Failure diagnostics with SVM in machine maintenance engineering

Abs ac — Failu e diagnos ics as a pa o condi ion moni o ing (CM) echnique is ine i able in mode n indus ial p ac ice. Condi ion Based Main enance (CBM) iden i ies all p oblems ha cause u he ailu es and sugges s main enance pe iods. Reducing main enance cos s and enhancing sys em a ailabili y a e la gely depends on in o ma ion p o ided by p ecise and accu a e ailu e diagnos ics. The app oach can be used widely in he se e al ield o he indus y. Da a acquisi ion is ela ed o measu emen hen da a p ocessing, ea u e ex ac ion is needed, inally ailu e iden i ica ion. In his pape Suppo Vec o Machine (SVM) is discussed how o be used o diagnosing machines and machine elemen s. The aim o using SVM is o diagnose he sys em a a ce ain momen o p edic i s ac ual s a e in he u u e. SVM is p og essing apidly se e al new ad ances a e e ealed as he pa o machine lea ning echniques. Due o expe imen s SVM e iciency could be app oxima ely 90% o e en highe . Keywo ds—Bea ing es - ig, ailu e diagnos ics, machine aul , machine lea ning, suppo ec o machine I. INTRODUCTION I is c i ical o main ain machine heal h and ex ending he li e ime o i s c i ical p ocesses, minimizing eme ging cos s du ing ope a ion. Diagnosing he impending ailu es is one o he signi ican end, p ognosis o he emaining use ul li e ime (RUL) o he equipmen is ano he majo challenge in schedule main enance ope a ions so ha maximize eliabili y. Scheduled main enance p ac ices end o educe machine li e ime and inc ease down- ime, esul ing in loss o p oduc i i y. In elligen moni o ing sys em can educe main enance cos s, a oid ca as ophic ailu es and inc ease machine a ailabili y. To de elop an e ec i e diagnos ic and p ognos ic sys em deep unde s anding o he bea ing beha io is well ad ised. Condi ion based main enance (CBM) as a leading main enance echnique in ol es moni o ing machine condi ion and p edic ing machine ailu e. I is c i ical as a pa o p e en i e main enance o educe cos s and inc ease eliabili y. Condi ion moni o ing (CM) is an e ec i e me hod o moni o ing machine s a e pa ame e s like ib a ion, empe a u e, wea deb is analysis and noise moni o ing. Lo o app oaches ha e been al eady de ined in main enance enginee ing o de e mine and moni o he ac ual s a e o o a y machines, ecip oca ing machines, and elec ical machines. Bea ings, gea s as basic o a y machine y a e success ully moni o ed by ib a ion signal analysis, cylinde p essu e signal can be moni o ed in in e nal combus ion engines and ecip oca ing comp esso s, measu ing o powe consump ion and hea dis ibu ion a e ypical o moni o ing elec ical machines. Fu he me hods include noise measu emen , oil wea deb is analysis, in a ed spec um analysis, cu en analysis, powe analysis. II. FAILURE DIAGNOSTIC All ailu e diagnos ics consis o h ee main s eps, da a acquisi ion and collec ion, da a p ocessing, and ailu e pa e n ecogni ion. (Fig. 1.) Fig. 1. Failu e diagnos ic s ages A e he measu emen p ocess he aw signal equen ly con ains lo o noise, i s signal- o-noise (SNR) a io is low. In his o m i is impossible o ob ain he necessa y in o ma ion abou he signal i s noise should be elimina ed o educed. S a is ical based ea u es o example ms alue, peak alue, mean alue, a iance, ku osis, c es ac o a e ypical ea u es o be ex ac ed om he signal. Time domain ea u es in machine aul diagnosis is published by se e al esea che s. [8] Mos ly, hey a e applied o in es iga ing non-pe iodic signals and ini ial aul s o bo h bea ings and gea s. Fo equency domain analysis Fas Fou ie T ans o m (FFT) is commonly applied