VIBRATION FEATURE EXTRACTION METHODS FOR GEAR FAULTS DIAGNOSIS -A REVIEW

Transcription

1 VIBRATION FEATURE EXTRACTION METHODS FOR GEAR FAULTS DIAGNOSIS -A REVIEW Nioslav Zuber, Rusmir Bajrić, Draga Cvetković 3 Faculty of Techical Scieces, Uiversity of Novi Sad, Trg Dositeja Obradovića 6, Serbia Public eterprise Elektroprivreda BiH, Coal Mies reka, Mije eroševica, Tuzla, BiH 3 Faculty of Occupatioal Safety, Uiversity of Niš, Čarojevića 0a, 8000 Niš, Serbia Abstract - The key poit of coditio moitorig ad fault diagosis of gearboxes is a fault feature extractio. The study of fault feature detectio i rotatig machiery from vibratio aalysis ad diagosis has attracted sustaied attetio durig past decades. I most cases determiatio of the coditio of a gearbox requires study of more tha oe feature or a combiatio of several techiques. This paper attempts to survey ad summarize the recet research ad developmet of feature extractio methods for gear fault diagosis, providig refereces for researchers cocerig with this topic ad helpig them idetify further research topics. First, the feature extractio methods for gear faults diagosis are briefly itroduced, the usefuless of the method is illustrated ad the problems ad the correspodig solutios are listed. The, recet applicatios of feature extractio methods for gear faults diagosis are summarized, i terms of idustrial gearboxes. Fially, the ope problems of feature extractio methods for gear fault diagosis are discussed ad potetial future research directios are idetified. It is expected that this review will serve as a itroductio summary of vibratio feature extractio methods for gear faults diagosis for those ew to the cocepts of its applicatios to gear fault diagosis based o vibratio.. INTRODUCTION Vibratio diagosis is the most commoly used techique to moitor the coditio of gearboxes. Gearbox is oe of the core compoet i rotatig machiery ad has bee widely employed i various idustrial equipmets. Faults occurrig i gearbox such as gears ad bearigs defects must be detected as early as possible to avoid fatal breakdows of machies ad prevet loss of productio ad huma casualties. Vibratio sigal collected from these equipmets durig operatio cotais valuable iformatio about the coditio of machie coditio. The vibratio sigal is ofte a compex sigal which cotais statioary, o-statioary ad oisy compoets. Therefore, the iformatio for maiteace decisios is ot readily available from these vibratio data uless the appropriate sigal processig techiques are chose []. Differet fault diagosis methods have bee developed ad used to detect ad diagose gear faults. Oe of the pricipal tools for diagosig gear faults is the vibratio-based aalysis because of the ease of vibratio measuremets [, 3]. By employig appropriate data aalysis algorithms, it is feasible to detect chages i vibratio sigals caused by fault compoets, ad to make decisios about the gearboxes health status [4] ad gear fault evaluatio. Feature extractio is a mappig process from the measured sigal space to the feature space. Represetative features associated with the coditios of machiery compoets should be extracted by usig appropriate sigal processig ad calculatig approaches [4]. Over the past few years, various techiques icludig Fourier trasform (FT), evelope aalysis (EA), wavelet trasform (WT) ad some other time frequecy distributios were employed to processig the vibratio sigals [5, 6]. Based o these processig techiques, statistic calculatio methods, autoregressive model (AR), sigular value decompositio (SVD), pricipal compoet aalysis (PCA) ad idepedet compoet aalysis (ICA) have bee adopted to extractig represetative features for machiery fault diagosis [7]. Eve though several techiques have bee proposed i the literature for feature extractio, it still challege i implemetig a diagostic tool for real-world moitorig applicatios because of the complexity of machiery structures ad operatig coditios. This paper attempts to summarize ad review the recet research ad developmet of feature extractio methods i fault diagosis of gear faults. It aims to sythesize ad place the idividual pieces of iformatio o this topic i cotext ad provide refereces for researchers, helpig them develop advaced research i this area.. FEATURE EXTRACTION..Time-domai feature extractio The time-domai sigal collected from a gearbox usually chages whe damage occurs i a gear. Both, amplitude ad cotet may be differet from those of the time domai sigal of a ormal gear. Root mea square reflects the vibratio amplitude ad eergy i time domai. Stadard deviatio, kurtosis, crest factor ad shape factor may be used to represet the time series distributio of the sigal i the time domai. First, five time-domai features, amely, stadard deviatio, root mea square, kurtosis, crest factor ad shape factor, are calculated. They are defied as follows [8]: () Stadard deviatio (STD) STD = ( ) (x i x ) where x i (,,) is ith samplig poit of the sigal x; is the umber of poits i the sigal, ad x is the average of the sigal. 4

