Application of thermal error in machine tools based on Dynamic. Bayesian Network

Transcription

1 Inernaonal Journal of Research n Engneerng and Scence (IJRES) ISS (Onlne): , ISS (Prn): Volume 3 Issue 6 ǁ June 2015 ǁ PP pplcaon of hermal error n machne ools based on Dynamc Bayesan ewor Xu Yang,Mao Jan College of Mechancal Engneerng, Shangha Unversy of Engneerng Scence, 333 Long Teng Road, Shangha , Chna Correspondence should be addressed o Jan Mao; mao@sues.edu.cn bsrac: In recen years, he growng neres oward complex manufacurng on machne ools and he machnng accuracy have solced new effors n he area of modelng and analyss of machne ools machnng errors. Therefore, he mahemacal model sudy on he relaonshp beween emperaure feld and hermal error s he core conen, whch can mprove he precson of pars processng and he hermal sably, also predc and compensae machnng errors of CC machne ools. I s crcal o oban he hermal errors of a precson machne ools n real-me. In hs paper, based on Dynamc Bayesan ewor (DB), a poneerng modelng mehod appled n hermal error research s presened. The dependence of hermal error and emperaure feld s clearly descrbed by graph heory, and he fuzzy classfcaon mehod s proposed o reduce he compuaonal complexy, hen formng a new mehod for hermal error modelng of machne ools. Keywords: machne ools; hermal error; DB; fuzzy classfcaon; modelng; I. Inroducon rfcal nellgence echnques have been used for many years now n he feld of hermal error modelng n machne ools. The hermal model forms one of he mos crcal elemens n machne ools. In he predcon of hermal error, mos research has focused on he prncple of regresson [1,2]. Chen [3] used a hree-layer rfcal eural ewor () wh a supervsed bac-propagaon ranng algorhm and he sgmod acvaon funcon o map he calbraed hermal errors o he emperaure measuremens. Zheang Unversy n 2002 wh he mproved BP neural newor on hree-dmensonal nonconac measuremen sysem s analyzed n hermal error modelng [4]. Hong Yang and Jun [5] proposed a fuzzy model adapaon mehod s used o updae n he hermal error model under dfferen processng condons. The radonal hermal error model canno handle abnormal suaons, and he srucure and he choce of he ype oo dependen on experence. Research on he applcaon of he Bayesan ewor n hermal error modelng of CC machne ools on he hermal error has opened up a new way, n order o beer solve he complexy and defec of hermal error modelng [6]. R. Ramesh [7] appled Hybrd Bayesan newor o solve hermal error measuremen and modelng problems n machne ools. bref explanaon of he heory of Bayesan ewor s presened as followng: The Bayesan ewor (B) s a graphcal model conssng of nodes represenng causes and effecs n real-world suaons and a se of edges each of whch connecs wo nodes, has been used n medcal dagnosc sysem, sofware esng, web nellgen navgaon, power sysem faul dagnoss, ec. Bayesan newor for a 1 2 x x, x, x, he on probably dsrbuon for x s gven by se of varables 1 2 (,, ) ( ( )) p x x x p x pa x (1) Where probably, 1 x denoes he varable and ( ) (,, ) (,, ) 1 pa x denoes he parens of node x. From he chan rule of p x x x p x x x (2) B s an effecve ool for complex sysems uncerany reasonng and daa analyss, bu he hermal error of machne ool research wh dfferences beween he worng condons are dfferen, hus requrng hermal error model mus have a srong ably o learn, and accordng o he curren worng updae he saus of he model resuls. B n dealng wh real-me racng daa sll has some lmaons, no good wh he expermenal daa 22 Page