ha ex ac ea u es, used o pe iodic signals, i can de e mine de ec s o bea ings and gea s. The main d awback o Fas Fou ie T ans o m (FFT) is ha i is only applicable o ans o ming a s a iona y signal. Fo non-s a iona y signal he Sho - ime Fou ie T ans o m [14] o he Wa ele ans o m [4] can be applied. Fea u e ex ac ion is domain speci ic and signal speci ic. The e a e some ways a ailable o de e mine he c oss-co ela ion be ween ea u es, classical s a is ics such as F- es , Chi-squa ed es , a ie y FAILURE DIAGNOSTICS WITH SVM IN MACHINE MAINTENANCE ENGINEERING K isz ián DEÁK1, Im e KOCSIS2, A ila VÁMOSI3, Zol án KEVICZKI4 1deak.k isz [email protected] 2[email p o ec ed]deb.hu 3[email p o ec ed]eb.hu 4zol an.ke iczki@schae le .com o me hods a ailable o e alua e ea u e pe o mance, a e applied o es he pe o mance o each indi idual ea u e [10] and he elie algo i hm is ano he classical me hod [6]. Fea u e ex ac ion is necessa y in machine aul diagnosis and gene al app oach is o ob ain as many ea u es as possible because mo e ea u es gi e mo e eliable in o ma ion. Bu lo o addi ional ea u es make he compu a ional ime and cos mo e and he abili y o he diagnos ics sys em o make e icien diagnosis is dec eased, mo eo e i ele an ea u es complica e he whole diagnos ics sys em educing i s capabili y o make e ec i e analysis. Fig. 2. shows he so-called peaking phenomenon [10] inc easing he numbe o ea u es can only imp o e he pe o mance ini ially, bu a e a c i ical numbe o ea u es, he pe o mance dec eases. Theo e ically, in ini e da a se s would enhance he capabili y o diagnos ics model bu ha ing so la ge models a e nea ly impossible in eal condi ions. Fig. 2. Peaking phenomenon [18] In o de o inc ease he pe o mance o he diagnos ics model ea u e selec ion is necessa y. In his p ocess he numbe o selec ed ea u es is dec easing o a alue ha e en accep able o accomplish p ope u he diagnosis. Remo ing he i ele an ea u es is one o he mos accep ed me hod in his ield. Mainly subse ea u e selec ion and indi idual ea u e selec ion a e used as wo basic app oaches o ea u e selec ion. Resea che s [12] de ined ha each ea u es should be anked on p io i y and less impo an one o be emo ed he o he s a e applied. SVM weigh all ea u es in he inpu space, and hese weigh s can be e alua ed du ing he aining p ocess [9]. Mo e impo an ea u es ge highe sco e o weigh s, less impo an ones ge smalle alues o nea ly ze o. SVM algo i hm was in en ed by Vladimi N. Vapnik and so ma gin was p oposed by Co inna Co es and Vapnik in 1993 and published 1995. SVM has been success ully applied o a numbe o applica ions anging om pa icle iden i ica ion, ace iden i ica ion, and ex ca ego iza ion, o engine knock de ec ion, bioin o ma ics, and da abase ma ke ing [2]. As o u he possible applica ions he e a e esea ches abou op imiza ion e.g. he Op imiza ion o he Shape o Axi-Symme ic Rubbe Bumpe s [20]. As i was men ioned ha app op ia e numbe o ea u es is well ad ised o op imize calcula ion ime and machine aul diagnosis sys em. Classi ie e o a e measu es; dis ance measu es; in o ma ion measu es; dependence measu es; and consis ency measu es [3] a e commonly used o measu ing he pe o mance o he model, classi ie e o a e measu es a e mos ly deba ed. Sea ching o minimum subse o ea u es is exhaus i ely sea ched ield. Ac ual condi ion o he machine can be ep esen ed by he ea u es ex ac ed om he da a se s. De e mining he p ede ined h eshold is a majo ask ea u e’s alue abo e a p ede ined h eshold may imply a possible ailu es, se e i y o he ailu e is indica ed by he de ia ion om he p ede ined h eshold. Gene ally, h eshold alue is