FAULT DIAGNOSIS OF LOW SPEED BEARING BASED ON ACOUSTIC EMISSION SIGNAL AND MULTI-CLASS RELEVANCE VECTOR MACHINE

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1 FAULT DIAGOSIS OF LOW SPEED BEARIG BASED O ACOUSTIC EMISSIO SIGAL AD MULTI-CLASS RELEVACE VECTOR MACHIE Achmad Widodo, Jog-Duk So, Bo-Suk Yag, Yog-Ha Kim, Ady C.C. Ta, Joseph Mathew Dog-Sik Gu 3, Byeog-Keu Choi 3 School of Mechaical Egieerig, Pukyog atioal Uiversity, Sa Yogdag-dog, am-gu, Busa 68739, Korea. CRC for Itegrated Egieerig Asset Maagemet, Queeslad Uiversity of Techology, George St. Brisbae, QLD 4, Australia. 3 Departmet of Mechaical ad Aerospace Egieerig, Gyeogsag atioal Uiversity, 445 Ipyeog-dog, Togyeog City, Gyeogsag am-do 65-6, Korea. achmadwid6@yahoo.com Abstract This study presets fault diagosis of low speed bearig usig multi-class relevace vector machie (RVM) ad support vector machie (SVM). A low speed test rig was developed to simulate various defects with shaft speeds as low as rpm uder several loadig coditios. The data was acquired from the low speed bearig test rig usig two acoustic emissio (AE) sesors uder costat loadig (5 k) with differet speed ( rpm ad 8 rpm). The aim of this study is addressed to search the reliable method for low speed machie fault diagosis. I this paper, two methods of multi-class fault diagosis based o classificatio techiques usig RVM ad SVM are preseted. I preset study, compoet aalysis was performed to extract the feature ad to reduce the dimesioality of origial data feature. Moreover, the classificatio for fault diagosis was also coducted usig origial data feature without feature extractio. The result shows that multi-class RVM gives promisig techique for fault diagosis of low speed machie.. ITRODUCTIO There are may idustries equipped by low speed rotatig machiery such as rollig machie i paper mill, steel pipe ad miig idustries. Also, low speed rotatig machie ca be foud i wid turbie power plat. As rotatig machiery, bearig is critical compoet ad sometimes it must carry heavy loads ad operate at high efficiecy ad reliability. Therefore, coditio moitorig ad fault diagosis of low speed bearig is very useful to guaratee the effectiveess ad reliability of this machie. Establishig itelliget system for faults detectio of low speed rotatig machie is a solutio. To face this issue, the research area i machie learig has bee applied to perform coditio moitorig, faults detectio ad classificatio. The AE method is a high frequecy aalysis techique which was iitially developed as a o-destructive testig (DT) tool to detect crack growth i materials ad structures. I the case of rollig elemet bearig, AE techique has bee studied deeply by researcher with their ow poit of view. Yoshioka ad Fujiwara have reported that AE parameters idetified bearig defects before they appeared i the vibratio acceleratio rage []. Morhai ad Mba 468

2 ICSV5 6- July 8 Daejeo Korea udertook a ivestigatio to ascertai the most appropriate threshold level for AE cout diagosis i rollig elemet bearigs []. Moreover, the research of low speed bearig moitorig also has bee coducted usig AE sesors. Aother research was coducted by Miettie ad Pataity that show the use of AE techique i moitorig of faults i extremely low speed rotatig rollig that vary from.5 to 5 rpm [3]. The result revealed that AE measuremet was very sesitive ad the fault was easily idetified uder laboratory scale. Jamaludi et al. ivestigated the applicability of AE for detectig early stage of bearig damage rotatig at. rpm [4]. It was coclude that parameters such as amplitude ad eergy provided valuable iformatio o the coditio of a particular low speed rotatig bearigs. I preset study, fault diagosis of low speed bearigs is preseted usig patter classificatio method based o relevace vector machie (RVM) [5]. Previous study by Li ad Li also has coducted bearigs fault detectio usig AE sesor [6]. However, the bearigs were rotated at high speed about rpm ad liear discrimiat fuctio of classifier was applied for fault classificatio. Moreover, we employ compoet aalysis that is aimed to support data preparatio process.. Compoet Aalysis. METHODS Compoet