Faults Classification of a Scooter Engine Platform Using Wavelet Transform and Artificial Neural Network

Transcription

1 Proceedgs of the Iteratoal MultCoferece of Egeers ad Computer Scetsts 9 Vol I IMECS 9, March 8 -, 9, Hog Kog Faults Classfcato of a Scooter Ege Platform Usg Wavelet Trasform ad Artfcal Neural Network J.-D. Wu, E.-C. Chag, S.-Y. Lao, J.-M. Kuo ad C.-K. Huag Abstract Ths paper descrbes the developmet of a mechacal fault dagoss system for a scooter ege platform usg cotuous wavelet trasform ad artfcal eural etwork techques. Most of the covetoal techques for fault dagoss a mechacal system are based prmarly o aalyzg the dfferece of sgal ampltude the tme doma or frequecy spectrum. I the preset study, a cotuous wavelet trasform (CWT) algorthm combed wth a feature selecto method s proposed for aalyzg fault sgals a scooter fault dagoss system. The artfcal eural etwork techque usg back-propagato ad geeralzed regresso are both used the proposed system. The effectveess of the proposed system usg two algorthms CWT techque for scooter fault dagoss are vestgated ad compared. The expermetal results dcated that the proposed system acheved a fault recogto rate over 95% the expermetal platform of scooter fault dagoss system. Idex Terms Fault dagoss system, Cotuous wavelet trasform, Artfcal eural etwork. I. INTRODUCTION Wth the rapd growth of sgal processg techology, the vbrato ad soud emsso sgals ca be used to motor the codto of a mechacal system. A effectve codto motorg ca prevet serous damage. There exst a umber of fault dagoss techques the feld, ad most of the covetoal techques are used to observe the ampltude dfferece tme or frequecy doma for damage dagoss. Meawhle, order-trackg aalyss s also used to avod the smearg problem frequecy-varyg sgals []. Ufortuately, most of the covetoal approaches are dffcult to deal wth the case where the machery operates uder o-statoary rotatoal speed, s based o the assumpto of statoary sgals, ad s heretly usuted for o-statoary. Tme-frequecy aalyss ca be used to mprove the drawback of the Fourer trasform. The prmary Mauscrpt receved October 9, 8. Ths work was supported the Natoal Scece Coucl of Tawa, the Republc of Cha, uder project umber NSC-97--E-8-8. J.-D. Wu s wth the Isttute of Vehcle Egeerg, Natoal Chaghua Uversty of Educato, Chaghua 5, Tawa (correspodg author phoe: ; e-mal: jdwu@cc.cue.edu.tw). E.-C. Chag, S.-Y. Lao, J.-M. Kuo, C.-K. Huag were wth the Isttute of Vehcle Egeerg, Natoal Chaghua Uversty of Educato, Chaghua 5, Tawa. advatage of tme-frequecy aalyss s the represetato of sgals both the tme ad frequecy domas. The short tme Fourer trasform (STFT) has bee appled to aalyze the sgals of the fault both the tme ad frequecy domas []. However, STFT has a lmtato of tme resoluto because of usg fxed tme wdows. O the other had, the cotuous wavelet trasform wth a adjustable wdow sze has bee prove to have hgher effcecy accurate formato of aalyss sgals. The cotuous wavelet trasform (CWT) wth more precse tme resoluto ca mprove the performace of STFT. Research terest mechacal fault dagoss usg wavelet aalyss has developed the last few decades. The wavelet aalyss techque has become oe of the mportat approaches the feld of mechacal fault dagoss. I 993, Wag ad McFadde used wavelet aalyss the gear vbrato sgals ad detected dfferet types of faults, ad the results exhbt wavelet trasform s effectve codto motorg of gear health [3],[4]. I 995, Newlad derved a harmoc wavelet techque ad appled t to traset aalyss of vbrato sgal [5],[6]. I, L preseted a de-osg method based o Morlet wavelet appled fault dagoss [7]. I 4, Meltzer ad De aalyzed the effectveess of the CWT acoustcal dagostcs of gearboxes by