e alua ed by expe ience, he alue ha di e he in ac s a us o he machine om he aul y condi ion. The Ku osis, he ou h no malized s a is ical momen , co esponds o he peak alue o he da a. Fo an undamaged bea ing, he alue is equal o h ee in equencies. Ku osis alue is mo e use ul, when i is compa ed wi h he RMS, c es ac o , and peak alue. The C es Fac o is he a io o he peak accele a ion o he RMS alue. C es ac o is a good indica o o small size de ec s; al hough, when localized damage g ows, he alue o he c es ac o dec eases signi ican ly because o he inc easing RMS. So, ku osis o 3 can be as h eshold o make di e ence be ween heal h and aul y bea ings. In eal indus ial ci cums ances he e is no enough da a o de e mine his alue in all wo king condi ions e e ing o all machines in di e en ope a ing en i onmen s. K-nea es neighbou [10], Bayesian classi ie , lea ning algo i hms as classical pa e n ecogni ion echniques a e equen ly applied o de e mine h eshold o bounda y om a ailable da a. Lea ning algo i hm inds he op imal decision unc ion au oma ically om he a ailable da a and disc imina e di e en pa e ns. Non-Linea classi ie s such as A i icial Neu al Ne wo ks (ANN) and SVM can be used in supe ised and unsupe ised lea ning. Classi ying da a is a common ask in machine lea ning. Gi en da a poin s belong o one o wo classes, and he goal is o decide which class a new da a poin is in. To de ine suppo ec o machines and i s linea classi ie s, a da a poin is iewed as a p- dimensional ec o a lis o p numbe s, and he pu pose o decide whe he i can be sepa a ed such wi h a (p − 1)- dimensional hype plane. This is called a linea classi ie . Bes hype plane should be chosen ha ep esen s he la ges sepa a ion o ma gin in o he wo d, be ween he wo classes. In his case he dis ance om he hype planes o he nea es da a poin on each side is maximized. I such a hype plane exis s, i is known as he maximum-ma gin hype plane and he linea classi ie i de ines is known as a maximum ma gin classi ie . Fig. 3. SVM classi ica ion p inciple [18] Supe ised lea ning pai s he inpu and ou pu da a. Fea u e ec o s ex ac ed om he signal can be used as inpu da a. SVM is sensi i e o noise in he signal especially when aw da a is used o he inpu o he SVM sys em. The pe o mance o he ained SVM can be e alua ed by using a se o es da a. In e nal coe icien s a e chosen by he supe ising lea ning. Dec easing he eal ou pu and he p edic ed ou pu is impo an o ge he aining esul as he op imal decision. III. ONE CLASS SUPPORT VECTOR MACHINES Co ec main enance ac ions is only possible i diagnos ics o he machine y is sa is y he equi emen s. The pu pose o his ac ion is o educe main enance cos and enhance eliabili y and sys em a ailabili y. The Suppo Vec o Machine (SVM) me hod can be in e p e ed as a ans o ma ion o pu he lowe dimensional da a o a highe dimension space. Suppo ec o machine cons uc s a hype plane o se o hype planes in a high o in ini e-dimensional space, which can be used o classi ica ion, eg ession. The hype planes in he highe dimensional space a e de ined as he se o poin s whose do p oduc wi h a ec o in ha space is cons an . SVM ge s non sepa able pa e ns o sepa a ed pa e ns he exis ing ailu e o incipien ailu e is ge ing mo e iden i iable because ailu e diagnos ics is in he highe dimensional space. The co e me hod o SVM is o use he maximal ma gin me hod o de ea he o e i ing p oblem ha makes he model i special da a se s. Small sample size p oblems a e sol ed by using he maximal ma gin app oach. Suppo Vec o Machine (SVM) is a s a e-o - he-a me hod, equen ly used as nonlinea classi ie o lea ning algo i hm which