ROLLING ELEMENT BEARING FAULT DIAGNOSIS BASED ON GENETIC ALGORITHMS. Yongxiang Zhang 1, R. B. Randall 2

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1 ICSV4 Cairn Autralia 9- July, 007 ROLLING ELEMENT BEARING FAULT DIAGNOSIS BASED ON GENETIC ALGORITHMS Yongxiang Zhang, R. B. Randall School of Mechanical and Manufacturing Engineering, Huazhong Univerity of Science and Technology,Hubei, Wuhan, , China School of Mechanical and Manufacturing Engineering, Univerity of New South Wale, Sydney, NSW 05, Autralia Abtract The rolling element bearing i a key art in many mechanical facilitie and the diagnoi of it fault i very imortant in the field of machinery health monitoring. Currently the reonant demodulation technique (enveloe analyi) ha been widely exloited in ractice. However, much ractical diagnotic equiment for carrying out the analyi give little flexibility to change the analyi arameter for different working condition, uch a variation in rotating eed, and different fault tye. Becaue the ignal from a flawed bearing have feature of non-tationarity, wide frequency range and weak trength, it can be very difficult to obtain the bet analyi arameter for diagnoi. However, the kurtoi of the vibration ignal of a bearing i different from normal to bad condition, and i robut in varying condition. Secondly, a genetic algorithm have a trong ability for otimization, the author reent a model and algorithm to deign the arameter for otimal reonance demodulation uing kurtoi a a criterion. The feaibility and effectivene of the rooed method are demontrated by exeriment and give better reult than the claical method of arbitrarily chooing a reonance to demodulate. The method give more flexibility in chooing otimal arameter than another otimization rocedure baed on the fat kurtogram.. INTRODUCTION Rolling element bearing are the heart of almot every rotating machine, including lane flying in the ky and train running on track. Bearing failure can ometime caue both eronal damage and economic lo, if the fault cannot be detected and diagnoed well in advance. Therefore they have received a lot of attention in the field of vibration analyi a they rereent an area where much can be gained from the early detection of fault. R. F. Burchill et al. [] reented the method of reonance demodulation to diagnoe the fault of rolling element bearing in the 970, and the SPM Comany later develoed an intrument to detect rolling

2 ICSV4 9- July 007 Cairn Autralia element bearing fault baed on meaurement of the reonant reone of an accelerometer excited by the fault. In the firt cae, there wa a general roblem to find the otimum reonance to demodulate, to give the bet earation of the bearing fault ignal from background noie. In the econd cae, the reonance frequency ued a a carrier wa that of the accelerometer itelf (arox. 33 khz), and wa not alway otimal []. With large machine and large fault, the reonance excited are often lower in frequency than 30 khz. With evolution of the technologie of the enor, ignal roceing and engineering meaurement, many aroache have been develoed in recent year, uch a wavelet analyi, EMD (emirical mode decomoition), cetral analyi and o on [3-9]. Although thee method have added to the develoment of the condition monitoring of rolling element bearing, much ractical diagnotic equiment for carrying out the analyi till give little flexibility to change the analyi arameter for different working condition. In many cae uch a comlicated working condition and variation in the rotational eed, the diagnoi enitivity i oor. Alo back in the 970, kurtoi wa uggeted a a mean of detecting the tranient ule ariing from gear and bearing fault, but once again little guidance wa given for chooing an aroriate frequency range for filtering bearing ignal to maximize the kurtoi [0]. Currently a number of reearcher have tetified that the ectral kurtoi of the vibration of rolling element bearing can better characterize the tranient which arie from the fault in a bearing and have develoed ome aroache to diagnoe the fault of a bearing at the ame time a indicating the otimum frequency band