plottg wavelet ampltude versus the rotatoal agle polar coordates [8]. I 5, Ya ad Gao preseted a approach to mache codto motorg ad health dagoss, based o the dscrete harmoc wavelet packet trasform (DHWPT) [9]. I, L et al. preseted a approach for motor rollg bearg fault dagoss usg eural etworks ad bearg vbrato aalyss []. I 4, Che ad Mob developed a method of tellget fault dagoss usg eural etwork classfer for detfyg the faults of rotatg machery []. I 5, Yag et al. developed a advaced sgal classfer for small recprocatg refrgerator compressors artfcal eural etworks ad support vector mache []. I the preset study, the CWT techque ad tme-frequecy aalyss are used to extract the feature of the dyamc characterstcs ad fault sgal from a scooter. The dagostc trouble code of a scooter ca be obtaed by usg spectrum tred feature method. A fault recogto techque based o eural etworks of back-propagato ad geeralzed regresso for a scooter health dagoss s preseted. Neural etworks classfers have a prove ablty the area of olear patter recogto by learg ad adaptg to the put from the scooter fault. Both of the eural etworks are ISBN: IMECS 9

2 Proceedgs of the Iteratoal MultCoferece of Egeers ad Computer Scetsts 9 Vol I IMECS 9, March 8 -, 9, Hog Kog used to verfy the effectveess of the preseted fault dagoss algorthm. There are three phases the preset fault dagoss system: the data acqusto phase, the feature extracto phase ad the fault classfcato phase, as show Fg.. I the feature extracto, the dagostc techque employs the wavelet trasform to decompose the tme-waveform sgals to two respectve parts the tme space ad frequecy doma ad to obta the feature of aalyss sgals. I the fault classfcato phase, the desg of the eural etwork dagoss algorthm s preseted to detfy the faults of the scooter. The prcples of wavelet trasform ad eural etwork the proposed system are descrbed the followg sectos. II. FEATURE EXTRACTION USING WAVELET TRANSFORM The wavelet trasform uses a seres of oscllatg fuctos wth dfferet frequeces as wdow fucto to sca or traslate the aalyss sgal. The wavelet techque has partcular advatages for characterzg sgals at dfferet localzato levels tme as well as frequecy domas. The wavelet algorthm used ths study s based o the results orgally developed by Goupllaud et al. [3],[7]. The prcples of cotuous wavelet trasform ad spectrum tred feature are descrbed the followg sectos. Let ψ () t be the basc wavelet fucto or mother wavelet, the correspodg famly of daughter wavelets cosst of t-b = a -/ ψ () ab, t a ψ where a s the scale factor ad b the tme locato, ad the -/ factor a s used esure that the eergy of the scaled ad traslated versos are the same as the mother wavelet. The wavelet trasform of sgal x() t s defed as the er product the Hlbert space of the L orm as follows: -/ * ab, ψ ab, W( a, b) = ψ (), t x() t = a x() t dt () Here the astersk stads for complex cojugate. Tme parameter b ad scale parameter a vary cotuously. The mother wavelet ψ () t s assumed to le L ( C) ad satsfes the admssblty codto: C = ˆ ψ ψ( ω) / ω d ω < - where L ( C) s the space of square tegrable complex fucto ad ψˆ ( ω) dcates the Fourer trasform of ψ () t. Wavelet coeffcets measure the smlarty of the sgal ad each daughter wavelet. I ths study, the Morlet wavelet [4] s used as the basc wavelet for feature extracto. Whe a wavelet fucto s chose, t s ecessary to decde the scales the wavelet trasform. For CWT aalyss, a arbtrary set of scales ca be used to buld up complete formato. I ths study, the scales are wrtte as follows: j δ j a = a, j =,,, J (4) j () (3) where a = δ t s the smallest resolvable scale ad δ j =.5, J=6. The choce of δ j deped o the wdth spectral space of wavelet fucto