Prediction of Machine Tool Condition Using Support Vector Machine

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Joural of Physcs: Coferece Seres Predcto of Mache Tool Codto Usg Support Vector Mache To cte ths artcle: Pegog Wag et al 0 J. Phys.: Cof. Ser. 305 03 Vew the artcle ole for updates ad ehacemets.

1 Joural of Physcs: Coferece Seres Predcto of Mache Tool Codto Usg Support Vector Mache To cte ths artcle: Pegog Wag et al 0 J. Phys.: Cof. Ser Vew the artcle ole for updates ad ehacemets. Related cotet - Research o earg lfe predcto ased o support vector mache ad ts applcato Chuag Su Zhousuo Zhag ad Zhegja He - Predcato of Crae Codto Parameters Based o SVM ad AR Xu Xuzhog Hu Xog ad Zhou Cogao - Fault Progoss ad Dagoss of a Automotve Rear Ale Gear Usg a RBF- BP eural etwork Ym Shao Je Lag Fegshou Gu et al. Recet ctatos - Tool Codto Motorg Of Cyldrcal Grdg Process Usg Acoustc Emsso Sesor A. Aru et al - Mache learg ased tool codto classfcato usg acoustc emsso ad vrato data hgh speed mllg process usg wavelet features P. Krshakumar et al Ths cotet was dowloaded from IP address o 8/09/08 at 0:45

2 9th Iteratoal Coferece o Damage Assessmet of Structures DAMAS 0 IOP Pulshg Joural of Physcs: Coferece Seres do:0.088/ /305//03 Predcto of Mache Tool Codto Usg Support Vector Mache Pegog Wag Qgfeg Meg Ja Zhao Juje L Xufeg Wag Theory of Lurcato ad Bearg Isttute X a Jaotog Uversty X a Cha E-mal:seor@sa.com Astract. Codto motorg ad predctg of CC mache tools are vestgated ths paper. Cosderg the CC mache tools are ofte small umers of samples a codto predctg method for CC mache tools ased o support vector maches SVMs s proposed the oe-step ad mult-step codto predcto models are costructed. The support vector maches predcto models are used to predct the treds of workg codto of a certa type of CC worm wheel ad gear grdg mache y applyg sequece data of vrato sgal whch s collected durg mache processg. Ad the relatoshp etwee dfferet egevalue CC vrato sgal ad machg qualty s dscussed. The test result shows that the tred of vrato sgal Peak-to-peak value surface ormal drecto s most relevat to the tred of surface roughess value. I treds predcto of workg codto support vector mache has hgher predcto accuracy oth the short term 'Oe-step' ad log term mult-step predcto compared to autoregressve AR model ad the RBF eural etwork. Epermetal results show that t s feasle to apply support vector mache to CC mache tool codto predcto.. Itroducto It s a key techology to evaluate ad predct the workg codto of CC mache tools for the purpose of esurg relale operato of mache tools ad mprovg the performace of mache tools. The CC mache tools are o a drecto of hgh speed hgh accuracy heavy-load ad compoud machg ad the mechacal structure s ecomg more ad more comple that t s dffcult to detect potetal falures early. Wthout tmely dagoss ad early warg early falures ca cause mache tools to work uder worse codto whch wll result creasg of rejecto rate fluctuato the qualty ad declato of productvty. For the purpose of reducg the defectve rate ad mateace costs t s very mportat to determe accurately ad tmely whether there are chages mache rug codto forecast the developmet tred of mache rug codto evaluate the workg codto of mache tools correctly ad make early maagemet ad predctve mateace accordg to the codto of mache tools. Due to audat workg codto formato estet vrato sgals of mechacal equpmet [] ths paper the tme sequece of vrato sgals the workg process s pcked to predct the treds of machg codto ad qualty. Tradtoal tme sequece aalyss techque ad predcto theory are maly ased o lear autoregressve AR model ad lear autoregressve movg average model ARMA whch ca ota etter predcto results o the lear system rather tha olear system. I recet years eural etwork model was successfully appled to o-statoary tme sequece predcto [] ut t ca ot e wdely used ecause of achevg emprcal rsk mmzato prcple oly. Support vector mache SVM [] s a ew mache learg method ased o statstc learg theory whch uses ew learg mechasm to realze structural rsk mmzato prcple ad s sutale for solvg the prolems such as olear hgh dmeso ad local mmum. Support vector mache ca esure hgher accuracy for a log-term predcto compared wth tradtoal regresso techques may practcal applcatos [34.]. Therefore forecastg model ased o Pulshed uder lcece y IOP Pulshg Ltd