2 pplcaon of hermal error n machne ools based on Dynamc Bayesan ewor reflec updaes o he model. Ths paper sees o address he ssue of developng a hermal error model ha accoun for a varey of operang condons whle ye generang accurae predcon. So wll propose fuzzy classfcaon and Dynamc Bayesan ewor o buld a hermal machne error model, a beer soluon of dynamc hermal error modelng problems. II. Fuzzy Dynamc Bayesan ewor Dynamc Bayesan ewor (DB) s a ype of B ha can model me-seres daa o capure he fac ha me flows forward, whch coupled wh he me consrans on he properes of he orgnal newor srucure. I has he advanage boh of model-based and daa-based mehods. nd wh he nroducon of me facor, he daa on he sae of he formaon of dfferen me, reflecs he developmen change rule represened by he varable, and s nuve, hgh precson and adapve for hermal error modelng of machne ools. The acual processng for precson CC machne ools, he hermal error generaed by many facors and here are many unceran facors, also he relaons among hese facors are perplexng, so he requremens of hermal error predcon model should no only be a srong nclusve of many complex facors, bu also he srucure of flexble funcon. In order o accoun for he parculary of hermal error, we presen he DB hermal error model heren s herefore very essenal. 2.1 Dynamc Model lhough he paern of hea ransfer n machne ools s very complex, hese are plausble cause and effec relaonshps ha mgh exs beween he varous elemens of he machne when subeced o varyng operang condons. Therefore, n order o carry ou he research of complex sysem and model should be smplfed [8] : 1. The assumpon of condonal probably n a fne me change process for all s smooh. 2. To solve he problems of hermal error n hs sudy, assumng an envronmen wh Marov naure, ha every sae hea dsoron emperaure and samplng pons are relaed o he me of samplng pons on emperaure and hermal deformaon saes. Bayesan newor srucure nference process, mang nferences and decsons based on pror p( x x ) probables. 3. ssumng ha he condonal probably of adacen me process s seady, whch 1 has nohng o do wh he me, you can easly ge he ranson probably p( x 1 x) n dfferen me. Based on he above assumpons, he esablshmen of DB should be consdered B B : he pror ne B 1,he ransfer ne B,he lmed me n praccal applcaon sage 1,2, T,hen we can ge: T 1, 2, T B 1 1 B 1 p x x x p x p x x (3) varable. If we use px x 1 1 o represen he probably of he curren sae occurs when any prevous me sae s x represens he value of he varable n me, probably dsrbuon of DB can be calculaed for any node as he followng shown: 1, pa x denoes he parens of node x. So, on T 1: 1: T B B (4) p x p x pa x p x pa x The research of hermal error on precson machne ools showed us he parameers of samplng pon emperaure and hermal deformaon daa had dscree feaures. In he expermen, he decson varable s always dscree, and ceran emperaure observaon s connuous, o solve such problems n pure dscree Dynamc Bayesan ewor have some dffcules. In hs regard, hs paper choose he calculaon mehod of dscree fuzzy DB ha fuzzy classfcaon echnques combned wh he dscree DB [9] o solve hese problems. I wll no only mae full use of he advanages of dscree DB whch has relavely faser nference speed compared wh connuous DB, bu also can acheve qualave reasonng under connuous observaon whou loss of nformaon provded. 2.2 Fuzzy Classfcaon In he fuzzy heory, an elemen x s he degree of X belongs o he se, hs degree means membershp. The elemen x mus also ex n ceran membershp wh oher ses, when 0 ( ) 1. Fuzzy se s defned n x and s afflaed wh and X,as he followng: 23 Page