2 () Root mea square (RMS) RMS = (x i) (3) urtosis (R) R = (x i x ( (x i x ) (4) Crest factor (CF) max x i CF = (x i) (5) Shape factor (SF) SF = (x i) x i Despite od traditioal time domai sigal aalysis, advaced methods of gearbox vibratio aalysis deal with 5 differet forms of vibratio time waveforms: raw sigal, time sychorized ad averaged sigal, residual sigal, differetial sigal, badpass filtered timewave filtered aroud gearmesh frequecy (Figure ). Figure. Alghorithm for calculatig differet time domai features for gearbox failures detectio Time Sychroous Averagig (TSA) is a fudametally differet process tha the usual spectrum averagig that is geerally used i FT aalysis. While the cocept is similar, TSA results i a time domai sigal with lower oise tha would result with a sigle sample. A FT ca the be computed from the averaged time sigal. The sigal is sampled usig a trigger that is sychroized with the sigal. The averagig process gradually elimiates radom oise because the radom oise is ot sychroous with the trigger sigal. Oly the sigal that is sychroous ad coheret with the trigger will persist i the averaged calculatio. With TSA the result is a time domai sigal with very low oise because the averagig is performed i the time domai, ot the frequecy domai. I additio it is posible to compute a FT of the averaged time sigal resultig i a spectrum with low ) oise. Whe time domai averagig is computed o a vibratio sigal from a real machie, the averaged time record gradually accumulates the compoets of the sigal that are sychroized with the trigger. Other compoets of the sigal, such as oise ad compoets from rotatig parts of the machie are effectively averaged out. This is the oly type of averagig that actually does reduce oise i the time domai. Aother importat applicatio of time sychroous averagig is i the waveform aalysis of machie vibratio, especially i the case of gear drives. I this case, the trigger is derived from the tachometer that provides oe pulse per revolutio of a gear i the machie. This way, the time samples are sychroized i that they all begi at the same exact poit related to the agular positio of the gear. After performig a sufficiet umber of averages, spectrum peaks that are harmoics of the gear rotatig speed will remai while o-sychroous peaks will be averaged out from the spectrum. As a typical features of the time sychized sigal the above metioed parameters are used as well as aother oe, FM0 parameter. FM0 is defied as (6) FM0 FM0 = PP x H h=0 P h where PP x is the maximum peak-to-peak value of sigal x, Ph is the amplitude of the hth harmoic of the meshig frequecy, ad H is the total umber of harmoics cosidered. After processig (Figure ) other features are defied also. (7) FM4 FM4 = (d i d ( (d i d ) ) where d i is the ith measuremet of the differece sigal of the sigal x ad d is the average of the differece sigal. The shaft frequecies ad their harmoics, the meshig frequecies ad their harmoics, ad all first-order sidebads are defied to be the regular meshig compoets. By removig the regular meshig compoets from sigal x, the so called differece sigal is geerated. FM4 is actually the kurtosis of the differece sigal. It is desiged to complemet FM0 by detectig damage isolated to oly a limited umber of teeth ad supposed to work well for detectio of iitial faults. (8) NA4 NA4 = (r i r N j= )) k= ( N ( (r jk r j ) where r i is the ith measuremet of the residual sigal of time record x i ad r is the average of r i, r jk is the kth measuremet i the jth time record residual sigal r j, r j is the average of r j, ad N is the umber of time records i a ru esemble. The complete data series collected is called a ru esemble. It is further divided ito N time records each icludig data poits. The residual sigal is geerated by removig the regular meshig elemets which iclude the shaft frequecies ad their harmoics, ad the meshig frequecies ad their 4