ad J determes the largest scale, δ t s the samplg terval. Whe the samplg frequecy s set as khz, the scales ca be obtaed the rage of. to 5..The cotuous wavelet power spectrum s defed as W( a j ). The tme-averaged wavelet spectrum s proposed to exhbt the dstrbuto of eergy of wavelet power spectrum the drecto of scale, s defed as j j N = N - W( a ) = W ( a ) (5) N,,,, where s the umber of samplg pots, j = J. I the applcato of fault dagoss, the sgal s sampled radomly ad the revoluto of the ege s ot stable, the eergy dstrbuto of tme average wavelet spectrum (TAWS) s dfferet from each other eve the same fault codto. I order to avod such a codto, a spectrum tred feature method s developed. By studyg the spectrum dstrbuto of varato for each fault spectrum, oe ca defe a rased tred of spectrum as ad a dropped tred of spectrum as betwee two eghbor scales. The feature vector ca be defed as follows: ( j+) W ( aj) ( j+) W( aj), W a > x(j)=, W a The feature vector s dagostc trouble code as the put for the fault classfcato usg eural etworks. Data acqusto Feature extracto (wavelet trasform) Fault detecto (eural etworks) Acoustc emsso sgals Feature vectors j =,,,, J - Data recorder Tme doma aalyss Frequecy aalyss Tme-frequecy aalyss Fault decso Fault classfcato Fgure Procedure of scooter fault dagoss. III. FAULTS CLASSIFICATION USING NEURAL NETWORKS I the desg of scooter fault dagoss schemes, a recogto method of scooter fault codto usg eural etworks s vestgated to evaluate the effectveess of the select feature set for a scooter dagoss. To determe f the proposed fault dagoss algorthm s able to correctly recogze dfferet scooter fault codtos s essetal. I ths paper, a multp percepto classfer traed wth error back-propagato algorthm ad geeralzed regresso eural etwork are used the fault dagoss system. The (6) ISBN: IMECS 9

3 Proceedgs of the Iteratoal MultCoferece of Egeers ad Computer Scetsts 9 Vol I IMECS 9, March 8 -, 9, Hog Kog expermetal comparso ad aalyss of the two algorthms are also descrbed scooter fault dagoss. The eural etwork usg a multp percepto classfer wth error back propagato (BP) algorthm based o supervsed learg rule s appled for trag ad testg the classfer the preset study [6]. A three- feed forward etwork wth sgmod actvato fucto s cosdered the frst fault classfcato. I the structure, each has a certa umber of odes ad all odes oe are coected wth all the other odes the succeedg, as show Fg.. Assocated wth each coecto, a umercal value s assged, whch s termed as weght. Iputs are submtted durg the BP algorthm trag sequetally. Durg the trag procedure, the weght ad bases of the etwork are teratvely adjusted to mmze the etwork performace whch s the mea square error betwee the etworks outputs ad desred outputs. The gradet descet search s performed to reduce the error through the adjustmet of weghts. The error s back propagated to chage the output ad hdde weghts. Ths trag process s repeated utl a sutable error s acheved. The trag process eeds a set of trag examples to update the weghts of the etwork. Provdg suffcet trag data s essetal order to esure accuracy of the classfer. Oce the etwork s suffcetly traed, the kowledge of the eural etwork wll perform the fault detecto. Feature Extracto Dagostc Trouble Code Network Trag Network Testg x x Iput sgals 3 w w j Error sgals l y y l value of y, gve oly a trag set. Assume that the f ( x, y ) represets the kow jot cotuous probablty desty fucto of a vector radom varables, x, ad a scalar radom varable. Let X be a partcular measured value of the radom varable x. The codtoal mea of y gve X s gve by E y X = - - yf ( X, y)dy f ( X, y)dy Whe the desty f ( x, y) s ot kow, t must usually be estmated from