for demodulation [-4]. Since genetic algorithm have adative feature and a trong ability to otimize arameter, thi aer reent a new aroach to detect the fault in rolling element bearing baed on a genetic algorithm and the kurtoi a a criterion.. THE CHARACTERISTICS OF ROLLING BEARING SIGNALS The key to fault diagnoi of a rolling element bearing i to cature the ecial ymtom ariing from their fault. Acceleration ignal meaured on the caing conit of two art: y ( t) = x( t) + n( t), where x (t) i the defect-induced imule reone and n (t) i the background noie, including vibration ignal generated by other comonent, uch a rotor unbalance and gear mehing. Becaue of the tructure and mode of oeration of rolling element bearing, x(t) ha ditinct feature a follow () Wide frequency: A a rolling element trike a localized defect in a very hort eriod, it excite a wide range of reonance of the tructure of the bearing ytem. For initial local defect, almot all frequencie are excited equally, but with extended all whoe urface tend to become moother with wear, not all frequency range are equally excited, and it become more imortant to find the reonance actually excited in each cae. () Small energy: The energy created by the defect i very mall, and tyically occuie le than one thouandth of the total ignal energy. A band ha to be found where the bearing ignal dominate over other comonent. (3) Nontationary ignal: Inciient bearing fault roduce a erie of reetitive hort tranient force, which in turn excite tructural reonance. Hence a reaonably veratile model for x (t) i the generalized hot noie roce []: x ( t) = X h( t τ ) where h (t) i the imule reone reulting from a ingle imact and where { X k } and {τ k}, k Z are equence of random variable which account for oibly random amlitude and random occurrence of the imact, reectively. The tochaticity of the occurrence { τ k } i caued by the random li of the rolling element, and the acing between the ule i a random k k k

3 ICSV4 9- July 007 Cairn Autralia variable that varie by aroximately % from the kinematic acing that would occur in the cae of no li. In [6] it i hown that becaue there i no memory of reviou li, the reulting ignal are not exactly cyclotationary, but can be termed eudo-cyclotationary and uefully treated a though cyclotationary. The amlitude { X k } rereent the time-varying amlitude-modulation of the imact, and tyically have a determinitic comonent caued by eriodic aage of the fault through the load zone and eriodic variation of the ignal tranmiion ath, and a tochatic comonent caued by random variation in load and bearing comonent geometry. Becaue ule are only generated by oitive force between the bearing comonent, the amlitude { X k } are alway non-negative. Becaue the ignal generated by a defective rolling element bearing have the characteritic mentioned above, it i difficult to recognize their fault through imle frequency analyi. An early develoed and widely ued technique to tackle thi iue i o-called enveloe analyi. The key to thi method i to chooe a good band-a filter. However, for fixed arameter of the band-a filter (uch a central frequency, bandwidth) which normally can t be changed with the bearing working condition, the filter choice may not alway be enitive enough for ome working condition and/or fault tye. A tyical examle i where a bearing run over a wide range of eed. When it run at very low eed, the defect may excite relatively low frequency reonance, while when it work at high eed, higher reonance frequencie may be excited. Thu, for a band-a filter with contant arameter, it can t meet the demand to detect the fault reciely for a bearing working over a wide eed range or varing condition. The kurtoi of the vibration ignal of a rolling element bearing can characterize the tranient which reult from the bearing fault, if they can be earated by an otimal filter from the background noie of harmle vibration. Hence we decide to utilize a genetic algorithm to otimize the arameter of the band-a filter uing a cot function baed on kurtoi. 3. THE ENVELOPE ANALYSIS BASED ON GENETIC ALGORITHM The key to ucceful enveloe analyi i to deign a band-a filter dynamically, whoe filter arameter can be varied with the bearing working condition. For a band-a filter, the ix arameter to be determined are that it attenuate no more than R db in the a-band, and ha Outut R R W W W W Fig Band-a Filter Sketch Ma Frequency at leat R db of attenuation in the to-band, W,W and W, W are the a-band and to-band edge frequencie, hown in Fig. Previouly thee arameter were choen according to ractical exerience; here we elect them uing a genetic algorithm, which ha the