3 harmoics. NA4 is created to overcome the shortcomig of FM4 that becomes less sesitive to the progressio of fault i both umber ad severity. For this reaso, it is supposed to be able to ot oly detect the oset of fault, as FM4 does, but also cotiue to react to the damage as it spreads ad icreases i magitude. (9) NB4 NB4 = (s i s N j= )) k= ( N ( (s jk s j ) where s jk is the kth measuremet i the jth time record evelope s j ; s j is the average of s j, ad N is the umber of time records i a ru esemble. The theory behid NB4 is that the damage o gear teeth will cause trasiet load fluctuatio that is differet from that caused by ormal teeth, ad that this ca be see i the evelope of the sigal. (0) Eergy ratio (ER) ER = (d i) (d i ) where d i is the ith measuremet of the differece sigal, ad d i is the ith measuremet of the regular meshig compoets, which iclude the shaft frequecies ad their harmoics, the meshig frequecies ad their harmoics, ad all first-order sidebads. ER is defied as the ratio of the root mea squares betwee the differece sigal ad the sigal cotaiig oly regular meshig compoets. () Eergy operator (EOP) EOP = (re i re ( (re i re ) ) where r ei is the ith measuremet of the resultig sigal re, ad re is the average of the resultig sigal. The eergy operator is the computed by takig the kurtosis of the resultig sigal... Frequecy-domai feature extractio Four frequecy-domai feature parameters are extracted from the frequecy spectrum of a gear vibratio sigal i this work. These frequecy-domai parameters may cotai iformatio that is ot preset i the time-domai feature parameters. They are defied as follows[9]: () Mea frequecy (MF) MF = X k k= where X k s the kth measuremet of the frequecy spectrum of sigal x ad is the total umber of spectrum lies. () Frequecy ceter (FC) FC = k= f kx k k= X k where f k is the frequecy value of the kth spectrum lie ad X k is the kth measuremet of the frequecy spectrum. (3) Root mea square frequecy (RMSF) RMSF = f k X k k= k= X k (4) Stadard deviatio frequecy (STDF) STDF = k= (f k FC) X k k= X k MF idicates the vibratio eergy i the frequecy domai. FC ad RMSF show the positio chages of the mai frequecies. STDF describes the covergece degree of the spectrum power..3. Time frequecy-domai feature extractio I Sectios. ad., the time ad frequecy-domai features are extracted from the vibratio sigals, respectively. I order to acquire additioal characteristic iformatio of gear damage, advaced sigal processig techiques are used. Gearboxes ofte operate uder some small fluctuatio aroud omial load/speed coditios durig their ormal service. These fluctuatios result i a variatio of both the modulatios ad their carrier frequecies (gear mesh harmoics) that blurs the sidebad compoets i the spectra of the vibratio measuremet, ofte makig it difficult to be recogized [0]. Such smearig effect ca be abated by the order trackig techique or the time sychroous averagig (TSA) that acquires the measuremets sychroized at idetical agle icremet istead of the idetical samplig period. Although TSA is a well-established techique for aalyzig gearbox vibratio sigals its commercial implemetatio is limited because of the requiremet for additioal shaft mouted ecoders to provide a measure of shaft agular positio ad sophisticated iterpolatio algorithms to resample the vibratio data. Sice such equipmet ad resources lead to icreased cost to applicatios, they are usually abset i most idustrial applicatios. I such cases, the covetioal method is to extract the measuremet over a shorter time duratio usig a slidig widow durig which the gearbox is presumed to operate uder statioary coditio. However, these shorter legth vibratio sigals are usually aalyzed usig Fourier trasforms that has limitatios such as the limited frequecy resolutio ad spectral leakage, while the small operatioal speed oscillatios cotiue to exist []. To avoid the extra cost icurred i implemetatio of TSA ad shortcomigs of the Fourier trasform based aalysis, a time domai methods wavelet trasform (WT) was recetly employed. WT is a relatively ew ad powerful tool i the field of sigal processig, which overcomes problems that other techiques face, especially i the processig of o-statioary sigals. WT is ot a self-adaptive sigal decompositio method essetially []. Combet ad Gelma have proposed optimal deoisig, usig Wieer filter based o the spectral kurtosis 43