a sample of observatos of x ad y. The probablty estmator f ( X, Y) s based upo sample values X ad Y of the radom varables x ad y, where s the umber of sample observatos ad p s the dmeso of the vector varable x: f ˆ( X, Y )=( ) (P+)/ (P+) π σ T = ( X-X ) ( X-X ) ( Y-Y ) exp - exp - σ σ A physcal terpretato of the probablty estmate f ˆ( X, Y) s that t assgs sample probablty of wdth σ for each sample X ad Y, ad the probablty estmate s the sum of those sample probabltes. Defg the scalar fucto T ( ) ( ) D=X-X X-X (9) ad performg the dcated tegratos yelds the followg: D Y exp - σ D σ = ˆ( )= exp - = Y X (7) (8) () x Fault Decso Fgure Structure of back-propagato algorthm for fault dagoss. The geeralzed regresso eural etwork (GRNN) was proposed by Specht [6]. It s a oe-passg learg algorthm whch ca be used for estmato of cotuous varables. The GRNN does ot requre a teratve trag procedure to coverge to the desred soluto as BP eural etwork. It approxmates ay arbtrary fucto betwee put ad output vectors, drawg the fucto estmate drectly from the trag data. If the varables to be estmated relate output to put varables, the GRNN ca be used to model the system, as stadard regresso techques. By defto, the regresso of a depedet varable y o a depedet x estmates the most probable value for y, gve x ad a trag set. The GRNN s a method for estmatg the jot probablty desty fucto (PDF) of x ad y, order to produce the estmated Whe the smoothg parameter σ s made large, the estmated desty s forced to be smooth ad the lmt becomes a multvarate Gaussa wth covarace σ I. O the other had, a smaller value of allows the estmated desty to assume o-gaussa shapes, but wth the hazard that wld pots may have too great a effect o the estmate [4]. Fg. 3 shows the block dagram of the GRNN archtecture whch s dfferet from the archtecture of BP algorthm. The GRNN cossts of four s: put, patter, summato ad output. The put uts are merely dstrbuto uts the frst. The secod has the patter uts that are dedcated to oe cluster ceter. The outputs of the patter are passed o to the summato uts the thrd. The summato uts perform a dot product betwee a weght ad a vector from the patter. The fal covers the output uts. ISBN: IMECS 9

4 Proceedgs of the Iteratoal MultCoferece of Egeers ad Computer Scetsts 9 Vol I IMECS 9, March 8 -, 9, Hog Kog..5 x x Ŷ(X) x Ampltude p Iput Patter Summato Output Fgure 3 Block dagram of GRNN algorthm. IV. EXPERIMENTAL INVESTIGATION OF FAULTS CLASSIFICATION I order to evaluate the proposed algorthms faults classfcato, a expermet s carred out to verfy the performace by measurg soud emsso sgals varous ege operato codtos. The soud emsso sgal of a scooter ege platform s measured by a mcrophoe, a data acqusto system ad subsequetly aalyzed usg CWT algorthm. After extractg the features of wavelet power spectra, the feature vectors are selected for the fault classfcato usg eural etworks. The expermetal setup of the scooter fault dagoss system s show Fg. 4. The measurg apparatus used the expermet cossts of a mcrophoe (PCB 3D), a data acqusto system (NI-64E), a optcal ecoder (PW-PH) for shaft speed measuremet ad dyamc sgal aalyzer (SR785). The soud sgal s recorded from the scooter uder wthout fault codto ad four dfferet fault codtos fve fxed ege revolutos ad a ru-up ege operato codto. The expermet s coducted by usg four sythetc faults, cludg leakg of the take mafold, pulley damaged, belt damaged ad clutch damaged. The samplg rate of the data acqusto system s khz. Acoustc emsso sgals tme doma that were measured uder dle codtos (8 rpm) are show Fg. 5. Mc. Data Data acqusto system Fber optcal optcal sesor sesor Dyamc sgal aalyzer Acoustc Acoustc emsso emsso sgal sgal Tachometer