4 ICSV4 9- July 007 Cairn Autralia ability to earch the otimal olution over the whole zone and give fat convergence to olve the roblem, in articular for nonlinear otimization roblem. The cheme for olution of the roblem i hown in Fig. Vibration Signal To generate GN band-a filter randomly according to genetic rule To feed vibration ignal to GN filter, and filter the ignal To take the enveloe of the filtered ignal, and obtain their ectra To calculate the kurtoi of the ectra of the filtered ignal Doe the kurtoi reach maximum? No Ye To contruct new generation of GN band-a filter by croover, mutation and heredity baed on the fitne of kurtoi To obtain the otimal filter To filter the vibration with the otimal filter, do enveloe analyi and obtain the enveloe ectrum of the bearing To diagnoe the fault of the bearing from the ectrum Fig The flow chart of the genetic algorithm (GN = genotye oulation) 3. Exreion of the arameter of a filter by the genotye The arameter of a filter mut be exreed by the genotye for a genetic algorithm. Here we rooe a coding aroach for the genotye baed on binary bit. We ue 49 binary bit to exre a filter, where R occuie even bit from the firt to the eventh bit, R occuie two bit from the eighth to the ninth bit, W, W, W, W each occuy ten bit and the order arrangement are the ame a R and R, the exreion being hown a follow. ******* ** ********** ********** ********** ********** R R W W W W Where * tand for 0 or. The genotye ha the relationhi with R, R, W, W, W and W hown by formula () to (6).

5 ICSV4 9- July 007 Cairn Autralia 7 i R = chrom() i () i= i R = chrom( i + 7) () i= 0 i ( 39) F W = chrom i + 04 (3) i = 0 i W = chrom( i + 9) W 04 (4) i= 0 i W = chrom( i + 9) W 04 (5) i = 0 i W = chrom( i + 9) W 04 (6) i= In the formula () to (6), F i amling frequency, chrom(i) tand for the binary bit of the genotye. Hence, if the genotye of a filter ha been determined, the arameter of a filter will be elected comletely. 3. Genetic algorithm oeration After the formula of the filter ha been exreed by genotye, the genetic algorithm can be carried out a follow. () Initial grou of genotye For tarting the genetic algorithm oeration, the initial grou of genotye mut be randomly generated. The ize of the genotye oulation (GN) i decided by exerience. From exeriment, we find that 40 GN 00 i uitable. In thi aer GN i equal to 60. () Fitne of genotye The fitne of a filter i an indicator to ditinguih the fault effectively for different bearing working condition. The advantage of the kurtoi a fitne arameter i that it take high value in the reence of the fault ignal x(t), wherea it i ideally zero when only background noie n(t) i reent. Thi i true when the imule reone generated by the imact are ufficiently well earated and when the ignal-to-noie ratio i ufficiently high. A a matter of fact, background noie often embodie trong vibration from everal cometing ource (e.g. harmonic of rotating art, random imule from friction and contact force, flow noie, etc.) which an a large frequency range and eriouly mak the ignal of interet. A a reult, the kurtoi i unable to cature the eakine of the fault ignal and hardly deart from a value of zero. In thi ituation, the kurtoi a a global indicator i not aroriate, and it i referable to aly it locally in different frequency band. Thi i exactly what the ectral kurtoi doe. According to Ref.[4], if y i the quared enveloe, then the ectral kurtoi can be calculated uing equation (7), to give a ingle value for each filter. mean( y ) kurtoi ( y) = (7) ( mean( y)) The value i ubtracted here to obtain a value zero for the quared enveloe of Gauian noie. The bet filter i choen a the one that give the highet value of kurtoi. Thi filter i retained and then re-ued to obtain the quared enveloe ignal and the quared enveloe ectrum. (3) Relicate