3 ( x, x ) x pplcaon of hermal error n machne ools based on Dynamc Bayesan ewor Frs, he fuzzy classfcaon process s dvded he sample space no several subses, whch s a subse of fuzzy ses. Fuzzy ses s he correspondng dscree DB node saus. Then defnes membershp funcon accordng o acual condon, ha membershp of fuzzy classfcaon s he characerscs of he response varable, no a specfc numercal sze [10]. Dscree B wh hdden pons and M observaon pons, along wh he me developmen can ge he dscree DB wh T me slces, f he observed value s only one combnaon of sae, so hs observaon dsrbuon of hdden varables are: p x, x, x,, x, x, x y, y, y,, y, y, y M 1 2 M T T T T T T p y pa y p x pa x,, p y pa y p x pa x x1, x1, x1,, xt, xt, xt 1,, T; 1,, M; 1,, In hs formula, he parens of noe,, x represens a value of X,value of y for observaon varable y. s accordng o ge fuzzy DB nference formula s: p x, x, x,, x, x, x Y, Y, Y,, Y, Y, Y M 1 2 M T T T T T T p y pa y p x pa x,, p( Y y ) 1 2 M y1, y1, y T p y pa y p x pa x x1, x1, x1,, xt, xt, xt,, 1,, T; 1,, M; 1,, Where p( Y y ) s he value of (5) (6) Y, pa( y ) denoes Y membershp n connuous observaon ha belongs o each saes. III. Developmen of DB Model on Thermal Error mng o mprove he effecveness and accuracy of abnormal suaon managemen n complex process sysem, hermal error should be suded and modeled n a scenfc and sysemac way. Ths paper proposed a DB framewor for hs purpose. The overall worflow s shown n Fgure 1. (7) 24 Page

4 pplcaon of hermal error n machne ools based on Dynamc Bayesan ewor Sage Ⅰ:Temperaure pons developmen Sage Ⅱ:DB developmen nalyss of hermal dynamc process ode deermnaon Deermne he locaon of emperaure sensor Opmzaon of emperaure sensor locaon Develop srucure Opmzaon of emperaure sensor locaon Opmzaon of emperaure sensor locaon Deermnae parameers Develop emperaure pons Parameers learnng wh condon monorng daa Sage Ⅲ:DB appled n hermal error Fgure 1. DB framewor of hermal error research 3.1 Temperaure Pons Developmen number of sudes on domesc and nernaonal machne ools show ha: one of he prmary facors ha nfluence machne ool accuracy s he rse n emperaure of he crcal elemens of he machne. The daa avalable from he machne on a real-me bass s he emperaure values as measured by he hermal sensors mouned a crcal locaons on he machne. Comprehensve experse hs paper esablshes a model of 14 nodes [11], respecvely: X,Y and Z axle nus and ral emperaures, moor emperaure, man shaf bearng emperaure, afer he bearng emperaure, he emperaure of he machne bed, spndle hermal error, hen obaned Dynamc Bayesan ewor model for hermal error of precson CC shown n Fgure Page

5 pplcaon of hermal error n machne ools based on Dynamc Bayesan ewor Man fron axle bearng 1 T8 Man fron axle bac bearng 1 T7 Man fron axle bac bearng 2 T13 The X axs gude T5 The moor T3 Man fron axle bearng 2 T10 envronmenal emperaure T11 The Y axs gude T6 Man fron axle bearng 3 T12 Thermal error d(l) The Z axs gude T9 The X axs nu T1 The Y axs nu T2 The Z axs nu T4 Fgure 2. DB model srucure for hermal error of precson CC 3.2 DB ppled n Thermal Error The above model and he dscree DB nference algorhms, consues he hermal error of DB. DB n addon o he newor srucure, also need o defne he parameers. For dscree DB, he condonal probably s an exper nowledge whch reacs expers vews of he causal relaonshp among he conneced nodes n he newor. Sae ranson probably beween wo me slces s random probably ha changes over me [12]. The specfc calculaon model can be expressed accordng o he condonal probably beween experse and nodes. The ranson probables of DB can be acqured by he pror nowledge of expers. Usng fuzzy classfcaon o dvde he expermenal measuremens of sae parameer doman, n hs paper respecvely dvded no fve saes {1, 2, 3, 4, 5}. ccordng o he formula (7), o calculae probables: p d L T, T, T whch means we can oban condonal probably a he correspondng dl ( ) of dfferen saes when T ( 1, 2,,13) ae any sae. Through he udgmen of values p1, p2, p3, p4, p5 o decde he sae of hermal error area, hen fnally predc hermal error value. IV. Conclusons (1) DB srucure s dfferen from he oher fng modelng heory, comes from he probably of daa, and combned wh he specfc language of graph heory clearly express he dependen relaonshps beween he varous facors affecng he hermal error. nd appled he fuzzy classfcaon and membershp he concep of he measuremen daa and oher scenfc probably dsrbuon, reducng he compuaonal complexy, concludng he probably dsrbuons, mang he numercal predcon and modelng has he hgh-precson hermal deformaon characerscs; (2) DB model s wdely used n he presen sudy n he feld of hrea esmaon and arge assgnmen, ec. ppled o he machne ools hermal error modelng s he curren research n he feld of hermal error for anoher aemp and applcaon, whch also provdes a new effecve way o sudy CC machne ool hermal 26 Page