sgal sgal Fault dagoss system system Fgure 4 Expermetal arragemet of scooter fault dagoss system. (e) Ampltude p p Tme (sec) Fgure 5 Soud emsso sgals measured from a scooter. wthout fault; leakage take mafold; pulley damaged; belt damaged; (e) clutch damaged. I order to evaluate the effectveess of the CWT for scooter fault dagoss, soud emsso sgals from each fault codto are aalyzed. The expermetal results of scooter wthout fault 8rpm ege speeds usg CWT represetato are show Fg. 6, whch preset the eergy dstrbuto of the soud emsso sgals tme-frequecy doma. The expermetal results of the other four faults 8rpm ege speeds are dcated Fg. 7. However, a ege practcal codtos may be operated by rug up or coastg dow. I the expermet of rug up vestgato, the ege operated at revolutos from 8 to 49 rpm. The expermet results of ru-up rotatoal speed codto usg CWT algorthm are dcated Fg. 8. O the bass of the tme-frequecy features thus obtaed, the trasets of the ru-up process ca be clearly observed. The expermetal results demostrated the CWT algorthm s effectve fault aalyss ad dagoss by usg soud emsso sgals. Frequecy (Hz) Tme (sec) Fgure 6 Tme-frequecy represetato of wavelet power spectrum wthout fault 8 rpm ege speeds. ISBN: IMECS 9

5 Proceedgs of the Iteratoal MultCoferece of Egeers ad Computer Scetsts 9 Vol I IMECS 9, March 8 -, 9, Hog Kog To further classfy the fault, the feature extracto of TAWS based o spectrum tred feature method s preseted. Fgure 9 represets the TAWS of fve codtos of ege dle operato. After processg of spectrum tred feature method, the feature vectors, show Fg., are dagostc trouble codes whch wll be provded for the eural etwork. The objectve of faults classfcato s to demostrate the effectveess of the proposed feature selected method. For ths purpose, the feature vectors each fault codto are appled to as the put of the eural etworks. There are data sets for each fault codto. I the fault classfcato expermet, 4 data sets of the data each fault codto are used for trag the etwork ad the remag 6 data sets of the data are used to test the etwork. The performace of the fault dagoss system to correctly classfy the faults to correspodg classes s evaluated. The fault recogto rate s defed as Number of correctly classfed samples Recogto rate = % () Total testg umber of samples TAWS (e) Frequecy (Hz) Frequecy (Hz) Tme (sec) Fgure 7 Tme-frequecy represetato of wavelet power spectrum wth varous fault 8 rpm ege speeds. leakage take mafold; pulley damaged; belt damaged; clutch damaged. Tme (sec) Fgure 8 Tme-frequecy represetato of wavelet power spectrum wthout fault ru-up codto Scale Fgure 9 TAWS of ege dle codto. Wthout fault; leakage of the take mafold; pulley damaged; belt damaged; (e) clutch damaged. Table shows the classfcato accuracy acheved s about 95 % by usg BP algorthm. I comparso, Table shows the result of GRNN classfer has acheved a overall classfcato rate of 99 % ege operato lower tha 5 rpm. Whe the ege operato speed s hgher tha 5 rpm, the fault recogto rate s decreased. The comparso dcated that the fault techque usg GRNN s more effectve tha usg BP algorthm the faults classfcato. Table. Performace of the recogto usg BP algorthm Revoluto codtos (rpm) Defect types dle Wthout fault 99.4% 99.4% 99.4% 99.4% 85% Leakage of the 99.4% 99.4% 99.4% 99.4% 99.5% take mafold Pulley damaged 96.3% 96.9% 98.8% 93.% 95.6% Belt damaged 97.5% 99.4% 99.4% 88.8% 98.8% Clutch damaged 99.4% 93.8% 98.8% 98.8% 85.6% Table. Performace of the recogto usg GRNN Revoluto codtos (rpm) Defect types dle Wthout fault % % % % % Leakage of the take mafold 99.4% 99.4% 99.4% 99.4% 99.4% Pulley damaged 99.4% 99.4% 99.4% 99.4% 98.8% Belt damaged 99.4% 99.4% 99.4% 9.5% 98.8% Clutch damaged 99.4% 99.4% 99.4% 99.4% 99.4% ISBN: IMECS 9