6 ICSV4 9- July 007 Cairn Autralia The artial children genotye come from the relication of the arent genotye, (whoe robability of fitne i higher the value P (relicative robability). The fitne robability λ i of a ignal from a filter i a follow q j Kurtoi( j) λ j =, q = q j (8) GN max Kurtoi( j) GN Here qmax = max( q j ), j =,, KGN. If λ j i larger than P, the genotye will be retained in the children genotye. (4) Croover A croover oeration i to chooe a air of arent genotye randomly, and according to two random number N and N (<N < N< 49) exchange egment bit of two genotye from the N-th bit to the N-bit reectively. The croover robability Pc i elected by exerience, hence the children genotye i GN * Pc/. (5) Mutation A mutation oeration i to elect Pm*GN arent genotye according to mutation robability Pm, then change each bit from original to 0 or original 0 to to form children genotye. (6) Terminating condition The genetic algorithm oeration i terminated when atifying one of the following condition: (a) The maximum value of the fitne doen t change during certain generation. (b) The fitne i larger than a given value. For examle, if kurtoi(y) > 5, the fault of a bearing can be recognized by exerience. j= 4. EXPERIMENTAL INVESTIGATION In order to tetify the feaibility and effectivene, ignal were ued that had been collected by N. Sawalhi at The Univerity of New South Wale. In the tet rig, a ingle tage gearbox i driven rimarily by a 3-hae electric motor, but with circulating ower via a hydraulic motor/um et. The inut and outut haft of the gearbox are arranged in arallel and each haft i uorted by ball bearing (Koyo 05), one of which i ued for invetigation. A rough fault wa introduced into the inner race of the ball bearing. Thi wa erformed uing electric ark eroion and generated a rough urface over half the inner race. The ignal were collected at a eed of 600 rm uing an accelerometer oitioned on the to of the gearbox caing near the bearing. It had reviouly been found that thi extended rough fault wa difficult to detect by conventional enveloe analyi. A tyical exerimental reult i hown in Fig 3. The defect frequency at which the ball ae the defect on the inner race (BPFI) can be etimated a 7. Hz at the eed 600 rm and the ule erie i modulated by the haft eed 0 Hz. According to the reviou analyi, we deigned a filter baed on the genetic algorithm, for which the arameter of the genetic algorithm are: GN=60, P = 0.59, Pc = 0.4, Pm = 0.0. A exlained above, when the kurtoi of the enveloe ignal reache, the fault ignal caued by a defective rolling element bearing can be earated from the background noie, o the target kurtoi i aumed to be 5. The arameter for the otimal filter were found to be: R = 3.9 db, R = db, W = khz, W = 4. khz, W =. 37 khz, W = 6.88 khz. When the vibration ignal i filtered by the otimal filter and then enveloe analyzed, the enveloe ectrum of the defect bearing i illutrated in Fig 3, and the kurtoi reache 3.6. From Fig 3(b), it i verified that the ectrum of the original vibration ignal cannot detect any bearing fault indication, while the ectrum from the enveloe analyi of the

7 ICSV4 9- July 007 Cairn Autralia otimal filter ignal not only eliminate the trong gear vibration ignal but alo indicate the defect frequency 7 Hz (including it econd and third harmonic frequencie 4Hz and 3Hz) urrounded by ideband aced at haft eed 0 Hz. Therefore according to thi information we can determine the fault and it location in the bearing, a well a the everity of the fault uing the amlitude of the ectrum. On the other hand, uing traditional enveloe analyi with the arameter of W = khz, W = khz (choen becaue there i a local reonance in the ectrum in thi range) we ee in Fig. 4 that we cannot get the deired reult for the ame ignal, ince the enveloe ectrum i dominated by harmonic of haft eed, in articular the gearmeh frequency (harmonic 