3 support vector mache ecomes oe of the research hotspots artfcal tellgece feld ad has ee wdely used [34].. Theoretcal Formulato SVM was tally developed y Vapk 995 []. It s ased o learly separale optmal separatg hyperplae ad s desged for classfcato. It ca e appled fucto appromato prolems ad also has good performace regresso prolems. The core thought of SVM s the troducto of olear mappg fucto whch maps orgal model to hgh-dmesoal space ad costructs optmal separatg hyper plae the feature space. It coverts a olear prolem of low dmeso space to a lear oe of hgh dmeso space y usg kerel fucto to realze the classfcato... Basc theory of SVM for fucto regresso [5 6] There are lear regresso ad olear regresso SVM. Let us cosder the followg lear regresso fucto. The goal s to estmate ukow real-valued fucto the relatoshp: f y where s weght vector s the as term s a multvarate put ad y s a scalar output. Itroducg o-egatve slack varales ad the optmzato prolem ca e epressed as Mmze C 0 C l Suject to 0 y y where C s a postve costat regularzato parameter ad s loss fucto. K f Lagrage equato s : l y C L l y 4 ad are Lagrage multpler. Dual prolem s: mamze j j y Q 5 Suject to y 6 9th Iteratoal Coferece o Damage Assessmet of Structures DAMAS 0 IOP Pulshg Joural of Physcs: Coferece Seres do:0.088/ /305//03

4 9th Iteratoal Coferece o Damage Assessmet of Structures DAMAS 0 IOP Pulshg Joural of Physcs: Coferece Seres do:0.088/ /305//03 Regresso fucto s: olear regresso fucto s: f 7 f K 8.. Least Square Support Vector Mache LS-SVM The complety of the SVM algorthm proposed y Vapk ad others s relevat to the umer of trag samples the larger the umer s the more comple the correspodg quadratc programmg prolem s. Low calculatg speed ca ot meet the demad of system dyamc modelg ad detfcato. I order to solve such prolems J.A.K.Suykes proposed a mproved algorthm called Least Square Support Vector Mache LS-SVM 999 [7] whch replaces osestve loss fucto wth quadratc loss fucto. Quadratc optmzato s chaged to lear equato y costructg the loss fucto so the tradtoal SVM's quadratc programmg prolem s coducted y solvg a seres of lear equatos whch the least square system s used as loss [4 ]. fucto ad equalty costrats SVM are replaced y equalty costrats O a set of put samples LS-SVM uses olear mappg to covert the o-lear trag data to hgh dmesoal feature space y whch o-lear fucto estmato prolem chages to lear fucto estmato prolem. ow set regresso fucto as y. I LS-SVM regresso estmato regresso prolem s: Least Square Support Vector Mache LS-SVM m e T s.t s e y 9 where e s error vector ad s regularzato parameter. Itroducg Lagrage multpler R 9 ca e chaged to: T m Jlssvm m e [ y e y ] 0 olear regresso estmato fucto ca e epressed as: y k.3. Predcto method ased o LS- SVM Tme sequece { t } t ca e predcted y SVM. We take r <r< samples from the whole tme sequece as trag samples ad the rest as testg samples. For more effcet use of lmted data t s recostructed that s to say trasform oe-dmesoal sequece to a matr form so that larger amout of formato s otaed. m m X 3 m m Y r rm rm r r 3

9th Iteratoal Coferece o Damage Assessmet of Structures DAMAS 0 IOP Pulshg Joural of Physcs: Coferece Seres 305 0 03 do:0.

fucto as followg: r m y K t 3 Here t=m+ r K s kerel fucto. t The the frst step predcto s: Here { r r } rm rml l r m r rm K 4 R 3. Epermetal detals 3.

After the preparatory work t egs grdg ad collectg the vrato sgals at the same tme. The vrato sgals are stoped collecttg ad the date are saved after the the grdg s fshed.

Fgure shows the sesors arragemet accelerometers were mouted o the cover of the grdg wheel spdle y magetc seat.

5 9th Iteratoal Coferece o Damage Assessmet of Structures DAMAS 0 IOP Pulshg Joural of Physcs: Coferece Seres do:0.088/ /305//03 Where m s emeddg dmeso maps ca e created as: f Oe step ahead predctve value s epressed as: : R m l f l l l m Learg samples ca e traed y the regresso fucto as followg: r m y K t 3 Here t=m+ r K s kerel fucto. t The the frst step predcto s: Here { r r } rm rml l r m r rm K 4 R 3. Epermetal detals 3.. Vrato data acqusto Fgure. Worm wheel grdg CC mache tools.. Fgure. Sesors arragemet. The workg codto of a worm wheel grdg CC mache tools fgure s motored. After the preparatory work t egs grdg ad collectg the vrato sgals at the same tme. The vrato sgals are stoped collecttg ad the date are saved after the the grdg s fshed.durg mache processg of all 8 gearsthe vrato sgals for each gear are collected. Fgure shows the sesors arragemet accelerometers were mouted o the cover of the grdg wheel spdle y magetc seat. 0# chael coects to B-as horzotal ormal drecto of grdg surface # chael coects to B-as vertcal sestvty s 500mv/g. Samplg frequecy s 0000Hz. B-as rotate speed s 3000r/m the processg C-as rotate speed s 8 r/m. Whe the grdg s fshed surface roughess Ra GB of each gear s measured y profle testg strumet as fgure 3 shows radomly selected terval of 80 degrees of two tooth face measured ad proe 4