4 (S) methodology, to ehace the small trasiets i gear vibratio sigals, i order to, detect local tooth faults such as pittig at early stage [3]. The problem of local fault detectio i gears ca be related to the more geeral problem of trasiet detectio i a sigal. I that purpose, a S detectio techique has bee proposed [4]. The S is a tool sesitive to o-statioary patters i a sigal ad that ca idicate at which frequecies those patters occur. Furthermore, the S ca be used to desig detectio filters that adaptively extract the fault sigal from the oisy backgroud [3]. From the S-based filtered residual sigal, called the S-residual, it is possible to defie the local power as the smoothed squared evelope, which ca be iterpreted as the sum of the time-frequecy eergy distributio weighted by the values of the S at each frequecy, ad so by the degree of o-statioary of the trasiets [3]. Wag [5] proposed to apply the resoace demodulatio techique which was based o evelope aalysis of the residual sigal after bad-pass filterig withi a excited resoace. Multiwavelet deoisig techiques suffer from such mai drawbacks as the fixed basis fuctios idepedet of the iput dyamic respose sigals ad the uiversal threshold deoisig [6]. This may lead to the loss of some critical but relatively weak iformatio i the fault feature detectio [6]. I order to overcome the above limitatios for effective gear fault detectio, a ovel method icorporatig the customized multiwavelet liftig schemes with slidig widow deoisig is proposed by the same authors. Proposed method outperforms various wavelet methods as well as S [6]. Higher order cumulat (HOC) aalysis is a ew techology, which has bee developed rapidly i recet years, that could be a importat tool for the processig of o-gaussia sigals, oliear sigals ad the blid sigal. Usig [7] the HOC method, this paper aalyzes sigal features of a gear system with a sigle fault ad complex fault. As the spectrum characteristics of the various faults are differet they ca be idetified from them. The results show that the method has a otable advatage i detectig the secodary phase ad higher order phase couplig characteristics of the vibratio sigal, ad is a effective method of fault diagosis for gear system. The effectiveess of the method uder low ruig coditios is good, however it decreases i the high speed state, due to each order multi-frequecy geerated by the meshig frequecy relatig to the rotatig speed that participate i the secodary ad higher order phase couplig vibratio. I the low speed state, the peaks are maily cocetrated i the low-frequecy zoe ad the fault type is easily idetified. As the speed icreases the fault feature become less obvious ad the distiguishig degree of various faults is reduced. Based o the versatility ad flexibility of Overcomplete ratioal dilatio discrete wavelet trasform (ORDWT), a fault feature extractio techique is proposed. The proposed techique [8] is applied i a rage of egieerig applicatios to extract fault features of various characteristics, icludig periodical impulses, AM/FM cotets ad trasiet vibratio cotets masked by overwhelmig oise. I the diagostic process, ORDWT is used as a pre-processig sigal decompositio tool, ad other auxiliary sigal processig approaches are employed to postprocess the recostructed wavelet sub bads of the vibratio sigals accordig to specific aalysis demads. 3. CONCLUSION This paper provides a review of the literature, progress ad chages over the years o feature extractio for fault detectio of gears usig vibratio sigal processig techiques. Time feature extractio methods try to offer more direct approach; however all of them do some sort of averagig o the sigal, which might suffer loss of time iformatio. This is a disadvatage whe operatig with sigals that have very short duratio or suddely occurrig compoet, like a sigal geerated from faulty gears. Timefrequecy techique are more advaced i localizatio of ostatioary gear fault feature from oe poit but from aother poit they are more complicate to implemet i practice. To date, various types of feature extractio methods have bee proposed. However, the questio of how to choose a suitable oe amog them to match the sigal structure remais a ope issue. REFERENCES [] H. Hog, M. Liag, Separatio of fault features from a siglechael mechaical sigal mixture usig wavelet decompositio, Mechaical Systems ad Sigal Processig, (007) [] E.B. Halim, M.A.A. Shoukat Choudhury, S.L. Shah, M.J. Zuo, Time domai averagig across all scales: A ovel method for detectio of gearbox faults, Mechaical Systems ad Sigal Processig, (008) [3] M.A. Jafarizadeh, R. Hassaejad, M.M. Ettefagh, S. 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