Application of Fault Phenomenon Vector Distance Discriminance in Woodworking Machinery System Fault Diagnosis

Transcription

1 84 JOURAL OF SOFTWARE, VOL. 6, O. 5, MAY 0 Applcaton of Fault Phenoenon Vector Dtance Dcrnance n Woodworng Machnery Syte Fault Dagno Yun-Je Xu School of Engneerng, Zhejang Agrcultural & Foretry Unverty, Ln an, Chna Eal: xyj9000@63.co Shu-Dong Xu School of technology, Zhejang Agrcultural & Foretry Unverty, Ln an, Chna Eal: dxu@zafu.edu.cn Quan-Sheng Men and Lang Fang School of technology, Zhejang Agrcultural & Foretry Unverty, Ln an, Chna Eal: {enq, lfang}@zafu.edu.cn Abtract Ang at the proble of dagno dffculty caued by too any factor of woodworng achnery yte, a nd of dagnong ethod baed on fault phenoenon wa preented. The reearch on woodworng achnery yte fault phenoenon pace arrved at concluon that the eergency of each fault phenoenon ubject to 0- dtrbuton. Therefore, phenoenon vector correpondng to each fault fored cluter whoe accuulaton pont expectaton of vector. After excluon of abnoral vector, the dtance dcrnaton wa ued to fault dagno to etablh expert yte baed on fault phenoenon vector. The confred reult wa return bac to fault databae o that the yte acheve elf-learnng of real-te dagno experence. Fnally, the exaple on wood-wool worng equpent prove that the dagnotc ethod ha charactertc of good real-te, ple operaton and hgh dagnotc accuracy. Index Ter woodworng achnery yte, dtance dcrnaton, fault phenoenon vector, fault dagno I. ITRODUCTIO The dagno of copote fault occurred n woodworng achnery a dffcult challenge at preent. It hard to dagnoe the copote fault exactly and coprehenvely due to the dverty and nfluence of fault. The purpoe of woodworng achnery fault dagno to dentfy whether the techncal tate noral and deterne the nature and te of fault fro nforaton related to echanc runnng. It eence to fnd a appng fro fault phenoenon pace to fault pace. In order to accurately fnd the relatonhp to axze extend, any cholar reearch on ncreangly coplex woodworng achnery yte and preented any fault dagno ethod baed on the dea of expert Manucrpt receved Deceber 9, 00; reved January 5, 0; accepted January, 0. yte. The fault dagno of woodworng achnery artfcal neural networ, grey odel [, ] and Support vector achne (SVM). In bac propagaton artfcal neural networ (BP-A), tradtonal eprcal r nzaton (ERM) ued on tranng data et to nze the error. Support vector achne (SVM) baed on tattcal learnng theory ued n any applcaton of achne learnng becaue of t hgh accuracy and good generalzaton capablte [3, 4].The expert yte baed on neural networ and genetc algorth ha dadvantage of low convergence peed of tranng of networ or aple, o t dffcult to coplete dagnoe ta that ha hgh real-te requreent [5, 6, 7, 8, 9]. Although Levenberg-Marquardt (L-M) algorth can overcoe the hortcong, L-M algorth a cobnaton of gradent ethod and Gau-ewton ethod. Wth t he ad of the approxate econd dervatve, the L-M algorth ore effcent than t he gradent ethod. Concerned wt h t he t ranng proce and accuracy, the L-M algorth uperor to vary learnng rate BP-A and SVM [0, ]. It greatly ncreaed coplexty of coputaton and dffculty of degn. Fault dagno expert yte baed on fuzzy theory can decrbe yte fuzzy tate, but the ey reaonng technology tll at the tage of theoretcal tudy and far away fro the applcaton. In contrat, t ple to degn and realze tradtonal fault dagno expert yte baed on rule. However, expert yte baed on rule ha two bottlenec of rule ang and nowledge acquton [,3]To reolve rule ang proble wth coplex trategy olvng rule eay to return to coplex algorth a neural networ and genetc algorth, the proble becoe coplex agan. Machne learnng played good effectng olvng proble of nowledge acquton, whle the achne learnng trategy not unveral and prone to nduce cobnaton exploon. Through the reearch on do:0.4304/jw