6 9th Iteratoal Coferece o Damage Assessmet of Structures DAMAS 0 IOP Pulshg Joural of Physcs: Coferece Seres do:0.088/ /305//03 the movemet drecto of the wheel processg grdg drecto perpedcular. The Ra values are lsted tale. Tale. Gear surface fsh the processg for 8 gears Raum Characterstc values To descre the system codto the character of the sgal should e aalyzed the purpose of characterstc aalyss s to trasform the orgal sgal to characterstc values ad fd out the relatoshp etwee characterstc values ad the system codto. O the ass of characterstc aalyss characterstc values whch have good regularty ad are sestve to codto chage ca e used as patter vector of fault dagoss [8]. The characterstc value s etracted from the vrato sgals whch are Metoed 3. such as: Mea Value Mea = X X 3 4 Stadard devato Value Std Skewess Value Skewess = Kurtoss Value kurtoss= Peak-to-peak Value Xr Value Pp= ma-m Xr= [ ] ; Xmea Value Xmea= Xrms Value Xrms = Xp Value ; ; Xp=mama -m. I order to elmate accdetal factors the vrato sgals are dvded to equal legth each as a su-sample. For each su-sample the average value of characterstc value s calculated such as Mea Std Skewess Kurtoss Pp Xr Xmea Xrms ad Xp. These average value treds ad surface roughess treds are compared Fg from whch we fd that the tred of B-as horzotal vrato sgal Peak-to-peak value fts well wth gear surface roughess tred. Thus B-as horzotal vrato sgal Peak-to-peak value s used as characterstc value of processg qualty codto predcto grdg mache. 5

7 9th Iteratoal Coferece o Damage Assessmet of Structures DAMAS 0 IOP Pulshg Joural of Physcs: Coferece Seres do:0.088/ /305//03 a Fgure3. Characterstc values compared wth measured roughess value: a B-as horzotal B- as vertcal. 4. Results ad dscusso I the paper Peak-to-peak values are etracted every secods from the vrato sgal grdg machg process whch form a sgal varale tme sequece to predct the workg codto. For gve tme seres t t t tme sequece predcto s to estmate the value of +k tme ased o the oservato value of hstorcal tme sequece whch s to fd out the relatoshp etwee future tme value ad hstorcal oservato value k s the predcto step whe k= t's Oe-step predcto; whe k> t's Mult-step predcto. I ths paper the Mea Asolute Percetage Error MAPE s appled to asses the predcto alty. 00 MAPE 4.. The choce of kerel fucto The Commo kerel fucto: Lear kerel fucto: k ; d Polyomal kerel fucto: k ; 6

cross-valdato method ca also e used to select. The feature space of RBF kerel fucto s fte dmesoal ad lmted samples the feature space s learly separale so t's a wdely used kerel fucto.

8 9th Iteratoal Coferece o Damage Assessmet of Structures DAMAS 0 IOP Pulshg Joural of Physcs: Coferece Seres do:0.088/ /305//03 3 Gauss Radal Bass Fucto RBF: k ep / 4 Sgmod fucto: k = tah [ v +c] For a specfc prolem whch kerel fucto to choose has ot ee determed the geeral rule s to select y eperece cross-valdato method ca also e used to select. The feature space of RBF kerel fucto s fte dmesoal ad lmted samples the feature space s learly separale so t's a wdely used kerel fucto. The RBF kerel fucto has lttle effect o short-term predcto of SVMs ut t shows etter alty log-term predcto [3]. I the paper RBF kerel fucto s troduced to make a predcto. 4.. The choce of LS-SVM parameters ad Emeddg dmeso The ma parameters are the regularzato parameter ad the kerel fucto wdth for LS- SVM usg RBF these two parameters maly determe the learg ad geeralzato alty of LS-SVM [9] Lterature [0] vestgated practcal selecto of hyper-parameters for support vector maches SVM regresso. For the purpose of automatc optmzato of parameters a wde rage Cross-Valdato method [] ad Grdchearch method are chose the paper whch are used commoly model parameters selecto. I addto the emeddg dmeso m 'Mult-step' ad 'Oe-step' predcto has a great mpact o the predcto accuracy. Fgure4 shows the Mea Asolute Percetage Error MAPE whe m takes dfferet values. ad are the optmal value whe chose y Cross-Valdato method ad Grdchearch method. Tale lsts the emeddg dmeso m ad whch makes the MAPE mmum Mult-step'ad'Oe-step' predcto. Fgure4. Emeddg dmeso's mpact o the predcto error of 'Mult-step' ad 'Oe-step'. Tale. LS-SVM parameter selecto LS-SVM m MAPE/ % parameter Oe-step e-step LS-SVM predcto results 7