3). We alo ued the fat kurtogram method [5] to roce the ame ignal, and obtained a omewhat imilar reult, however, it hould be realized that the fat kurtogram ha a limited range of oible centre frequencie, in articular when the bandwidth i wide. The total frequency band i divided ucceively into, 4, 8.etc band, which thu ecifie the centre frequencie for each bandwidth, wherea uing the GA method of thi aer, the centre frequency,bandwidth and lower and uer edge of the filter are otimized indeendently Fig 3 The vibration ignal and their ectra for a defect bearing (inner defect) (a) Original vibration ignal (b) The amlitude ectrum of original ignal (c) The amlitude ectrum of the band-a filter (d) The ignal filtered by the BP filter (e) The enveloe ignal (f) The enveloe ectrum Fig 4 Traditional enveloe analyi (a) The ignal filtered by the traditional BP filter (b) The traditional enveloe ectrum

8 ICSV4 9- July 007 Cairn Autralia 5. CONCLUSION In thi aer, the author reent an aroach for diagnoi of rolling element bearing baed on kurtoi of the bearing tranient ignal and a genetic algorithm to elect an otimum banda filter. The advantage are firtly that becaue the ectral kurtoi of the bearing vibration ignal robutly indicate the tranient correonding to the bearing fault, it i a good dynamic fault indicator under comlicated bearing working condition. Secondly the genetic algorithm baed on ectral kurtoi ha a trong ability to otimize the arameter for the enveloe analyi very fat and with minimal contraint on centre frequency and bandwidth. The exerimental invetigation ha tetified the feaibility and effectivene in comarion with traditional enveloe analyi and even with an alternative otimization method baed on the fat kurtogram. 6. ACKNOWLEDGEMENTS The firt author wihe to exre hi gratitude to The China Scholarhi Council for financially uorting him a a viiting rofeor at The Univerity of New South Wale. REFERENCES [] R. F. Burchill, Reonant tructure technique for bearing fault, Proceeding of Mechanical Failure Prevention Grou, Novemember 97, Gaitherburg, Md.. [] H. Engja, J. Lie, Vibration analyi ued for detection of roller bearing failure, Norwegian Maritime Reearch 3, 3-33(977). [3] Huang Dihan, A wavelet-baed algorithm for the Hilbert tranform, Mechanical Sytem and Signal Proceing0(),5-34(996) [4] P. Te, Y.H. Peng, R. Yam, Wavelet analyi and enveloe detection for rolling element bearing fault diagnoi their effectivene and flexibility, Journal of Vibration and Acoutic 3 (3), (00). [5] J. Altmann, J. Mathew, Multile band-a autoregreive demodulation for rolling-element bearing fault diagnoi, Mechanical Sytem and Signal Proceing 5 (5), (00). [6] J. Antoni, R.B. Randall, Differential diagnoi of gear and bearing fault, Journal of Vibration and Acoutic 4 (), 65 7(00). [7] Cheng Junheng, Yu Dejie, Yang Yu, A fault diagnoi aroach for roller bearing baed on EMD method and AR model,mechanical Sytem and Signal Proceing 0, (006) [8] N.E. Huang, et al., The emirical mode decomoition and the Hilbert ectrum for nonlinear and non-tationary time erie analyi, Proceeding of the Royal Society of London A 454 (998) [9] Yuh-Tay Sheen, Chun-Kai Hung, Contructing a wavelet-baed enveloe function for vibration ignal analyi, Mechanical Sytem and Signal Proceing 8, 9 6(004). [0] D. Dyer, R. M. Stewart, Detection of rolling element bearing damage by tatitical vibration analyi, Journal of Mechanical Deign 00, 9-35(978). [] Jérôme Antoni, The ectral kurtoi: a ueful tool for characterizing non-tationary ignal, Mechanical Sytem and Signal Proceing 0, 8 307(006). [] Jérôme Antoni, R.B. Randall, The ectral kurtoi: alication to the vibratory urveillance and diagnotic of rotating machine, Mechanical Sytem and Signal Proceing0, (006). [3] Jérôme Antoni, Fat comutation of the kurtogram for the detection of tranient fault, Mechanical Sytem and Signal Proceing, 08 4(007). [4] N. Sawalhi, R. B. Randall, H. Endo, The enhancement of fault detection and diagnoi in rolling element bearing uing minimum entroy deconvolution combined with ectral kurtoi, Mechanical Sytem and Signal Proceing, In re (007).