 Feature Fusion None of the features employed herein are effective by themselves. Data

fusion should be performed to ensure correct interpretation of the action of

various features. For instance, if only the interstitial features were used, it would

be useful to employ some data fusion algorithms to aid in interpretation. Table 1

shows the effectiveness of the interstitial features for three important capabilities:

the ability to clearly distinguish between load change and tooth damage, the

ability to indicate imminent damage prior to macroscopically observable damage

(via the borescope), and the ability to provide indication of the extent of the

damage. It is seen that Interstitial Kurtosis provides an excellent indication of

imminent damage; however, it is not very good at providing a measure of the

extent of the damage.

Table 1: Summary of interstitial parameter effectiveness

Figure 37 shows the results of fusing a kurtosis-based feature and an

RMS based feature using fuzzy logic blending functions to provide an overall

health vector26. This kind of data fusion allows us to take advantages of the

strengths of various features and therefore track with high confidence the health

of the machine.

Interstitial Kurtosis

Interstitial Envelope Spectrum

InterstitialRMS

Able to clearly distinguish between load change and imminent tooth damage

Yes

No

No

Able to indicate imminent damage during transition to failure (prior to tooth cracking visible via borescope)

Yes

Yes

Yes

Able to provide some indication of the extent of the gear tooth damage

No

Yes

Yes

41

Figure 37: Gear component health vector based on kurtosis and RMS

4.4 Model-Based Feature Identification To further enhance the ability to correlate machine health with features,

machine models may be used. One approached being used on the MDTB is to

model the tooth cracking as a change in stiffness of the gear teeth. Figure 38

and Figure 39 show a finite element model of the MDTB gear teeth. Figure 40

and Figure 41 show the results without and with a crack. The result of nonlinear

analysis of this model was different stiffness profiles for cracked and uncracked

teeth, as shown in Figure 42.

0

1

-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0Time from Shutdown (Hours)

Nor

mal

ized

Gea

r Too

th H

ealth

Par

amet

ers 11:29 No

visible damage

14:29 Two broken teeth

17:44 8 teeth missing

12:29 One broken tooth, one cracked

42

Figure 38: Finite element model of MDTB gear teeth (with contact)

Figure 39: Detail of tooth model: a) showing elements; b) showing crack

location

Crack

43

Figure 40: Contact model of gear with no cracks

Figure 41: Contact model of gear with cracked tooth

44

Figure 42: Effective torsional stiffness profile of a cracked and uncracked tooth

The stiffness of Figure 42 may then be input to a beam model of the

MDTB shaft (Figure 43), and the model may be exercised to produce time

waveforms. To exercise the model, a constant torque is applied at the motor and

generator ends, and the variable stiffness is introduced as a spring at the gear

mesh (Figure 44). Features may be extracted from the output time waveforms

and compared to test data27,28.

0

100000

200000

300000

400000

500000

600000

700000

0 5 10 15 20 25 30

φ (Degrees)

Stif

fnes

s (in

-lb/ra

d)

Cracked

Uncracked

One Tooth

45

Figure 43: Finite element model of MDTB rotor (beam model)

Figure 44: Close up of MDTB rotor beam model showing schematically the

location of the variable spring stiffness associated with mesh

Variable Stiffness SpringRigid Links

(Constraint Equations)

Variable Stiffness SpringRigid Links

(Constraint Equations)

46

Some preliminary results of feature extraction on the waveform output

from the finite element analysis are shown in Figure 4529. Note that, for this finite

element model, only one cracked tooth was input, so that results may only be

compared to MDTB data up to the time the first tooth crack was detected via

borescope. Note further that the gears in the MDTB, which are actually helical,

were modeled as spur gears. In addition, only torsional degrees of freedom were

allowed in the rotor model. Additional modeling is required to include the effects

of the helical gear and to allow coupling of the torsional motion with translation,

which will allow direct comparison with accelerometer data.

Figure 45: Results of comparison of FM4 from MDTB test and finite element model results

0

5

10

15

20

25

3/19/98 23:00 3/20/98 0:00 3/20/98 1:00 3/20/98 2:00 3/20/98 3:00Date/Time

FM4

Experimental FM4

Model Results


3:00 AM: One broken, one cracked tooth

47

Research associated with model-based feature correlation is in its infancy.

However, the promise is great. To extend the experimental transition-to-failure

testing and correlation to a complex helicopter gearbox, for instance, would be

prohibitively expensive. However, if we are able to generate models of

experimental systems such as the MDTB and correlate experimental feature

extraction with features from the model, we will be able to understand the

relationship between extracted vibration features and damage. This

understanding may be transferred via only moderately complex models to a very

complex gear system without requiring that the complex system actually be run

to failure. This would provide immeasurable benefit to machinery OEMs,

operators and maintainers.

Another potential benefit of model-based feature development is the ability

to apply the methodology to assess the effects of changing operating conditions

on the life of a component. This allows the operator/maintainer to employ the

right machine for the right job. For example, using model-based feature

assessment and prognostics, a helicopter with damage to a bearing might be

demonstrated able to safely operate for only ten hours at full torque, but may be

permitted to continue to operate at low torque for one hundred hours. This

allows the fleet manager flexibility and facilitates full asset utilization.

48

Chapter - 5 Conclusion This paper has reviewed by example the basic methodology of feature

extraction. Facilitated by the use of actual transition-to-failure data from the

MDTB, we examined specific example features and compared the effectiveness

of various preprocessing schemes. We also compared the example features to

two features often used for helicopter gearbox diagnostics. We examined the

advantages of feature fusion and of model-based feature extraction by

considering examples. As a result, we have increased our understanding of the

overall feature extraction methodology and how it fits into a typical smart sensor

architecture.

On the basis of our increase in understanding, we arrive at the following

conclusions:

• Feature extraction emulates how a human assesses data

• Different features may be required for different failure modes.

• Feature extraction allows storage and transmission of large amounts of

information in the form of small amounts of data. This facilitates the

incorporation of large numbers of smart sensors in a system without

data/information overload.

• Feature extraction requires intelligent preprocessing. Preprocessing is

one of the most important and one of the least emphasized aspects of the

feature extraction process.

• Feature selection requires a prior knowledge of the failure process.

• Feature extraction requires automated evaluation of the condition of the

sensor, signal conditioning, etc.

• Component health evaluation may require the fusion of information from

several features.

• Model-based feature extraction will allow information gleaned from simple

systems to be applied to more complex systems.

49

Many research topics associated with feature extraction remain

incompletely explored. Nevertheless, it is evident that feature extraction, clothed

in smart sensor systems and system health management systems, is making its

way onto industrial and military platforms.

50

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Vibration Feature Extraction for Smart Sensors

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