aalysis is a techique of multivariate statistical aalysis that ca liearly or oliearly trasforms a origial set variables ito a substatially smaller set variables. This techique has bee widely applied to virtually every substative area icludig cluster aalysis, visualizatio of high-dimesioality data, regressio, data compressio ad patter recogitio. I this research, compoet aalysis is used to extract the optimal feature ad to reduce the dimesio of origial features by meas of pricipal compoet aalysis (PCA) [7] ad idepedet compoet aalysis (ICA) [8]. This paper do ot review the theory of compoet aalysis, iterested readers are suggested to refer to the metioed papers.. Relevace Vector Machie Origially, RVM is derived ad experimeted o biary classificatio; it is desired to predict the posterior probability of membership of oe of the classes give the iput x. It follows the statistical covetio ad geeralize the liear model by applyig the logistic sigmoid fuctio σ(y) = /(+e -y ) to y(x) ad adoptig the Beroulli distributio for P(t x), the likelihood is writte as [5] = t t P( t x) = σ { y( x ; w)} [ σ{ y( x ; w)}] () However, ulike the regressio case, we caot itegrate the weights aalytically, ad so are deied the closed-form expressio for either the weight posterior p(w t,α) or the margial likelihood P(t α), with α a vector + hyperparameters. The approximatio procedure proposed by MacKay [9], which is based o Laplace s method. While metioig a extesio to multi-class problem, the origial formulatio of RVM essetially treats the K multi-class problem as a series o oe-agaist-all biary classificatio problem. This would traslate ito traiig biary classifiers idepedetly. The likelihood i Eq. () is geeralized to stadard multiomial form: K P( t w) = σ { y ( x ; w )} () = k= k k t k 469

3 ICSV5 6- July 8 Daejeo Korea where t k is the idicator variable for observatio to be i class k; y k is the predictor for class k. Moreover, a true multi-class likelihood ca be stated K P( t w) = σ{ y ; y, y,..., y (3) = k= k t k K } where the predictors of each class y k is coupled i the multiomial logit fuctio (or softmax) y k e σ ( yk ; y, y,..., yk ) = y y y (4) K ( e + e e ) Iterested readers who eed detail explaatio of this method are suggested to refer to the paper writte by Zhag ad Malik []..3 Support Vector Machie The basic idea of applyig SVM to patter classificatio ca be stated as follows: first, map the iputs vectors ito oe features space, possible i higher space, either liearly or oliearly, which is relevat with the kerel fuctio. The, withi the feature space from the first step, seek a optimized liear divisio, that is, costruct a hyperplae which separates two classes. However, this techique ca also be exteded to multi-class classificatio. A complete descriptio about SVM is available i Ref. []. I the liear separable case, there exists a separatig hyperplae whose fuctio is w x + b = (5) which implies y i (w x + b = ), i =,, (6) By miimizig w subject to this costrai, the SVM approach tries to fid a uique separatig hyperplae. Here w is the Euclidea orm of w, ad the distace betwee the hyperplae ad the earest data poits of each class is / w. By itroducig Lagrage multipliers α i, the SVM traiig procedure amouts to solvig a covex quadratic problem (QP). The solutio is a uique globally optimized result, which has the followig properties w = α i y i xi (7) i Oly if correspodig α i >, these x i are called support vectors. Whe SVM are traied, the decisio fuctio ca be writte as f ( x) = sig + α i yi ( x xi ) b (8) i= The method of low speed bearig fault diagosis is preseted i Figure. I this figure, AE sigals are acquired from the developed test rig of low speed machiery fault simulator. The acquired sigals are the preprocessed through evelopig techique to highlight the bearig characteristic frequecies. I additio, feature extractio is coducted by calculatig statistical features ad mea peak ratio (MPR) based o acquired sigals. Peak fidig is addressed to obtai the peaks of bearig characteristic frequecy after evelopig process ad the compared with calculated bearig frequecies. Frequecy comparator is aimed to validate bearig characteristic frequecy from evelopig process ad the calculated oe. Fially, fault diagosis of low speed bearigs is coducted by relevace vector machie (RVM). 3 47