is able o e alua e au oma ically dependency be ween da a and de ined as a eg ession p oblem. SVM es ima e he connec ion be ween p edic i e a iables and explana o y a iables. Maximal ma gin app oach and ke nel me hod a e combined in SVM o make p edic ion as Fig. 4. p esen s. Suppo Vec o Machine (SVM) is a classi ica ion and eg ession me hod. Suppo Vec o machines uses hypo hesis space o a linea unc ions in a high dimensional ea u e space. SVM can be ained wi h a lea ning algo i hm om op imiza ion heo y. Fig. 4. SVM based diagnos ics classi ie a chi ec u e Good sepa a ion is achie ed by he hype plane ha has he la ges dis ance o he nea es aining da a poin o any class, he unc ional ma gin. The SVM decision unc ion is an applica ion o he ke nel unc ion and Lag angian op imiza ion me hod is used o ob ain he op imal decision unc ion om he aining da a [7]. SVM is gene ally sui able o wo-class asks. The decision unc ion is used o p edic he ou pu o a gi en inpu . The maximal ma gin me hod is applied o imp o e he accu acy o he p edic ion. Fo machine lea ning algo i hms, he ke nel ick is a way o mapping obse a ions om a gene al se S in o an inne p oduc space V (equipped wi h i s na u al no m), wi hou ha ing o compu e he mapping explici ly. I can ans o m he p oblem om a lowe dimension o a highe dimension, while he compu a ion complexi y does no change. T ans o ming he p oblem om a lowe o a highe dimension makes he app oxima ion unc ion mo e lexible wi h i s da a, educing he isk o empi ical e o . Wi h ewe SVs (suppo ec o s, da a aking e ec ) he gene aliza ion abili y is imp o ed. Fu he mo e, as he decision unc ion is comp ised o SVs, ha ing ewe SVs can educe he compu a ion complexi y. The op imal solu ion o he SVM is achie ed by he use o a quad a ic op imiza ion p oblem. The con ex p ope y o he o mula ion makes he solu ion unique. The SVM u ilizes he Lag angian op imiza ion me hod o sol e his p oblem. The o iginal op imal hype plane algo i hm p oposed by Vapnik in 1963 was a linea classi ie . The o iginal p oblem is de ined in ini e dimensional space. Some imes he se s o disc imina e a e no linea ly sepa able in ha space. Howe e , in 1992, Be nha d E. Bose , Guyon and Vapnik sugges ed a way o c ea e nonlinea classi ie s by applying he ke nel ick o maximum-ma gin hype planes. The esul ing algo i hm is o mally simila , excep ha e e y do p oduc is eplaced by a nonlinea ke nel unc ion. Polynomal ke nels, Gaussian adial basis unc ion a e used equen ly. In s a is ical lea ning heo y he p oblem o supe ised lea ning is o mula ed as ollows. Taking a se o aining da a {(xi, yi)} in Rn  R sampled acco ding o unknown p obabili y dis ibu ion P(x, y), and a loss unc ion V(y, (x)) ha measu es he e o , o a gi en x, (x) is p edic ed ins ead o he ac ual alue y. The p oblem consis s in inding a unc ion ha minimizes he expec a ion o he e o on new da a ha is, inding a unc ion ha minimizes he expec ed e o [16]: dxdy)y,x(P))x( .y(V Maximum ma gin is gi en as [15]-[17]:     d 1i 2 i w bwx mina g)x(dmina gina gm Fo calcula ing he SVM we see ha he goal is o co ec ly classi y all he da a. Fo ma hema ical calcula ions we ha e, I yi= +1; I yi= -1; wxi + b ≤ 1 Fo all i; yi (wi + b) ≥ 1 In his we p esen he QP o mula ion o SVM classi ica ion [15]-[17]-[18]-[19]. This is a simple ep esen a ion only. SV classi ica ion:    l 1i i 2 K , C min i y i (xi)  1 - i, o all i i  0 SVM classi ica ion, Dual o mula ion:     l 1i l 1j jijiji l 1i i α)x,xK(yyαα 2 1 α min i 0  i  C, o all i; 0y l 1i ii    Va iable i is called slack a iable and i measu es he e o made a poin (xi, yi). T aining SVM becomes qui