9 9th Iteratoal Coferece o Damage Assessmet of Structures DAMAS 0 IOP Pulshg Joural of Physcs: Coferece Seres do:0.088/ /305//03 I tale m ad are chose to predct Peak-to-peak Value sequece of vrato sgals the grdg process. I ths sequece the fst 00 cosecutve pots are selected for regresso trag samples whle the rest 59 pots are used for the test samples. The predcto results of 'Oe-step' ad 'e-step' are respectvely show Fgure5 ad Fgure6. Fgure 5. 'Oe-step' predcto. Fgure 6. 'e-step' predcto LS-SVM compared wth autoregressve AR model ad the RBF eural etwork Tale 3 shows the MAPE comparso etwee LS-SVM ad oth the autoregressve AR model ad the RBF eural etwork 'Oe-step' ad 'e-step' predcto. Tale 3. LS-SVM compared wth autoregressve AR model ad the RBF eural etwork MAPE/ % Predcto model Oe-step e-step autoregressve AR RBF eural etwork LS-SVM Coclusos Ths paper dscusses the relatoshp etwee dfferet egevalue CC vrato sgal ad machg qualty t also refers to sestve drecto error. I treds predcto of workg codto SVMs s appled to estalsh 'Oe-step' ad 'Mult-step' predcto model whch makes predcto for grdg machg codto. The test result shows that the vrato sgal Pp value surface ormal drecto s most relevat to surface roughess value addto SVMs ca make a etter result oth the short term 'Oe-step' ad log term mult-step predcto. SVMs shows etter predcto alty the short term 'Oe-step' ad log term mult-step predcto compared wth eural etwork predcto model. Therefore whe the vrato sgal Pp value surface ormal drecto s used as egevalue t's feasle to motor ad predct CC machg codto y SVMs.. Ackowledgmets Ths research work s facally supported y the atoal Scece ad Techology Major Specal Project of Chao. 009ZX The authors would lke to thak the revewers for ther valuale commets o the paper. 8

10 9th Iteratoal Coferece o Damage Assessmet of Structures DAMAS 0 IOP Pulshg Joural of Physcs: Coferece Seres do:0.088/ /305//03 Refereces [] Zhag X. Research o large rotary machery operato state detecto ad predcto. PhD thess. X 'a Jaotog Uversty X a Cha998. [] Vapk V. The ature of Statstcal Learg theory. [M ]. ew York: Sprger-Verlag [3] Yag J Y Zhag Y Y Zhao R Z. Applcato of Support Vector Maches Tred Predcto of Vrato Sgal of Mechacal Equpmet[J]. Joural of a jaotog uversty : [4] Che B J. Load forecastg usg support vector maches: A study o EU ITE competto 00 [ R ]. Tae: atoal Tawa Uversty00: -. [5] Gu S. Support vectormaches for classfcato ad regresso. ISIS Techcal Report Southamp to: Uversty of Southamp to998. [6] Burges C. A tutoral o support vector maches for patter recogto. DataMg ad Kowledge Dscovery S ; : 67. [7] Suykes J. A. K. & Vadewalle J Least squares support vector mache classfers. eural Processg Letters [8] L Y. Research o Kerel Based Fault Recogto ad Codto Forecastg for Mechacal Power ad Trasmsso Systems. PhD thess. atoal Uversty of Defese Techology. Chagsha Cha 007. [9] Xag Z Zhag T Y Su J C.Modellg of olear systems ased o recurret leastsquares support vector maches[j]. Joural of System Smulato : [0] Cherkassky V Ma Y Q. Practcal selecto of SVM parameters ad ose estmatofor SVM regresso. eural etworks [] Mchael W. BroweCross-Valdato Methods[J]. Joural of Mathematcal Psychology :

An Introduction to. Support Vector Machine

An Introduction to. Support Vector Machine A Itroducto to Support Vector Mache Support Vector Mache (SVM) A classfer derved from statstcal learg theory by Vapk, et al. 99 SVM became famous whe, usg mages as put, t gave accuracy comparable to eural-etwork