4 ICSV5 6- July 8 Daejeo Korea Bearig Characteristic Frequecy Calculatio Acoustic Emissio & Vibratio Sigal Feature Calculatio Evelopig Feature Extractio Mea Peak Ratio (MPR) Frequecy Comparator Peak Fidig Fault Diagosis (RVM, SVM) Figure. Block diagram of fault diagosis scheme. 3. EXPERIMET The low speed machiery fault simulator was developed to coduct research o low speed coditio moitorig ad fault diagosis []. This test rig eables modellig of bearig ad gearbox faults uder differet loadig coditios; i particular, steady load, impact load, axial load ad rumble at low speed as low as rpm. At the drivig ed, the shaft is attached to a reductio gear box (.:) through a couplig. The costat radial load ca be applied close to the drive-ed support for log period that is measured by load cell. AE sesor (type R3a from Physical Acoustic Corporatios) with frequecy rage 5-53 khz was attached o the top of the bearig housig usig magetic holder as show i Figure.. Data acquisitio process was used to record cotiuous AE waveform. A laptop computer coected to PCI board to form the Micro-DiSP system is capable of 8-bit, MHz A/D coversio, o board processig. A total 5 waveforms were captured for each coditio for spectral averagig. Figure. Locatio of AE sesor ad accelerometer. The bearig used i this study is a cylidrical roller bearig, SKF F37, with the ier rig ad outer rig are separable. The test bearig eables a easy access to the raceway for seeded defects ad to observe the surface coditio. The faults of crack ad spall was simulated by a hair-lie scratchig usig diamod bit ad gridig usig air-speed gridig tool, respectively. All type seeded defect bearigs used i this study (Figure 4) are listed as follows: ier-race crack (IFC), ier race spall (IF), outer-race crack (OFC), outer-race spall (OF), small spall o roller (BF), medium spall o roller (BF). I additio, the ormal bearig was also experimeted for bechmarkig. Totally, we have 6 classes of faulty bearigs ad oe ormal coditio for fault diagosis simulatio. I this study, measuremet has ivolved acoustic emissio sesor. The AE techique has bee successfully applied i bearig defect detectio i the high frequecy rage over khz [4,3]. I this experimet, the sigals were acquired usig acoustic emissio sesor with a samplig frequecy of 5 khz for secod. 4 47

5 ICSV5 6- July 8 Daejeo Korea (a) (b) (c) (d) (e) (f) Figure 4. Seeded defects o the bearig: (a) IFC, (b) IF, (c) OFC, (d) OF, (e) BF, (f) BF. 4. FEATURE EXTRACTIO AD SIGAL PROCESSIG The time series sigal ca be used to perform fault diagosis by aalysig acoustic sigal obtaied from the experimet. Statistical methods have bee widely used that ca able to preset the physical meaig of time data series. For istace, the use of overall root-meas-square (RMS) ad crest factor (ratio of peak value to RMS) has bee applied for detectio of localized defects [4]. Moreover, probability desity has also popularly bee used for bearig defect detectio [5]. I preset study, statistical method is employed to ivestigate the characteristic of the system by calculatig 4 statistical feature parameters i time ad frequecy domai preseted as follows: mea, RMS, shape factor, skewess, kurtosis, crest factor, etropy error, etropy estimatio, histogram lower ad upper, peak value, RMS frequecy, frequecy ceter ad root variace frequecy. To detect rollig elemet bearig failures, we also performed evelope aalysis to show bearig characteristics frequecies by isolatig other uwated sigals. Evelope aalysis typically refers to sequece of the followig procedures: () Bad-pass filterig (BPF), () Sigal rectificatio, (3) Hilbert trasform of low-pass filterig, ad (4) Power spectrum. The purpose of BPF is to reject the low-frequecy high-amplitude sigals to elimiate radom-oise outside the pass-bad. I the preset study, we employed six bad-pass settig for evelopig: BPF: 5-5 khz, BPF: 5-5 khz, BPF3: 5-35 khz, BPF4: khz, BPF5: khz, BPF6: 75- khz. From the evelopig process, six features called mea-peak ratio [6] are calculated usig the followig equatios. mpro = ( P A ) j s j= log As (9) ( Pj As ) + ( Psi As ) j= j= mpri = log () As where b Sk k= a As = () ( b a) Figure 7 shows the evelope spectra of a outer-race defective bearig with a hair lie scratch (OFC) at a rotatig speed of 8 rpm. It shows the six evelope spectra of AE data usig 5 47