6 Proceedgs of the Iteratoal MultCoferece of Egeers ad Computer Scetsts 9 Vol I IMECS 9, March 8 -, 9, Hog Kog (e) j Fg.. Feature vectors of ege dle codto. Wthout fault; leakage of the take mafold; pulley damaged; belt damaged; (e) clutch damaged. V. CONCLUSIONS I ths paper, a scooter fault dagoss system based o cotuous wavelet trasform techque ad faults classfcato usg artfcal eural etwork for the purpose of the fault detecto has bee developed. Wavelet aalyss, whch allows the soud emsso sgals of frequecy cotet wth tme to be vsualzed, ca extract key features usg tme-frequecy represetato of soud emsso sgals from a scooter. A feature selecto method called spectrum tred feature method was proposed. The selected feature vectors are dagostc trouble codes correspodg to ther fault codto. The features are subsequetly used for the tellget classfer to evaluate the performace of proposed fault dagoss system. The proposed dagoss system usg GRNN method was able to reach a fault recogto rate of about 99%. The expermetal results show that the proposed fault dagoss system wth eural etwork ca be effectvely used scooter dagoss of varous faults through measuremet of scooter soud emsso sgal. [3] Wag, W. J., & McFadde, P. D. (996). Applcato of the wavelet trasform to gearbox vbrato sgals for fault detecto. Joural of Soud ad Vbrato, 9, [4] Wag, W. J., & McFadde, P. D. (995). Applcato of orthogoal wavelets to early gear damage detecto. Mechacal Systems ad Sgal Processg, 9, [5] Newlad, D. E. (995). Progress the applcato of wavelet theory to vbrato aalyss. Proceedgs of ASME 5th Beal Coferece o Mechacal Vbrato ad Nose, Bosto, 3, [6] Newlad, D. E. (999). Rdge ad phase detfcato the frequecy of traset sgals by harmoc wavelets. Amerca of Mechacal Egeers, Joural of Vbrato ad Acoustcs,, [7] L, J. (). Feature extracto of mache soud usg wavelet ad ts applcato fault dagoss. NDT & E Iteratoal, 34(), 5 3. [8] Meltzera, G., & De, N. P. (4). Fault dagoss gears operatg uder o-statoary rotatoal speed usg polar wavelet ampltude maps. Mechacal Systems ad Sgal Processg, 8, [9] Ya, R., & Gao, R. X. (5). A effcet approach to mache dagoss based o harmoc wavelet packet trasform. Robotcs ad Computer-Itegrated Maufacturg,, 9 3. [] L, B., Chow, M. Y., Tpsuwa, Y., & Hug, J. C. (). Neural-etwork-based motor rollg bearg fault dagoss. IEEE Trasactos o Idustral Electrocs, 47(5), [] Che, C., & Mob, C. (4). A method for tellget fault dagoss of rotatg machery. Dgtal Sgal Processg, 4, 3 7. [] Yag, B. S., Hwag, W. W., Km, D. J., & Ta, A. C. (5). Codto classfcato of small recprocatg compressor for refrgerators usg artfcal eural etworks ad support vector maches. Mechacal Systems ad Sgal Processg, 9, [3] Goupllaud, P., Grossma, A., & Morlet, J. (984). Cycle-octave ad related trasforms sesmc sgal aalyss. Geoexplorato, 3, 85. [4] L, J., & Qu, L. (). Feature extracto based o morlet wavelet ad ts applcato for mechacal fault dagoss. Joural of Soud ad Vbrato, 34(), [5] Zheg, H., L, Z., & Che, X. (). Gear fault dagoss based o cotuous wavelet trasform. Mechacal Systems ad Sgal Processg, 6, [6] Hayk, S. (999). Neural etworks a comprehesve foudato. Macmlla College Publshg Compay, New York. ACKNOWLEDGMENTS Ths study was supported by the Natoal Scece Coucl of Tawa, the Republc of Cha, uder project umber NSC-97--E-8-8. REFERENCES [] Ba, M. R., Jeg J., & Che, C. (). Adaptve order trackg techque usg recursve least-square algorthm. Amerca of Mechacal Egeers, Joural of Vbrato ad Acoustcs, 4(4), 5 5. [] Kle, R., Igma, D., & Brau S. (). No-statoary sgals: phase-eergy ad smulatos. Mechacal Systems ad Sgal Processg, 5(6), ISBN: IMECS 9