2 JOURAL OF SOFTWARE, VOL. 6, O. 5, MAY probablty dtrbuton of fault phenoenon and cluterng charactertc of phenoenon group caued by fault, the paper appled the dea of dtance dcrnaton n dagnoe trategy. The dagno reult wa feedbac to fault databae, whch provde good oluton to olvng two proble of tradtonal expert yte baed on rule, o that the coplexty of yte tructure and oftware degn dffculty greatly reduced and dagnotc effcency and engneerng practcablty greatly enhanced. Fnally, Monte Carlo aplng and exaple of hydraulc excavator prove that the dagnotc ethod ha charactertc of good real-te, ple operaton and hgh dagnotc accuracy. The pecfc arrangeent of the paper a follow: Secton buld atheatcal odel of fault phenoenon vector; Secton 3 deterne ey technque of fault phenoenon vector dtance dcrnaton ethod; Secton 4 perfor ulaton verfcaton of the ethod tang wood-wool worng equpent a exaple; Secton 5 conclude our wor. II. FAULT MODEL ESTABLISHMET A. Matheatcal Decrpton of Fault Vector Phenoenon There are any factor led to fault of woodworng achnery yte, ot of whch are not ajor. Under the nfluence of any non-eental factor, the phenoenon repreented by fault that caued by few ajor factor appeared rando. There are followng fact: a fault ay lead to ultaneou ultple phenoenon; occurrence of a fault phenoenon ay be caued by dfferent fault; ultple poble fault phenoenon caued by a fault not certan, but tattcally law. Aue the fault of yte are ngle fault. We can now fro tattc that there have n type of fault n the runnng htory of yte S, whch for a fault et F = { F n}, where F the -th type fault. We can alo now that there are type of fault phenoenon caued by n type fault, the et of whch I = { I }. Defne vector D = ( d, d, d), d B = {0, }, ( ) whoe coponent a boolean varable to repreent a fault phenoenon group, whch called a fault phenoenon vector. Aong the, d = ay that the -th phenoenon n et occur, d =0 ay t doe not occur. A phenoenon caued by a fault conttute a vector, for the fault F, the et conttuted by all poble fault phenoenon vector exactly a ubpace of denonal boolean pace, whch denoted a V. For dfferent fault F and F j ( j ), the conttuted ubpace V and V j are not dfferent, but there ay be coon ground. If V and V j are bacally ae, and the patal dtrbuton of fault phenoenon probably ae, the fault V and V j are n a fuzzy et, n other word, t dffcult to dtnguh the two fault fro the phenoenon. Each denon of fault phenoenon ubject to 0- dtrbuton and repectvely ha a expectaton p, then the fault phenoenon vector ha a expectaton µ. All fault phenoenon vector caued by F the vector faly around µ n the pace. In other word, the fault phenoenon vector caued by each fault a natural cluterng whoe accuulaton pont the expectaton vector. Wth the above defnton, fault dagno becoe uch a proble: gven a fault phenoenon vector D, to deterne wth a ethod, o that D. V B. Etablhent of Expert Syte Model The whole fault dagno yte an expert yte. The proce of wood-wool worng equpent fault dagno hown n Fg.. Cont of three an tage flow a follow: (a) Retrevng Accordng to the current fault phenoenon and ypto of the wood-wool worng equpent, retreve the lar cae fro a databae. If the cae uted to the current fault phenoenon of the equpent Current tate of equpent Fault databae Retrevng Reve ndex Store Retrevng cae Judge Slar cae Reaonng achne Dagno ucce probablty order table Syntheze Tranfer Deterne dagno ucce probablty baed on probablty Fault phenoena vector Mae a concluon of dagnoe Suted cae Dtance deternat on rule databae Explan achne Mae a concluon of dagnoe Fgure. Fault dagno expert yte odel

3 844 JOURAL OF SOFTWARE, VOL. 6, O. 5, MAY 0 copletely, quote the cae drectly and ae a concluon. (b) Modfyng It tae fault phenoenon vector a nput and to reaon wth explaned dtance dcrnaton rule and pat fault data. The reaonng achne ued a dagnotc probablty order table of dagno reult accordng to dcrnaton analy rule, where the fault wth axu probablty the preferred reult, and other are opton by decreang order of probablty. If the cae not atched copletely, The dagnotc probablty order table wll be avalable to antenance peronnel for reference of further confr, ue the Dtance deternaton rule databae, part fault charactertc and acton record [6] etc. to Reaonng, adjut, rewrte, atch and yntheze the cae whch ha been retreved accordng to the current fault phenoenon of equpent. (c) Storng Mae the corrected cae n eepng wth the dagno of the current fault phenoenon, and ae a concluon. At the ae te, the confred reult wll be fed bac to fault databae for record to prepare for the next dagnotc reference. The dtance dcrnaton wa ued to fault dagno to etablh expert yte baed on fault phenoenon vector. The core of fault dagno that t can eorze/tore the forer fault, t envronent and the proce accurately, furtherore, t ue the pat dagno experence, proce and ethod to coplete the current dagno through analogy and aocaton whle dagnong. Therefore, fault dagno baed on fault phenoenon