Hybrid Dynamic Continuous Strip Thickness Prediction of Hot Rolling

Transcription

1 Hybrid Dynamic Coninuous Srip Thickness Predicion of Ho Rolling Lijie Sun, Cheng Shao and Li Zhang Absrac Shor-erm forecasing in srip hickness of ho rolling is criical o rolling echnology, so ha dynamic conrol can be accomplished o increase producion and improve produc qualiy. Predicing srip hickness behavior has been always a challenging ask due o is complex and non-linear naure. Auoregressive inegraed moving average(arima) model has been verified wih a beer shor-erm forecasing performance, for he problem of low muli-sep predicion accuracy, he rolling sraegy is proposed o updae model parameers, which develops rolling ARIMA(RARIMA) model. In addiion o improve he overall forecasing accuracy of srip hickness, hybrid forecasing of ime series daa is considered. Hybrid forecasing ypically consiss of an ARIMA predicion model for he linear componen of ime series and a nonlinear predicion model for he nonlinear componen. In his paper, back propagaion neural nework(bp) is furher inroduced o forecas he residual of RARIMA model, and rolling ARIMABP(RARIMABP) coninuous forecasing model will be developed, in which rolling forecasing mechanism is used. To he effeciveness of he comprehensive evaluaion mehod, a sabiliy evaluaion index is presened, in addiion, he proposed mehod is examined on he wo groups of srip hickness daa from 6mm srip finishing mill group of ho rolling and he resuls are compared wih some of he basic forecas mehods. The resuls show ha he proposed hybrid mehod could provide a considerable improvemen for he forecasing accuracy and sabiliy. Index Terms ARIMA; BP; hybrid predicion; rolling updaing I. ITRODUCTIO OT only srip hickness accuracy of ho rolling affecs usabiliy and operaion process, bu also srip hickness deviaion impacs on saving meal effec[], while i is he mos difficul o conrol in he process of producion. Shorerm forecasing of srip hickness is criical o rolling echnology so ha dynamic conrol can be accomplished o increase producion and improve produc qualiy. However, i presens non-saionary random characerisics of srip hickness samples in shor-erm forecasing and modeling o predic is more difficul. Foundaion iem: Projecs(4AA48) suppored by he aional High-ech Research and Developmen Projec (863) of China Sun Lijie is wih Insiue of Advanced Conrol Technology, Dalian Universiy of Technology, Dalian, 64, China, Docoral sudens( LIJIE98855@6.com) Shao Cheng is wih Insiue of Advanced Conrol Technology, Dalian Universiy of Technology, Dalian, 64, China, Professor, docoral uor ( cshao@dlu.edu.cn). Zhang Li is wih School of Informaion, Liaoning Universiy, Shenyang, 36, China, Professor (corresponding auhor o provide phone: 3878, zhang_li@lnu.edu.cn). Predicing srip hickness behavior has been always a challenging ask due o is complex and non-linear naure. There are, essenially, wo ways can be used o accomplish he srip hickness predicion[]. The firs, known as predicion by fundamenals, consiss of idenifying he main facors affecing he srip hickness, analyzing how rolling variables inerac wih each oher, and finally, building a causal model, such as regression model. An alernaive way of predicing process parameers of ho rolling is o use ime series model, in which fuure srip hickness behavior is inferred from is own hisorical daa. I is difficul o build mahemaical model because he process of ho rolling mill is a non-linear sysem, in which los of processing parameers such as rolling force, roll speed, fricional force, emperaure, roll-gap ec. have been ineraced. Thus a number of daa-driven models have been successfully applied o shor-erm predicion behavior. These models can be divided ino wo caegories: ()Classical saisical models such as MA(Moving Average), AR(Auo-Regressive), ARMA(Auo-Regressive Moving Average), and ARIMA(Auo-regressive Inegraed Moving Average)[3]. Anoher ypical model is Grey model [4]. These models are ypically linear, only aking hisorical values of he prediced variable as inpu daa, hence compuaionally less expensive; ()on-convenional machine learning models based on ime series such as As(Arificial eural eworks)[5], SVM(Suppor Vecor Machines)[6], and Fuzzy Logic[7]. The machine learning also are called black-box or daa -driven models, and hey are non-parameric modeling mehods ha only use hisorical daa o learn he sochasic dependency beween pas and fuure. Srip hickness predicion aims a high accuracy and reliabiliy. Unlike one-sep predicion, muli-sep predicion is more difficul[8], since i have o deal wih various addiional complicaions, like accumulaion of he error, accuracy reducion problem, and increasing uncerainy[9]. I has been verified ha no single mehod or model works well in all siuaions. In general, i is more effecive o combine individual models for making forecass[]. Then, wo new forecasing mehodologies are emerging, namely combined forecasing and hybrid forecasing[]. Combined forecasing model ackles he ask in wo seps, wih he firs sep being o make forecass using muliple plausible model, and he second sep being o combine hese forecass using weighing algorihms. The key of his predicion sraegy is o seek effecive weighs in order o improve he predicion performance. For example, srip flaness and gauge complex conrol based on combined GA-BP algorihm wih muli-encoding was proposed in