6 ) ICSV5 6- July 8 Daejeo Korea six differet bad-pass filter rages BPF~ BPF6 as metioed i previous sectio. The vertical dot-lies i the figures idicate the BPFO (4.76*8/6 = 6.35 Hz) ad its harmoics. From the AE result show i Figure 7, although the BPFO ad its harmoics are clearly visible i all bad pass filter rage, BPF5 ad BPF6 shows the most sigificat result with relatively high mpro, ad 4.75, respectively. A high mpro idicates higher peak values over the average spectrum. 4 x -8 HPF[5-5]kHz 3.53 mpro=6. 3 x -7 HPF[5-5]kHz mpro= Power spectrum (µv rms 5 x HPF[5-35]kHz mpro= x -6 HPF[35-55]kHz.54 mpro= x HPF[55-75]kHz mpro= Frequecy (Hz) Frequecy (Hz).8 x -8 HPF[75-]kHz mpro=4.75 Figure 7. Evelope spectra from OFC bearig at 8 rpm. Totally, features are calculated from 4 statistical features ad 6 features of mea-peak ratio. The features are too may for performig fault diagosis; it ca be burde ad degrade the performace of classifier. Therefore, feature extractio ad reductio usig compoet aalysis is proposed i this study. Compoet aalysis through ICA, PCA ad their kerel is expected ca highlight the saliet feature amog coditios of the machie ad reduce the dimesio of origial features. Feature reductio is performed by calculatig eigevalue of covariace matrix i the compoet aalysis [7], the the features which correlated to highest eigevalue are selected as data iput for classificatio. 5. RESULTS AD DISCUSSIO I this study, classificatio techiques through SVM ad RVM are employed for simulatig fault diagosis. SVM based multi-class classificatio is applied to perform classificatio process usig oe-agaist-oe [8]. Sequetial miimal optimizatio (SMO) proposed by Platt [9] is used to solve the SVM classificatio problem. RBF kerel (K= exp( x x j /γ ) is used as kerel fuctio of SVM to map the iput data ito feature space. To select proper kerel parameters (C, γ ), we used cross-validatio techique to obtai good performace of classificatio ad to avoid overfittig or uderfittig problem. Furthermore, RVM employs multiomial logistic regressio for multi-class classificatio. To solve the stadard multiomial form, the compoets of weights w k i Eq. () are estimated from the traiig data, ad the the ewto s method is employed to perform maximum likelihood estimatio of w k. A clear descriptio of this method is preseted by Zhag ad Malik []

7 ICSV5 6- July 8 Daejeo Korea Table shows the classificatio performace usig origial features with SVM. I this case, all classificatio results are bad, eve failed. Testig errors are high although SVM has bee performed usig RBF kerel with optimized kerel parameters by cross-validatio. Employig multi-class RVM for this case gives better performace, but they still have bad performace (Table 3). The percetage of miimum errors of RVM is.4%. The existece of irrelative features i data iput are suspected to be a reaso why the classificatio performaces are bad. Therefore, implemetatio of feature extractio ad reductio by compoet aalysis is suggested to icrease the performace of classificatio. Table Classificatio result of origial data usig SVM Sigal RBF Kerel parameters (C, γ) Testig error, % #SV AE, rpm, 5 k (,.5) AE, 8 rpm, 5 k (,.5) Table 3 Classificatio result of origial data usig RVM Sigal Testig error, % #SV AE, rpm, 5 k AE, 8 rpm, 5 k.4 87 Tables 4 ad 5 preset the result of fault diagosis based o AE sigals usig SVM ad RVM, respectively. SVM classificatio techique ad ICA feature extractio reach success with testig error.4% for AE sigal from bearig at rotatig speed 8 rpm. Aother success is also obtaied from SVM classificatio ad ICA with testig error.