vector a nd of ethod realzed through analogy [7, 8], and t degn ode to utlze the pat degned cae drectly ntead of the uary of degn experence. III. KEY TECHIQUES A. Rule-Baed Dagnotc Expert Syte In the rule-baed yte, nowledge repreented n the for of producton rule. A rule decrbe the acton that hould be taen f a ypto oberved. The eprcal aocaton between pree and concluon n the nowledge bae ther an charactertc. Thee aocaton decrbe caue-effect relatonhp to deterne logcal event chan that were ued to repreent the propagaton of coplex phenoena. The general archtecture of thee yte nclude doan ndependent coponent uch a the rule repreentaton, the nference engne and the explanaton yte. Bac tructure of a clacal rule-baed expert yte hown n Fg.. Expert dagno experence utably foratted cont the ba for the clacal expert yte approach. Fault dagno requre doan pecfc nowledge foratted n a utable nowledge repreentaton chee and an approprate nterface for the huan-coputer dalogue. In th yte the poble ypto of fault are preented to the uer n a creen where the uer can clc the pecfc ypto n order to tart a earchng Fault databae Knowledge bae Dtance deternaton rule databae Uer nterface antenance peronnel Inference engne Expert Fgure. Bac tructure of a rule-baed expert yte. proce for the caue of the fault. Addtonal nforaton about checng or eaureent ued a nput that, n cobnaton wth tored nowledge n the nowledge bae gude to a concluon [9, 0,, 3]. B. Reaonng Rule Forulaton The forulaton of rule need to reolve proble of fault data table degn. Table the degned fault data table of F, where each lne repreent a fault phenoenon vector. Ung the above ethod, we can buld fault data table for each F. Each fault phenoenon obey tandard 0- dtrbuton, the value of whch hown n (). The expectaton of each phenoenon p j, where repreent that the phenoenon caued by the -th fault; j F TABLE I. DATA TABLE OF F Phenoenon uber I I I 3 I 4 I Total

4 JOURAL OF SOFTWARE, VOL. 6, O. 5, MAY repreent that th phenoenon the j-th phenoenon n the et; the aple data aount of th fault; I jt repreent that the t-th fault phenoenon vector of fault caued by the j-th coponent. I jt t= µ = ( p j ),,, = ( ),, () The varance a (): r = ( S ) j = (,, t= ( I jt p ) j ),, Covarance between dfferent phenoenon a (3): = [ = [ σ ] uv u v= I uivp( Iu, Iv )] u v= = ( I u, Iv () (3) Where, P ) the jont probablty of two fault phenoenon, whch ha only four cae a (4): P(0,0) P(0,) P( I, I ) = (4) u v P(,0) P(,) The reearch on woodworng achnery yte fault phenoenon pace arrved at concluon that the eergency of each fault phenoenon ubject to 0- ndependent and ha the ae dtrbuton, That denoted a I, I,..., I n. Wth fnte expected value µ = E( I j ) and fnte varance σ = D( I j ). Let Sn = I + I + + I n. Sn σ We now D( S n ) = nσ, D( ) = Alo we n n S now that E( n ) = µ. n We now fro the large nuber law,by chebyhev nequalty, then for anyε > 0, a (5): Sn σ P µ ε n nε. (5) Thu, for fxed ε a (6): Sn P µ ε 0 n (6) A n. Equvalently a (7): Sn P µ < ε. n (7) That when the nuber of aple goe to nfnty, the expectaton lt of aple equal to that of the overall hown n (5-7) and aple varance equal to that of overall, the covarance of aple equal to that of overall []. A Table how, the expectaton of I caued by F equal to p =93/000 =0.93. Furtherore, the expectaton fault phenoenon vector of fault F µ, whch the accuulaton pont accordng to probablty dtrbuton n the pace of all fault phenoenon caued by F. The dcrnaton analy dea ndcate that when perfor dtance dcrnaton of all µ and fault phenoenon vector to be dagnoed, then the fault phenoenon vector poble belong to the x-th pace. That the probablty that t caued by the x-th the larget. In th way, the order reult fro lttle to large wll led to ort of dagnoe probablty decendng. The dtance here can be Eucldean dtance a (8), or be Mahalanob dtance a (9): D = µ µ = ( d j p ) T j ( D D ( x, G) = ( D ) µ ) Where, (8) µ (9) the nvere atrx of covarance atrx. The Eucldean dtance ntutve, whle the Mahalanob dtance need to copare and dcrnate the tandard overall phenoenon caued by each fault, o to a reflect realty. In the practcal applcaton, Mahalanob dtance need to now the nvere atrx of covarance atrx aong all phenoenon, whch nvolve nvere operaton, o t e relatvely coplex. C. Degn of Learnng Strategy When the yte bult, we hould uarze expert dagno experence and nput. The autoatc learnng n yte runnng proce can add