Continuous Wavelet Transform and Neural Network for Condition Monitoring of Rotodynamic Machinery

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IEEE Instrumentation and MeasurementTechnology ConferenceBudapest, Hungary, May 21-23,2001.

Continuous wavelet transform and neural network for condition monitoring of roto-dynamic machineryT Kaewkongka, Y H J oeAu, R Rakowski andB E J onesThe Brunel Centre for Manufacturing Metrology,Brunel University, Uxbridge,MiddlesexUB83PH, UKPhone: (+44)01895274000ext.2608,E-mail: [email protected]

Abstract - This paper describes a novel method of rotodynamicmachine condition monitoring using a wavelet transform and aneural network. A continuous wavelet transform is applied to thesignals coUectedf romaccelerometer. The transformed images arethen extracted as unique characteristic features relating to thevarious types of machine conditions. I n the experiment, our typesof machine operating conditions have been investigated: a bal-anced shaft , an unbalanced shaft, a misaligned shaft and a defec-tive bearing. The back propagation neural network (BPNN) isusedas a tool toevaluate the pegormance of the proposed method. Theexperimental results result in a recognition rate of 90percent.Kevwords-Wavelet transform, neural network, rotodynamic ma-chinery.

I. INTRODUCTIONWith ever growing competition in industry, the need for ma-chine condition monitoring has become more important. Areliable condition monitoring system will significantly reducefailure and unplanned maintenance, and hence the huge atten-dant cost due to machine downtime. Often, the system isused with an operator who assists in the interpretation of themachine signals for early failure detection and fault diagnosis.Nowadays there are two kinds of methods available for bear-ing maintenance: statistical bearing life estimation and bear-ing condition monitoring and diagnostics [11. Statisticalbearing life estimation predicts the fatigue life of a bearing.However, its application has many limitations, since unusualoperating conditions can severely decrease a bearings life.Bearing life estimates become unreliable leading to unex-pected breakdown. On the other hand, bearing condition anddiagnostics canbea very reliable method because it gives up-to-date information about the condition of a bearing. Themore popular techniques used for bearing condition monitor-ing are vibration and acoustic emission analyses.

11. PREVIOUS WORKCurrently, there are many conventional methods for identify-ing and diagnosing bearing faults. Based on the representationof a signal during its processing, a method can be referred toas time-domainor frequency-domain.

Time domain methods are usually sensitive to impulsiveos-cillations. Characteristics arising fiom the defects beingmonitored, alsoknown as features, of the raw time signal canbe extracted from a machine. Typical features are the r.m.s.value, peak value[2], crest factor, kurtosis [3] and the shape,size and orientation of a bearing locus derived from orbitalanalysis. These features, once established toberelated to thedefect being monitored, often yield satisfactory results.However, if the signal generation mechanism is complex,time-domain methods are often not refined enough.Frequency domain methods assume that the signal beinganalyzed has components that are periodic. Thus, a defectproduces a periodic signal at the characteristic defect fre-quency. Examples of the frequency-domain methods includespectrum analysis, cepstrum analysis, high frequency reso-nance technique(HFRT) [4] and holospectrum[SI . Amongthem, spectrum analysis seems to dominate the fault diagnosisscene. The main limitation of spectrum analysis is that al-though a local transient will contribute towards the overallfrequency spectrum, its location on the time axis is lost.There is no way of knowing whether a particular frequencycomponent exists throughout the life of the time signal orduring just one or a few selected periods. Unfortunately,many monitoring situations demand knowledge of not just thefrequency composition of a transient but also its time ofoc-currence. For instance, when a rolling element passes a lo-calized defect in a bearing, it generates a transient in themeasured signal, as does the contact of a damaged tooth withother teeth in a gearbox. A machine with rapidly varyingspeed is another example of transient events.The continuous wavelet transform(CWT), a joint time- andfrequency-domain echnique, is proposed in this paper. CWTis capable of indicating abrupt changes in machine conditions[6]. naddition, it can give a better representation of the sig-nal than conventional methods, providing fuller informationon the machine operating condition. CWT is used here toproduce a 3-D image from the measured signal. Features arethen extracted from the image to be used as inputs to a backpropagation neural network, the tool used for assessing thediscriminatorypower of CWT.

0-7803-6646-8/01/$10.00 02001 IEEE

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5BI" a 0c I " I

U--Ea

I Feature I

7 I 7 . ' ,, I ! , , I~ "Time

WaveletTransform

sensor Hxtraction

condition

Fig. 1. The proposed condition monitoringofrotodynamic machinery block diagram.