e challenging when he numbe o aining poin s is la ge. A numbe o me hods o as SVM aining ha e been p oposed [15]-[17]-[19]. IV. EXPERIMENTAL STUDY In gene al, SVM applica ions can be classi ied in o wo ca ego ies: ailu e diagnos ics such as no el y de ec ion and mul i- ailu e disc imina ion; and secondly eliabili y da a analysis, such as eliabili y p edic ion and sys em eliabili y assessmen . The e a e some examples whe e SVM can be used in main enance enginee ing. Plane a y gea boxes a e widely used in machine indus y and o he hea y-du y indus y such as helicop e s, hea y-du y ucks, and o he la ge-scale machine y. Plane a y gea boxes a e able o unde ake hea y-du y asks wi h high o que need. The e a e wo app oach o in es iga ing machine elemen , bea ings o gea ailu es, li e- es s and sho - e m es s by c ea ing a i icial aul s on he bea ing elemen s. Manual pi ing damage expe imen s we e designed and implemen ed o p o ide ib a ion da a co esponding o di e en le els o gea pi ing damage. In ou esea ches, spa k e osion was c ea ed wi h EDM o lase machine. To alida e he uzzy app oach es - ig had been buil which has 5 indi idual olle bea ings. One o hem was moni o ed by measu ing ib a ion accele a ion le el. The lis o measu ing ins umen s ha a e used in he measu emen : - PCB 603C01 accele ome e - Bea ing es - ig (Fig. 5.) - NI 9234 DAQ - NI Lab iew Sound and Vib a ion Measu emen - TESTO 476 s oboscope - Soundbook measu emen sys em Fig. 5. Bea ing es ig o alida ion Fo he measu emen w i en in his pape , PCB603C01 accele a ion senso was used. I was a ached s ongly on he op o he bea ing house wi h magne p o iding enough o ce o keep he senso and p oduce ideal ci cums ances o u he ope a ions. Bo h Soundbook ib a ion measu emen sys em, Samu ai So wa e, and Na ional Ins umen (NI) de ices we e used o he measu emen , namely NI DAQ 9234. NI DAQ 9234 has a 4-Channel, ±5 V, 51.2 kS/s pe Channel, 24-Bi IEPE de ice wi h 51.2 kS/s pe -channel maximum sampling a e; ±5 V inpu , 24-bi esolu ion; 102 dB dynamic ange; an ialiasing il e s. So wa e-selec able AC/DC coupling; AC-coupled (0.5 Hz), so wa e-selec able IEPE signal condi ioning (0 o 2 mA), sma TEDS senso compa ibili y, NIST- aceable calib a ion a e he ypical ea u es o his de ice used in he bea ing ib a ion measu emen s. Di e en i ual ins umen s we e buil in Lab iew so wa e o make ib a ion and spec um measu emen . The simples applied is showed in Fig. 6. 1bwxi Fig. 6. Vi ual Ins umen (VI) o ib a ion measu emen In his esea ch, spa k e osion was c ea ed wi h lase machine (Fig. 7.) hen geome ical measu ed unde Olympus BX61 op ical mic oscope. A i icial spall was 658 um in diame e and 257 um deep on he inne ing o he 6206 ype bea ing. Being a plas ic cage bea ing balls could be emo ed easily be o e c ea ing he aul . BPFI was calcula ed, basically by 2880 1/ min engine speed, exac o a ion speed was measu ed and BPFIs we e ecalcula ed. Fig. 7. A i icial bea ing aul on he inne ace BPFO (ball passing equency ou e ace), BPFI (ball passing equency inne ace), FTF ( undamen al ain equency), BSF (ball spin equency) can be calcula ed in Hz wi h he ollowing o mulas by knowing he con ac angle (), o a ion speed ( ), numbe o olle s, ou e ing diame e (D), and inne ing diame e (d) o he bea ing. Acco ding o calcula ions engine speed is 48 Hz, BPFO 171,84 Hz, BPFI 260,16 Hz, FTF 19,2 Hz, BSF 112,32 Hz by using he ball bea ing in he alida ion es . Fig. 8. indica es he ime domain spec um o he bea ing, ib a ion alue is no mal. Fig. 8. Time domain spec um o he measu ed bea ing F equency-domain (FFT) analysis o he ib a ion signal is he mos