2 lieraure[]. In addiion, DS(Dempser-Shafer) evidence heory fusion algorihm is ypically applied in he combined forecasing models[3]. Hybrid model merges wo ime domain models. The firs model is used o idenify he ime series dynamics and he remaining model is used o approximae he residuals[4]. On he oher hand, oher hybrid models are made of a preprocessing block, which decomposes he ime series ino several sub-series using WT(wavele ransform)[5-6] or EMD(empirical mode decomposiion) echnique[7]. Afer ha, convenional or machine learning based models are used o forecas he sub-series. By merging he obained sub-series forecasing resuls, he forecas of original ime series is achieved. I is necessary o save he daa rend, namely, higher predicion accuracy is imporan in he muli-sep predicion. Many sudies have shown ha ARIMA is an effecive forecasing mehod wih high forecasing accuracy in -sep ahead predicion as demonsraed [8], bu he informaion is progressively los in he ieraive muli-sep forecas[9], and predicion accuracy gradually declines. For his problem, curren soluions rely heavily on he compensaion funcion in residual model, ha is, inroducing oher algorihm o improve he predicion accuracy of ARIMA model, which increases he compuaional complexiy significanly. As is known o all, he predicion principle of ARIMA is ha he model equaion is obained by fiing and he fuure poin is compued according o he correlaion coefficiens. Considering real-ime volailiy of srip hickness, in order o rack he changes, here is he evidence o assume ha real-ime updaing ARIMA model equaion coefficiens in he process of predicion can improve is predicion accuracy. In addiion, he sudies also have shown ha he error of he radiional predicion mehod(also called residual) should be given enough aenion. I has verified ha he compensaion effecs of predicion deviaion can improve he accuracy of predicion for original prediced resuls[]. So i is an efficien way o improve he predicion accuracy ha inroducing he predicion deviaion esimaion o form a new predicion mehod in he radiional way[]. A presen, many scholars a home and abroad have ried o form hybrid ARIMA ime series forecasing model o solve low predicion accuracy problem in many research fields[-3]. Based on his experience, i will be ried o combine rolling ARIMA wih error compensaion aemp o obain beer predicion resuls in his paper. onlinear forecasing performance of BP neural nework has been widely used and recognized[4-5], and previous research more confined o he saic forecas. A presen, i is verified ha he rolling mechanism can increase he predicion accuracy and robusness[6-7], so his mechanism is also used in error compensaion from BP neural nework. On heoreical basis of rolling ARIMA model and BP neural nework, a new hybrid dynamic coninuous forecasing model will be proposed for srip hickness of ho rolling. In his paper, i is he main goal o build a kind of forecasing mehod, which can obain muli-sep predicion wih high performance and provide enough ime o predic he srip hickness values in advance so ha ime delay problem can be avoided in dynamic conrol of srip hickness. Firsly, experimenal daa is colleced from sampling device o ibaanalyzer sofware in he compuer, in which ibaanalyzer is used preliminary analysis of srip hickness in order o deermine effecive srip hickness daa. The performance in his paper is compared wih oher models using hree indexes, in which he firs wo are widely used o evaluae predicion accuracy of model, he hird evaluaion index is pu forward o access he sabiliy of he model. Second, i is verified ha ARIMA model is suiable for forecasing srip hickness of ho rolling in his paper, and rolling updaing sraegy is proposed o fi ARIMA model coefficiens in real ime in order o keep rend informaion of srip hickness, which is formed a new ARIMA model denoed as RARIMA model. I is helpful in improving he forecasing performance wihou increasing compuaional complexiy. I is known o all ha ARIMA is a kind of linear mehod, and i is an efficien way o improve he predicion accuracy ha inroducing he predicion deviaion esimaion o form a new hybrid predicion mehod in he radiional way. BP neural nework is adoped as nonlinear forecasing model, and i is necessary o build BP neural nework wih rolling forecasing performance. A kind of dynamic rolling sraegy is presened, which is o se oupu node as and realize muli-sep predicion hrough rolling forecas mechanism according o rolling dynamic predicion idea so ha i avoids renewing he ne. Thus i is saving ime and space complexiy. Finally, a hybrid forecasing model denoed as RARIMABP is buil, which consiss of RARIMA predicion model for he linear componen and rolling BP neural nework predicion model for he nonlinear componen. Through comparing he forecasing resuls of muliple predicion mehods, i is verified ha hybrid forecasing sraegy proposed in his paper is beneficial o overall forecasing efficiency for srip hickness of ho rolling in aspecs of predicion accuracy and sabiliy. II. PRELIMIARIES A. Experimenal daa acquisiion Objec of his sudy was srip finishing mill group of ho rolling from a cerain seel mill, which consiss of nine racks wih he widh of 6mm rolling surface and.3 mm srip arge hickness. Experimenal daa is colleced from he sampling device o ibaanalyzer sofware in he compuer, in which ibaanalyzer sof is used as preliminary analysis, hen programming for processing he daa is underaken on Malab Ra fla. Two differen baches of exi srip hickness are seleced on Sepember in, and he par of he signals from he ninh roll are shown in Fig. and Fig., in which ordinae unis are mm. The sample daa plays an imporan role in he predicion process of srip hickness, and he seleced daa mus cover enire daa space and represenaive. Therefore, he daa sample number is sufficien o reflec he mill sae in he case of he inerval is.s. The firs se of rolling exi daa is from :33: o :33:4 in Fig., and he second se of rolling exi daa is from :45: o :45:4 in Fig., in which sampling ime is 4s. Two groups of exi hickness daa under he ninh rack are exraced, and each group of daa conains daa samples, in which 5 as he raining samples for fiing predicion model, and 5 as esing daa. Two groups of srip hickness daa are shown in Fig.3 and Fig.4, respecively.