111 METHODOLOGYThe proposed method of machine bearing faults recognit(Fig. l), using continuous wavelet transform and bapropagation neural network consistsof three steps.Step 1Applying continuous wavelet transformContinuous wavelet transform of a time-signal f(t) is definedby [71

The quantityyabt) =- t - b given in the definition isreferred to as the wavelet function. The position variablebshifts the wavelet function along the time axis t off(t) whilethe scale variablea expands or compresses the wavelet func-tion !&b(t).ComparedtoFourier transform, the scale variablea is equivalent to the inverse of the frequency. The definitionalso suggests that Fda,b) is the correlation coefficient be-tween the wavelet function !f&(t) and the time-signdf(t) atthe scaleaand positionbof K,b(t).

h ( a )

The continuous wavelet transform was applied to the accel-eration signalsfromthe four machine conditions: (a) balancedshaft, (b) unbalanced shaft, (c) misaligned shaft and (d) de-fective bearing. Samples of these signal are as shown in Fig.2.CWT was applied to these signals to calculate the coeffi-cients Fda,b), which were then displayed as a grey-scalemap with the vertical and horizontal axes denoting respec-tively the scaleaand positionb,which is equivalent to time t,as shown inFig. 3for the four different conditions. Althoughthere is general similarity between them, subtle differencesare clearly visible.

-51 J Time0 200 400 600 800 1000 1200 1400 1600 1800 200010a3

cE O

'-10E me

5UI.-E OEa me

5~ Defeciiebearing I 1-50 200 400 600 800 1000 1200 1400 1600 1800 2000

Fig.2. Acceleration signals from the four bearingconditions

Step2 PreprocessingImage preprocessing was performed using the method ofthresholding or binarising [8]. It was applied to the grey-scale CWT image to convert the colour of each pixel intoeither black or white.

(4Fig.3. Transformed mages of (a) Balanced shaft,(b) Unbalanced shaft, (c) Misaligned shaftand (d) Defective bearing

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(b)Fig. 4. The original image (a) and its binary image (b )

A binary image has the obvious advantage that whenclassification using neural networks is done, the computationtime will be much shorter, as multiplication involving a0or 1is much easier to perform. Fig. 4a and 4b show a sampleimage before and after binarising.Step 3ClassifyingThe back-propagation neural network (BPNN) [9], with thearchitecture as shown in Fig. 5, was used to classify bearingfaults. The network has an input layer, a hidden layer and anoutput layer. The values of the pixels composing the CWTbinary image provided the inputs to the neural network; and 4nodes, representing the bearing conditions of normal,unbalanced, misaligned and defective bearing were availableas outputs.Through a process of trial and error based on minimizing themean square error (MSE), the choiceof 12nodes in the firsthidden layer and 18 nodes in the second hidden layer weredetermined to be optimal.

1 1 1 1 1 1

Fig. 5 . BPNN architecture

Inputlayer

Hidden layers 1

Hidden layers 2

Output layer

Fig.6. Schematic process of BPNN

The valueNE T appearing at a node in a layer is computed bysumming the products of all inputs leading to that node withtheir corresponding weights plus a bias. This value thenforms the argument of a transfer functionf that produces anoutput for the node. In vector notation, given the input vectorX, the weight vectorW ,nd the bias vector 6, the output isgiven by

The transfer functionf is the commonly used sigmoid func-tion defined as1f =1+ (3)

The sigmoid function acts as an output gate that canbeopened(0) or closed (1). Thecomputing processas describedis schematically shown inFig. 6.The Back-propagation algorithm is used to obtain the correctweights and biases in a training process. A setof training datawithknown outputs is fed into the network. The weights areinitially set to random values; the biases are fixed at unity.The input data are presented to the network; outputs are cal-culated and compared with the desired outputs. The normal-ized mean square error (MSE) is then calculated and propa-gated back to adjust the weights on the neural connection.This process is repeated for a large number of epochs until theerror is relatively low and acceptable, which allows the net-work to classify the test set correctly.

IV. EXPERIMENTAL, VERIFICATION OF THEPROPOSEDMETHODExperiments were conducted on a rotodynamic test rig, Fig.7, consisting of a rotating shaft driven by a DC motor at 20revhec. The shaft, supported in two bearings, carried 4 discswith attachable masses in order to produce rotating unbal-ance. The two bearings were a FAG 20205K.T.C3 self-

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TableICorreation coefficient results

Baanceshaftest sets

Fig. 7. Test rig set-up

Unbaanced Misaigned Defectiveshaft shaft bearing

aligning single row taper-bore bearing and an FAG 6304 ballbearing. Radial vibration at the two bearings was measuredusing two PCB 333A12 accelerometers, one on top of thenon-drive end housing while the other on top of the drive-endhousing labeled as #1 and#2 respectively in Fig. 7.The ac-celeration signals, having been low-pass filtered at 1 kHz foranti-aliasing, were sampled into a Labview data acquisitionsystem.Measurements were obtained fkom four different machineconditions: balanced shaft, unbalanced shaft, misaligned shaftand defective bearing. For each condition, twenty signalswere collected which were divided into two equal sets of teneach. Thefirstset was used for training the neural networkwhile the second set was used for testing it.As mentioned in Step2, it was the binarisedCWT image of asignal that was being usedin training and testing. The imageconsisted of 64 scales and 250 time intervals giving a resolu-tionof 64x250=16000 pixels.