widely used app oach o de ec ing olle - bea ing de ec s. The in e ac ion o de ec s in olling elemen bea ings p oduces impulses. Impulses gene a e he na u al equencies o bea ing elemen s and housing s uc u es, ha causes peaks in he ib a ion ene gy spec um. Compa ing he calcula ed aul equencies wi h he measu ed alues he exac aul s can be e ealed. Fig. 9. p esen s he ib a ion spec um o he bea ing. Fig. 9. F equency domain spec um o he measu ed bea ing The gene al algo i hm o SVM based diagnosis can be seen on Fig. 10. Tes and aining da a ed he sys em and make pe o mance e alua ion by using ea u es. Fig. 10. Algo i hm o bea ing aul de ec ion wi h SVM [21] Diagnosis a e app oxima ely 90% was eached in he expe imen s hus SVM me hod could be applied e icien ly in machine aul diagnos ics. Se e al measu emen s we e pe o med by applying bea ings wi h di e en aul s. SVM diagnos ics sys em is able o dis inguish heal hy and aul y bea ings. Fu he expe imen s a e planned o in es iga e ou e ace aul s, cage aul s and ball aul s. Mo o Cu en Signa u e Analysis, MCSA es s a e planned as well, a me hod o moni o ing machine y in he indus y by means o i s elec ical cu en s. Mo o cu en signa u e analysis (MCSA) has p o en o be a highly aluable p edic i e main enance ool. V. CONCLUSION Condi ion Moni o ing (CM) is i al pa in main enance enginee ing. P ope main enance can educe cos and imp o e eliabili y. Lo o me hods a e used o diagnose he machines o hei componen s such as o a y machine ies e.g. bea ings, gea s. These machine elemen s end o su e se ious damages ha a e measu ed by mos ly ib a ion measu emen echniques because o i s simplici y. Addi ional measu emen s can be used such as empe a u e measu emen , wea deb is analysis, oil analysis o c ea e a complex diagnos ics condi ion moni o ing sys em. SVM has been success ully applied o a numbe o applica ions in indus y. Classi ying da a is a common ask in machine lea ning, linea and non-linea classi ica ion is applied used hype plane o sepa a e poin s belongs o wo classes. Ke nel ick is a way o mapping obse a ions om a gene al se S in o an inne p oduc space V. I can ans o m he p oblem om a lowe dimension o a highe dimension. SVM has lo o applica ion in main enance enginee ing. The SVM has been used o diagnose ailu e in olling elemen bea ings, induc ion mo o s, machine ools, pumps, comp esso s, al es, u bines, and a ious o he machines. Enginee ing expe imen s show he easibili y and e ec i eness o his me hod, he diagnosis a e nea ly 90% o e en mo e so SVM me hod can be applied e icien ly in many in es iga ions. Tes igs measu emen s a e p o ed he e iciency o SVM ools in machine aul diagnosis. La e as pa o u he expe imen s bea ing wi h ou e ace aul s, cage aul s, ball aul s will be examined. Mo eo e , Mo o cu en signa u e analysis (MCSA) could be applied as a mode n ool o machine diagnos ics. Mul iplied measu emen s using bo h ib a ion and mo o cu en signa u e analysis is possible o enhance he e iciency o he sys em, e en empe a u e measu emen could be used o make mo e accu a e measu emen s. REFERENCES [1] B.SREEJITH, A.K.VERMA & A.SRIVIDYA 2008. Faul diagnosis o olling elemen bea ing using ime-domain ea u es and neu al ne wo ks. P oceedings o Thi d IEEE In e na ional Con e ence on Indus ial and In o ma ion Sys ems ICIIS 2008. Kha agpu ,India. [2] BENNETT, K. P. & CAMPBELL, C. 2000. Suppo Vec o Machines: Hype o Hallelujah? SIGKDD 2. [3] DASH, M. & LIU, H. A. 2003. Consis ency-based sea ch in ea u e selec ion. A i icial In elligence, 151, 155-176. [4] DAUBECHIES, I. 1990. 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