Milling-Tool Wear-Condition Prediction with Statistic Analysis and Echo-State Networks

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1 llg-tool Wer-oo Preco wh Sc Aly Echo-Se ework Guoog Wg & Ru Grou Ve Uvery of Techology, Ve, Aur ABSTRAT: Tool wer he mo commoly oberve uvoble ue mel mllg. The wor or mge cug ool wll cue merl lo mche hu-ow. To ckle h problem, we propoe ew meho for precg he wer coo of e-mllg ool. Fr, we op c-ly echque o lyze he collece. Seco, we elec ereg feure be o Pero-correlo coeffce (P). Flly, hoe feure re pple pu o he o clle echo-e ework o prec ubeque ool wer coo. The expermel reul heorecl ly boh emore h he propoe meho perform beer h ve fee-forwr eurl ework (FF) me-ere eurl ework (TS). ITRODUTIO llg he mchg proce of ug rory cuer o remove merl from workpece progreg (or feeg) reco gle w.r. x of he ool (Grcí-eo 05). I cover we vrey of ffere opero mche vryg from mll vul pr o lrge, hevyuy gg mllg opero. Due o he upremg propery of he rllg proce, mooh ool urfce lwy mple hgh quly of prouco,oherwe, he prouc re uccepble. For ce, ull ool my er he urfce ecree he fgue rece of he workpece. A wor ool c cue more frco whch wll cree he cug emperure le o reource we. Tool wer moorg preco h rce coerble mou of reerch eo he p ece, ool wer h gre effec o he fl prouc prevouly meoe. Therefore, effce oluo houl be propoe o olve h problem. There re my ype of ool wer, for exmple, roug wer of he cug ege, crer wer o he rke fce, frco cue flk ool wer o forh. Severl prmeer for cug wer hve bee vege, e.g., he cug pee, feeg re, cug eph. I rece yer, pley of meho hve bee propoe o help o prouce hgh quly prouc. Geerlly, hee meho re mly ug c echque, gl-proceg meho, eurl ework o o. The repreeve meho clue: A propoe o ue couc pecrum (A e l. 0) where De Jeu ue curre gl o lyze he ool wer coo (De Jeu e l. 003). (Ghoh el.007) (Plmy e l.008) propoe o ue Fee-Forwr eurl ework (FF) for moorg ool wer. O he oher h, (ollm e l.04) rouce meho for re exrco from mulmeol eory h coer me. Th meho be o exrcg ucceve feure from mchery eory gl. Accorg o he lerure, he foremeoe meho work fe for he ool-wer ue. However, he he problem h pr of he meho oly focue o gle feure gore oher oe lke ple or ble ro whch le o urelble moorg reul whle oher o coer he me vro ue. I fc, he mchg proce me ere proceure he po ool coo hppe be o pror e. I cor, h pper we regr ool wer chgg proce me ere proceure geerg equel po oe me ervl. A ech me ep of he ervl, oe po wll be geere whch my epe o prevou,, or po. To cheve uble mufcurg, we propoe h pper ovel meho for precg mllg-ool helhy e be o echo-e ework (ES). Thee re ew ype of recurre eurl ework h hve he bly o memorze. The mjor vge of ES he mplcy of her mplemeo rg. We ue cl ly echque for exrcg muleor feure of mchg ool. Sce cug

2 ool re grully chgg over me, ES ope he precor of ex helhy e. The m corbuo of h pper c be brefly ummrze follow: () A ool wer preco meho propoe be o c ly echque echo e ework. () A umercl compro wh exg meho (TS FF) prove, howg he preco ccurcy of our echque. The re of he pper orgze follow. I eco, we rouce he expermel e he gl-colleco eup. I eco 3, we propoe our m lgorhm for ool-wer-e preco. I eco 4, we rouce he cofguro of ES pree he mulo reul. We e he pper wh coclug remrk reerch reco. T 8.00 m, mplg re 50HZ, f (x) he gl fuco. T T 0 f ( x) () EPERIET DATA SET AD SYSTE STRUTURE Oe pecfc url mllg mche ue for he experme. The mche opere o ge expermel -e uer vrou coo. To collec he mchg-procee-geere, hree ffere ype of eor re lle rou he ool everl poo. Thoe eor re couc emo, ro curre eor. The geere orgze 67 mlb ruc rry wh fel how (Goebel 996). The experme ve o 6 ffere uy ce. Ech ce wh vrou umber of ru. Tool flk wer meure rregulr me ervl. For ech meureme, oe h o op he whole mchg proce. We cqure he experme reul e from ASA repoory (Agogo & Goebel 007). (Goebel 996) gve he cocree rouco of he experme eup. I ecompe he chrcerc of he ue phycl evce, for ce, he ze of workpece, ype of merl er. I lo ecrbe he vrou expermel coo e.g. poo of lle eor, fee re, cug pee eph. The collece gl from ll eor re preprocee before eerg he url compuer. The preproce co o mplfyg flerg hoe, he feeg procee o wo evce. The curre gl of ple moor recly fe o compuer whou furher proce. The mjor reo for ug evce h c mooh he gl mke more cceble for gl proceg. oreover, proporol o he eergy coe of he gl (Goebel 996), ccorg o he Formul. The whole proce epce Fgure. I Formul, Fgure. Expermel eup. 3 THE PROPOSED ETHOD I h eco, we fr rouce wy o elec ppropre feure for he e. The gve bref rouce of he ES moel key globl prmeer (pecrl ru, pry of reervor, ze of ES, pu clg lekg re). Flly, he pecfc ep for mplemeg he propoe meho le ou. 3. Feure exrco eleco The collece rw lwy co oe, borml po oher uexpece problem. To ob goo e for he ly, he mo vluble eco-relev feure houl be exrce elece. Be o ue (Dog el. 006) (Wg e l. 03.), we coer he followg feure exrce from rw whch re le Tble. F he bbrevo of cre fcor, P/AR he pek o verge ro kewe. Dffere feure repree vrou formo bou ool heh e, for ce, he meure of vryg quy whch lo rele o he eergy of gl. Kuro ce he plu of gl Skewe chrcerze ech egree of ymmery of he rbuo rou me. urlly, o ll feure re vluble, bu hr o ece whch oe more eve o he ool wer. A goo feure houl pree coe re wh efec propgo (Wg e l. 03.). I h pper, we ue P, whch meure he epeece of wo or more rom vrble, o