% for iput data from AE sigal at rotatig speed rpm. I this case, performace of PCA feature extractio is bad i producig data iput for SVM. Ucorrelated features from PCA are ot satisfied to make iput data as liear as possible for determiig hyperplae i SVM. AE Data rpm, 5k 8 rpm, 5k Table 4 SVM classificatio result of AE sigal Compoet RBF kerel aalysis parameters (C, γ) Testig error, % # SV ICA (8, ). 4 PCA (,.5) ICA (4, 4).4 39 PCA (,.5) Table 5 RVM classificatio result of AE sigal Data Compoet aalysis Testig error (%) # RV rpm, 5k ICA PCA rpm, 5k ICA.4 44 PCA I the case of fault diagosis based o RVM, ICA ad PCA feature extractio, accuracies are better tha SVM techique. Extracted feature by ICA from AE sigal at rotatig speed 8 rpm give.4% testig error. This accuracy is similar to SVM with same data. It ca be said that RVM is able to be competed with SVM techique. I additio, the performace of RVM ad PCA feature extractio outperforms SVM ad PCA techiques. The results are excellet with 6.% ad 4.8% for PCA feature extractio of AE sigal at rotatig speed rpm ad

8 ICSV5 6- July 8 Daejeo Korea rpm, respectively. These results are promisig for establishig itelliget fault diagosis of low speed bearig based o RVM classificatio techique. 6. COCLUSIO I this paper, the study of fault diagosis of low speed bearig based o AE sigal has bee preseted. Fault diagosis is coducted usig classificatio techique through relevace vector machie (RVM) ad support vector machie (SVM). The classificatio process gives a comparative study betwee RVM ad SVM i fault diagosis of low speed bearig. I this study, RVM outperform SVM based o experimetal work. REFERECES [] T. Yoshioka ad T. Fujiwara, Applicatio of acoustic emissio o detectio of rollig bearig failure, ASME Productio Egieerig Divisio Publicatio 4, (984). [] A. Morhai ad D. Mba, Bearig defect diagosis ad acoustic emissio, Joural of Egieerig Tribology, I Mech E, Part J 7(4), 57-7 (3). [3] J. Miettie ad P. Pataity, Acoustic emissio i moitorig extremely slowly rotatig rollig bearig, Proceedig of COMADEM 999, Suderlad, UK, 999, pp [4]. Jamaludi, D. Mba, R. H. Baister, Coditio moitorig of slow-speed rollig elemet bearigs usig stress waves, Joural of Process Mechaical Egieerig 5E(E4), 45-7 (). [5] M. E. Tippig, Sparse Bayesia leaig ad relevace vector machie, Joural of Machie Learig Research, -44 (). [6] C.J. Li, ad S.Y. Li, Acoustic emissio aalysis fro bearig coditio moitorig, Wear 85, (985). [7] I. J. Jolliffe, Pricipal Compoet Aalysis, Spriger, ew York, 986. [8] A. Hyvarie ad E. Orja, Idepedet compoet aalysis: algorithm ad applicatios, eural etworks 3, 4-43 (). [9] D.J.C. MacKay, The evidece framework applied to classificatio etwork, eural Computatio 4(5), (99). [] H. Zhag ad J. Malik, Selectig shape features usig multi-class relevace vector machie, Techical Report o. UCB/EECS-5-6, Uiversity of Califoria at Berkeley, 5. [] V.. Vapik, The ature of Statistical Learig Theory, Spriger, ew York, 999. [] J.C. Robertso, R.G. Caada, K.R. Piety, Vibratio moitorig o slow speed machiery: ew methodologies coverig machiery from.5 to 6 rpm, Proceedig of the Iteratioal Coferece o Profitable Coditio Moitorig, 996. [3] J. Shiroishi, Y. Li, S. Liag, T. Kurfess, S. Dayluk, Bearig coditio diagostic via vibratio ad acoustic emissio measuremets, Mechaical System ad Sigal Processig (5), (997). [4] T.I. Liu ad J.M. Megel, Itelliget moitorig of ball bearig coditio, Mechaical System ad Processig 6, (99). [5] B.A. Paya, I.I. Esat, M.. Badi, Artificial eural etwork based fault diagosis of rotatig machiery usig wavelet trasform as a processor, Mechaical System ad Sigal Processig, (997). [6] Y.H. Kim, A.C. C. Ta, J. Mathew, B. S. Yag, Coditio moitorig of low speed bearigs: a comparative study of the ultrasoud techique versus vibratio measuremet, Proceedig WCEAM 6, 6, pp. 6. [7] A. Widodo, B.S. Yag, T. Ha, Combiatio of idepedet compoet aalysis ad support vector machies for itelliget faults diagosis of iductio motors, Expert Systems with Applicatios 3(), 99-3 (7). [8] C.W. Hsu, C.J. Li, A compariso of methods for multiclass support vector machies, IEEE Trasactio o eural etwork 3(), (). [9] J. Platt, Fast traiig of support vector machies usig sequetial miimal optimizatio, i: B. Scholkopf, et al. Advaces i Kerel Methods-Support Vector Learig, MIT Press, Cambridge,