6 pplcaon of hermal error n machne ools based on Dynamc Bayesan ewor error. (3) Thermal error model based on DB aes full use of he pror nowledge and sample daa, and can dynamcally predc hermal error accordng o he me of machne ools, and wh he ncrease of sample o oban daa updaed. I can reflec he change of worng condon of machne ools n he process of reasonng, o mae beer mee he needs of real-me compensaon. In summary, hs paper use DB srucure for hermal error of machne ools o mae a seres of useful analyss and exploraon, ge he correspondng conclusons. Based on DB srucure n he sudy of hermal error s novely, hs paper s for furher sudy on he expermenal daa and model combnaon. cnowledgemens We would le o acnowledge he suppor of he aonal aural Scence Foundaon of he People s Republc of Chna (o ). References [1] R. Ramesh, M.. Mannan,.. Poo. Error compensaon n machne ools a revew. Par I: Geomerc, cung-force nduced and fxure dependen errors. Inernaonal Journal of Machne Tools and Manufacure 40 (2000) [2] R. Ramesh, M.. Mannan,.. Poo. Error compensaon n machne ools a revew: Par II: Thermal errors. Inernaonal Journal of Machne Tools and Manufacure 40 (2000) [3] J.S. Chen. Fas calbraon and modelng of hermally nduced machne ool errors n real machnng. Inernaonal Journal of Machne Tools and Manufacure 37 (2) (1997) [4] Fu Longzhu, Chen Yalang, D Ruun.BP neural newors compensaon dmensonal surface non-conac measuremen sysem hermal deformaon error research [J]. Elecrcal and Mechancal Engneerng, 2002,19 (4): [5] Hong Yang, Jun. dapve model esmaon of machne ool hermal errors based on recursve dynamc modelng sraegy[j]. Inernaonal Journal of Machne Tools&Manufacure,45(2005):1-11. [6] Ba Fuyou. Thermal error of CC machne ools based on Bayesan ewor modelng research [D]. Maser degree hess of Zheang Unversy, [7] R. Ramesh, M.. Mannan,.. Poo, S.S. Keerh. Thermal error measuremen and modelng n machne ools. Par II. Hybrd Bayesan ewor suppor vecor machne model. Inernaonal Journal of Machne Tools & Manufacure 43 (2003) [8] Xao Qnu, Gao Song. Bayesan ewor n he applcaon of nellgen nformaon processng [M]. Beng: aonal Defense ndusry press, [9] Sh Janguo, Gao Xaoguang. Dynamc Bayesan ewor and s applcaon n auonomous nellgence operaons [M]. Beng: The Publshng House of Ordnance Indusry, [10] Chen Hayang, e Hongyng, Pan Jnbo. Traffc lgh auonomous nellgence decson based on Dynamc Bayesan ewor [J]. Journal of X'an Polyechnc Unversy, 2014,28 (4): [11] Yang Janguo. Inegraed CC machne ools error compensaon echnology and s applcaon [D]. Shangha Jao Tong Unversy docoral hess, [12] Wu Tanyu, Zhang n, L Lang. Esmaon of he r Comba Threa based on Fuzzy Dynamc Bayesan ewor [J]. Fre Conrol and Command Conrol, 2009,34(10): Page