3 rk feure. The wy of compug P how Formul. P Tble. Summry of exrce feure Feure e vlue Vrce xmum F Kuro P/AR Skewe 3. ES moel ( x x)( z z) x Expreo () ES ew ypology of recurre eurl ework (R), fr propoe by (Jeger & H 004). I h ve wy of geerg he eurl ework ue ler regreo lgorhm o r he ework. Recely, ES h rce bg mou of reerch effor. I h pley of ucceful pplco, epeclly ymc per recogo, robo corol me ere preco (Jeger & H 004) (Sh & H 007). The ypcl ES follow he rucure epce Fgure. I h hree ffere lyer whch re he pu lyer, he reervor he oupu lyer. For gve mchg yem, he pu : (3) where T he rug me of mllg yem,,, V, V, A A re A/D moor curre, ble/ple ro couc emo from ble/ple, repecvely. A rge rge y oupu y ( ) VB R gve, whch kow flk wer, he cul oupu wll be (), he oupu meo, here. W he wegh mrx from pu o reervor W he romly geere x ( x ) vr ( x x) mx x ) F ( ( ( KURT x PAR ( ( SKEW x ' u( ) [ T( ), ( ), ( ), V ( ), V ( ), A( ), A ( )] ( x x) ( z z) )) 4 )) 3 coeco mrx from reervor o reervor. ou ou W R he coeco wegh mrx from reervor o oupu. ( ) g( W Fgure. Bc ES rucure. I he l phe, ES romly geere he-lyer coeco whch clle reervor. The pu-o-reervor coeco-mrx reervor er-coeco wll be romly geere kep fxe urg he rg phe. Geerlly, ES re pple o uperve emporl mche lerg k. To r he () ES, y houl cloe eough o y rge ccorg o ere ccurcy. Hece, we c mmze he error rge meureme E (, ), ypclly by ug he Roo-e-Squre-Error (E) o cheve bove gol, he formul : E(, rge ) ou [ T ( ); ( ); ( ); V ( ); V ( ); V ( ); V ( ); A ( ); A ( ); x( )]) (4) Oce he pu fe o ES, he reervor e x() wll be upe wh followg formul: ~ x f ( W [ T( ), ( ), ( ), V ( ), V ( ), A ( ), A ( )]' ou Wx( ) W x( )) (5) x( ) ( ) x( ) x ~ ( ) (6) Where f he cvo fuco he lekg re whch ue he memory lo fcor of ES for he p e. Here, we chooe gmo moel he cvo fuco. The oupu lyer efe ler combo of he reervor e pu: (7) Where [:;:] for colum vecor (or mrx) coceo, g he oupu cvo fuco. The compug performce of ES epe o he followg key prmeer: The pecrl ru, whch ue for geerg he echo e oe ee o mke ure h he mxmum egevlue of pecrl ru lwy le h. The pry of reervor, whch ece he mou of coeco mog euro. The ze of ES, whch he mou of euro embee he reervor. T T ( rge )