confored fault phenoenon vector nto fault databae. The ort accordng to probablty fro large to lttle wll caue dagno, whch ean t ay be wrong to tae the fault at the ot front a dagno reult. The dcrnaton ay caue tae, whch the fact that can not atered by people. If the eprcal data very rch, the poblty of dagno wll be very all. A to tae, the yte wll be the econd dagno, whch raned econd n the probablty of falure a a dagnotc output, and o on. The torage for affect the proble olvng effcency, wherea regulaton and evaluaton affect the proble olvng accuracy. The atchng degree of the fault and fault phenoenon can be expreed a (0): n D ( c, c ) = W ( X Y ) / n (0) = Where D the atchng degree of fault c and fault phenoenon c ; W the weght of charactertc paraeter ; n the nuber of all ypto; X and

5 846 JOURAL OF SOFTWARE, VOL. 6, O. 5, MAY 0 Y are repectvely the ntal character or the concluon credblty of fault c and fault phenoenon c. If D =, t ndcate that the fault and fault phenoenon are ot uted, naely atched copletely; f D = 0, the fault and fault phenoenon are copletely dfferent [9]. Experence data not all vald. Accordng to expert experence, the fault phenoenon vector that obvouly not correpondng to fault phenoenon correpond to a fault, whch dentfed a abnoral. The abnoral hould not be dcarded drectly, but added nto databae after arng. The reaon that f the abnoral after a ajor proble n drect dpoal wll caue the yte to contnue to drop later, the yte wll be cottng a erou error. When conductng dtance dcrnaton, thee abnoral data hould be excluded to avod affect of all probablty abnoral on dcrnaton analy. If th abnoral occur frequently afterward, the frequency of abnoral wll naturally large. Accordng to the abnoral deternaton forula (), t wll not tll n the cope of abnoral. D µ α%, D = (,, ) D () Where, α the abnoral dcrnaton ndex that can be controlled. D. Dagnoe Algorth Degn Dagno algorth flow a follow: Step : Input fault phenoenon to be dagnoed Dx = ( d, d, d n ). Step : For all fault F, =,, n. (a) Copute expectaton vector µ of F wth (); (b) A to all fault phenoenon vector of F, to conduct abnoral dcrnaton wth (); (c)ung all abnoral vector, re-copute expectaton µ of F. Step 3: A far a to be dagnoed vector D x, copute European (or Mahalanob) dtance D of each fault wth (8) or (9). Step 4: Order D fro all to large to obtan dagnoe probablty order table P n / Step 5: The antenance peronnel confr fault accordng to probablty fro all to large. Step 6: The confr reult fed bac to fault data table. The dagnoe probablty order table the probablty P /. P n / ean of fault whoe nuber orted n the -th poton of the table. A to the dagno reult, f t caued by the -th fault, t ndcate that the frt dagno ucceful. If t caued by the -th fault, then the frt dagno falure and econd dagno ucceful. And o on. IV. MODEL SIMULATIO A. Sulaton Algorth Degn The ulaton algorth baed on the above dagno algorth. The tandard to eaure t effcency dagnotc ucce rate DFR of the -th dagno and accuulatve ucce rate DFR, the defnton of whch hown n () and (3). DFR = n / M () Where, n the frequency of vector to be dagnoed after te dagno; M the total te of dagno. Where, DFR = = n M (3) DFR the percentage that fault be dagnoed after te of dagno. Obvouly, = the fault detecton rate. = the probablty that olate fault to two eleent, and o on. The ulaton algorth a follow: Step : A to all fault =,, n, ue Monte Carlo ethod to aple accordng to fault phenoenon vector. Each fault generate group of aple data. Step : Extract a fault x ung rando ethod and then extract a fault phenoenon vector D x. Step 3: To dagnoe wth dagno algorth and P preent probablty order table /. n Step 4: Repeat Step and Step 3 M te. Step 5: For =,, n, tattcal n. Copute DFR and DFR, then output. B. Sulaton Reult Analy A to MQ330-type wood-wool worng equpent yte, there are total 7 typcal fault: rollng bearng fault eccentrc d fault the gear and rac fault tool change Spndle fault cran-connectng rod echancal fault wor pece ntallaton fault and feed drve tructure fault. That denoted a I, I,, I7. The dtrbuton paraeter of yte fault and correpondng phenoenon hown n Table. Degn fault databae wth the ethod of Table and conduct ulaton, where the dtance dcrnaton ue Eucldean dtance. M=000, =000. The abnoral dcrnaton ndex α = 30. Each fault aple to generate 000 vector and extract 000 aple for ulaton. The output reult hown n Table 3 and Table 4.