V . RESULTSANDDISCUSSIONClassification results of 40 events fi-om the accelerometersignals of all four types of machine conditions are given inTable I . It shows the output value from the back propagationneural network after the network has been trained. For thesimilar pattern, the output value is around unity, rather thanzero. In contrast, for a poor match, the value returned isaround zero.To examine the results, the maximum output is used to iden-tify the bearing condition. The symbols in the second columnfrom the left indicate the following:

I w 1 0.221 -0.011 0.001 0.791

-0.08-0.02

Defective -0.02bearing -0.05 0.00 0.42

0.24 -0.02 0.00 0.78

R = classified correctlyW = misclassified

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The signals were classified correctly36times out of 40 with arecognition rate of 90percent. However, due to the fact thatan intensity pixel being less than the threshold value had to beomitted, this brought down the recognition rate. Therefore,ifan extracted image consists of many light intensity pixels, itmay not find enough significant intensity pixelsto representthe characteristic features efficiently. In other words, theshape of the extracted image is distorted by the lack of pixelswhich contain the unique pattern for each bearing condition.Therefore, this may lead to incorrect results.VI. CONCLUSIONS

Condition monitoring of rotodynamic machinery has beeninvestigated by using the continuous wavelet transformedimage as a characteristic feature of each signal condition andthe back propagation neural network as a classification tool.Results are summarised below:1) A major contribution of this work is the introduction of anew feature extraction method and feature representation forcondition monitoring using continuous wavelet transform.Image processing techniques have been employed to removethe broadband noisefrom the signal before the final stage ofclassification is performed using a back-propagation neuralnetwork.2) The wavelet transform has the main advantage that it prc-vides information of the signal on scale (frequency) as well ason time. The transformed image therefore contains informa-tion in both time and frequency which enhances the ability todiscriminate properly between the four types of bearing con-dition.3) Theclassification error is due to the omissionof some pix-els by binarising and it is dependent on the thresholdvalue. Itis believed that if the setting of the threshold level is opti-m i s e d , a possible higher recognition rate wouldbeachieved.

ACKNOWLEDGMENTSThe authors wish to gratefully acknowledge the Royal Thaigovernment for its support, also thank Corus, Middlesbor-oughUK , which kindly provided material help and advice forexperimentation, the support of EPSRC (Grant GRh444200)and the nine industrial collaborators including theUK Na-tional Physical Laboratory within the INTErSECT FaradayPartnership Flagship Project (1998-2002) entitled AcousticEmission Traceable Sensing and Signature Diagnos-tics(AESAD)(Proect website:htt p:/ / www brunel . ac.uk/ r esearch/ bcmmaesad/ ) .

REFERENCESY . Li, S. Billington, C. Zhang,T.Kurfess,S . Danyluk andS .Liang,Adaptive prognostics for rolling element bearing condition,Mechanical Systems and Signal Processing, Vo1.13(1), pp.103-113,1999.S. Zhang,R.Ganesan, and G. D. Xisbis, Self-organizing neural networks for automated machinely monitoring systems, MechanicaSystems and Signal Processing, Vo1.10(5), pp. 517-532,1996.C.Pachaud,R. Salvetat and C. Fray, Crest factor and kurtosis contributions to identify defects inducing periodical impulsive forces, Me-chanical Systems and Signal Processing, Vol.l1(6), pp. 903-916, 1997.J. Shiroishi,Y . Li, S . Liang,T. Kurfess andS . Danyluk, Bearing condition diagnostics via vibration and acoustic emssion measurement,Mechanical Systems and Signal Processing,Vol.l1(5), pp. 693-705,1997.L. Qu, X . Liu, G. Peyronne andY . Chen,TheHolospectrum: A newmethod for rotor surveillance and diagnosis, Mechanical Systems andSignal Processing,Vo1.3(3),pp. 255-267, 1989.H Suzuki,T.Kinjo,Y . Hayshi,M. Takemoto and K. Ono, Wavelettransform of acoustic emssion signals, Joumal of Acoustic Emssion,L. Gaul andS. Hurlebaus, Identification of the impact locationonaplate using wavelets,Mechanical Systems and SignalProcessing,Rafael C. Gonzales, RichardE.Woods, Digital Image Processing,(Addison Wesley), 1993.B. A. Paya andI. I. Esat, Artificial neural network based fault diagnostics of rotating machinery using wavelet transforms as a preprocessor,Mechanical Systems and Signal Processing, Vol.l1(5), pp. 751-765,1997.

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Continuous Wavelet Transform and Neural Network for Condition Monitoring of Rotodynamic Machinery

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