4 Geerlly, wh bgger umber of euro, ES perform beer whle lo cree he complexy of ES he me me. Ipu-clg mp he pu o he rge of euro cvo fuco. Lekg-re c be regre he pee of he upe ymc of he reervor creze me (Lukoevcu 0). I ummry, compre wh clcl R, he vge of ES re: () Romly geere reervor coeco uppor rch-ymc erl e for he preco of he oupu. () Romly geere coeco mrx from pu o reervor from reervor o reervor, whch re kep fxe urg rg proce, overcome he low compug effcecy ue of R. (3) For complex o-ler problem, he ler combo of reervor e c lwy ge ccure oluo. 3.3 Specfc ep for mplemeo I h eco, we rouce our meho for ool wer preco. The m e o ue cl echque for exrcg ueful formo eployg ES o eme ool helhy e. The propoe meho ummrze follow: Sep : ollec rw e from eor U mke ppropre cofguro for ES, W for W. Sep : le he e: remove mke up he me or borml vlue. Sep 3: Be o he clee from eco ep, ue c ly echque o exrc he mo vluble relev formo for eco: we op 8 ffere feure. Sep 4: Ue Pero correlo coeffce (P) o rk hoe feure for ech ype of gl. Sep 5: Ue pr of he procee pu o r ES: oe c mully ge he prmeer for ES. Sep 6: Apply he re of he pu o ES prec he comg e. Sep 7: Reur ool wer coo VB. 4 EPERIETS 4. ofguro Accorg o he ecrpo of he expermel e, we coer oe rug ce oe me ere proce. For ech ce, oe pecfc ES ege o prec he ool wer coo. The cofguro of ech ES mully cqure. Sx ffere rug ce re ue o r ES vle he ccurcy of he preco. The elece e re lbele ce, ce, ce 3, ce, ce ce 3, repecvely. (8) To evlue he performce of he propoe lgorhm, we lo compre he mulo reul obe hrough ES, FF TS meho. I he experme, he flk wervb meure geerlly ccepe prmeer for evlug he ool wer coo. VB oberve urg he experme meure he ce from he cug ege o he e of he brve wer o he flk fce of he ool. The meureme Formul Smulo reul To reuce he meo of pu, P pple for rkg feure, he oe wh he op core elece for fuure preco. The ly reul for ffere uy ce re le Tble. Becue of he lmo of pge, we oly l ou pr of P rkg reul of 6 uy ce. We mpleme he propoe lgorhm ATLAB, for ll mulo, ech rug ce ue me rg vlo e. Tble. P rkg. mca mcd Vb_ble Vb_ple AE_ble AE_ple ASE ASE SE ( ( ) rge ( ))

5 The mulo reul re le Tble 3. All uy ce hve he me mulo proce bu wh ffere cofguro. The overll mulo reul how h ES lwy perform beer erm of preco ccurcy. Tble 3. The mulo reul e ES TS FF 4.8e-4.5e-3.5e-3 9.0e-5 3.7e-4.3e e-4.8e-3 6.0e-3 9.7e-4 3.0e-3 3.9e-3 4.8e-4.8e-3.e-3 3.9e-3.5e-3 5.6e-3 5 OLUSIO Th pper rouce ew echque for precg he ool wer e be o c ly echo-e ework (ES). Fr, he c ly ue for elecg vluble feure of pu, he he elece feure re fe o ES o r he eurl ework prec ubeque ool- wer e. The mulo reul how h our meho perform beer h TS FF. To he be of our kowlege, h he fr me ES were ue for mllg-ool-wer preco. A he cug proce eelly me ere proce, o ES hve gre poel he precve-mece problem of yber- Phycl Prouco Syem (PPS). Therefore, our fuure reerch wll focu o pve ES for PPS. AKOWLEDGEET Th work fue by he Docorl ollege - yber-phycl Prouco Syem (PPS) Projec, Ve Uvery of Techology, Aur. The uhor woul lke o ckowlege he ce of Dr. ohme Am Be S for he excelle uggeo gve urg he prepro of h pper. Dog,J.el.,006.Bye-ferece-be eurl ework for ool wer emo. The Ierol Jourl of Avce ufcurg Techology, 30(9-0), pp De Jeu, R.T.R. e l Drver curre ly for eorle ool brekge moorg of mllg mche. Ierol Jourl of che Tool ufcure, 43(5), pp Grcí-eo, P.J. e l.05. A ew precve moel be o he PSO-opmze uppor vecor mche pproch for precg he mllg ool wer from mllg ru expermel. The Ierol Jourl of Avce ufcurg Techology, pp.-. Goebel, K.F geme of ucery eor vlo, eor fuo, go of mechcl yem ug of compug echque. Uvery of lfor, Berkeley. Ghoh, e l Emo of ool wer urg mllg ug eurl ework-be eor fuo. echcl Syem Sgl Proceg, (), pp Jeger, H. & H, H Hreg olery: Precg choc yem vg eergy wrele commuco. cece, 304(5667), pp Lukoevcu,. 0. A prccl gue o pplyg echo e ework. I eurl ework: Trck of he re (pp ). Sprger Berl Heelberg. ollm, A e l. 04. Tme ere reg for coo eme progoc. Jourl of ufcurg Techology geme, 5(4), pp Plmy,P. e l Preco of ool wer ug regreo A moel e-mllg opero. The Ierol Jourl of Avce ufcurg Techology, 37(-), pp.9-4. Sh, Z. & H, Suppor vecor echo-e mche for choc me-ere preco. IEEE Trco o eurl ework, 8(), pp Wg, J. e l. 03. Tool lfe preco for uble mufcurg /epooce REFEREES Agogo, A & Goebel, K llg D Se. I USA: ASA Ame Progoc D Repoory A,.S.e l. 0. The mllg ool wer moorg ug he couc pecrum. The Ierol Jourl of Avce ufcurg Techology, 6(5-8), pp