6 JOURAL OF SOFTWARE, VOL. 6, O. 5, MAY TABLE II. DISTRIBUTIO PARAMETER OF SYSTEM PARAMETER AD CORRESPODIG PHEOMEO Reult of Table 3 how that the nuber of abnoral of each fault lttle, whch content wth actual tuaton. In Table 4, one te fault detecton rate a hgh a The three te accuulatve dagno TABLE III. UMBER OF EXCLUDED ABORMAL. Fault nuber F F F 3 F 4 F 5 F 6 F 7 uber of abnoral The -th dagno F F F 3 F 4 F 5 F 6 F 7 I I I I I I I I I I TABLE IV. DIAGOSIS SIMULATIO RESULT Dagno ucce probablty Mdagno probablty Cuulatve ucce rate ucce rate up to when =3, whch ean the probablty that olate fault to three eleent can up to The reaon vector dtrbuton paraeter of F 4 and F 5 very cloe. Fro the above defnton we can now that thee three fault can be regarded a a fuzzy group. At the oent, we can regard the a a fault, o one te fault detecton rate up to The data reult analy ndcate that th nd of dagno ethod baed fault phenoenon vector dcrnaton effectve. V. COCLUSIO The paper preented a nd of woodworng achnery yte dagno ethod baed on fault phenoenon vector dcrnaton analy. Startng fro the cluterng charactertc of fault phenoenon vector, conduct reaonng rule degn baed on the dea of dcrnaton analy dea. The expert yte odel wa bult ung deternaton and excluon of abnoral. Fnally, ulaton llutraton of MQ330-type woodwool worng equpent prove that the dagnotc ethod ha charactertc of good real-te, ple operaton and hgh dagnotc accuracy. However, the technque a new branch of artfcal ntellgence, o ytec frut are tll not abundant, theore are tll not ature, and the reearch and applcaton are tll n the explorng tage. If we apply t n achnery fault dagno yte, the technque of fault phenoenon vector and fault, retrevng and atchng, elf-tudy ethod, etc. would need further proved. Wth the ncreang coplcaton of the equpent and yte, fault dagno baed on fault phenoenon vector wll becoe an effectve ethod n the fault dagno real. ACKOWLEDGMET The author wh to than Shu-Dong Xu. Th wor wa upported n part by a grant fro the Scence and Technology Agency of Zhejang Provnce General Progra Project o. 007C080, Chna; Technology Agency of Zhejang Provnce R & D Progra Plan Project o. 008C0006-, Chna. REFERECES [] L Zhang, Jan-Hua Luo, Su-Yng Yang, Forecatng box offce revenue of ove wvth BP neural networ, Expert Syte wth Applcaton, vol.36, pp , Aprl 009. [] Wann-Yh Wu, Shuo-Pe Chen, A predcton ethod ung the grey odel GMC (, n) cobned wth the grey relatonal analy: a cae tudy on Internet acce populaton forecat, Appled Matheatc and Coputaton, vol.69, pp.98-7, 005. [3] Gavn C. Cawley and cola L.C. Talbot, Fat exact leave-one-out cro-valdaton of pare leat-quare upport vector achne, eural etwor, vol.7, pp , Deceber 004. [4] Xue-Cheng X, Aun-eow Poo, Saw-Kang Chou, Support vector regreon odel predctve control on a HVAC plant, Control Engneerng Practce, vol.5, pp , 007. [5] Zogg D, Shafa E and Geerng H P., Fault dagno for heat pup wh paraeter dentfcaton and cluterng, Control Engneerng Practce, vol. 4, pp , 006. [6] Yun-Je Xu, Wen-Bn L, Forecatng of the total power of woodworng achnery baed on SVM traned by GA, 00 The nd Internatonal Conference on Coputer

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