3 Srip hickness(mm) Srip hickness(mm) Fig.. Original signal from he firs bach of plae Fig.. Original signal from he second bach of plae The firs group of daa The raining sample The es sample Srip hickness sample poin Fig.3. The firs group of daa The second group of daa The raining sample The es sample Srip hickness sample poin Fig.4. The second group of daa B. Dynamic rolling forecasing mechanism In general, forecasing sraegies are divided ino wo kinds, namely, dynamic and saic predicion. Dynamic predicion underakes muli-sep predicion in he seleced cerain esimaed inerval, while in he saic predicion, only rolling -sep ahead predicion is implemened, in which real values insead of he prediced values are added o he esimae inerval in each sep predicion. In he predicion process, saic predicion is chosen wihin he sample or model fiing esimae, and dynamic predicion mus be used ouside he sample. I is obvious ha he saic predicion can no grasp nonlinear flucuaion characerisics of srip hickness, so in his paper, dynamic sraegy is applied in muli-sep predicion of srip hickness. To fairly compare he performances under differen forecasing models, five differen forecasing horizons are applied, including, 3, 5, 7 and 9-sep ahead, respecively. In he case of -sep ahead, he M observaions are used o predic he -sep ahead value. For he forecasing horizons more han sep, rolling forecasing mechanism is used. For insance, 3-sep ahead forecasing is performed based he available M- observaions and he prediced values of he wo daa poins which are closes o he predicion poin bu currenly unavailable from observaion. In fac, he second closes poin is prediced firs and he firs closes poin is prediced based on M- observaions and he prediced value of he second closes poin. Similarly, 5, 7 and 9-sep ahead forecass make use of he closes 4, 6, and 8 prediced daa poins, respecively. C. Evaluaion indicaors The goal of his paper is o obain higher muli-sep predicion accuracy and sabiliy for srip hickness of ho rolling. The performance of he proposed forecasing model is compared wih oher models using hree indexes, in which he firs wo are widely used o evaluae predicion accuracy of model[8], he hird evaluaion index is pu forward o access he model sabiliy. The firs index is he roo mean square error(rmse), which compares he prediced ime-series daa wih he real ime-series daa. The RMSE is defined as, RMSE f o () Where f denoes he prediced value for srip hickness a momen, and o refers o he real value of srip hickness a momen. The second index is he mean absolue error (MAE), which is defined as, f o MAE () The hird index is he error variance(ev). For he variance represens he degree of daa off cener and may measure he flucuaion magniude of a bach of daa. Under he condiion of he same sample size, he greaer he variance, he more unsable he daa is. EV is defined as, EV = f o f o (3)

4 Where f o is he average error of srip hickness predicion. III. ARIMA AD RARIMA A. ARIMA forecasing model ARIMA is a popular saisical model for ime series analysis and forecasing applicaions[9-3], which is expressed in he formula (4), d B X B u (4) Where p B B B B, formula,,,3, B B B B X q, and p B.In he is he srip hickness ime series; is normal whie noise wih mean value and a variance; i,, p and j,, q is being i esimaed coefficien; B represens backward difference operaor. B. Seing he orders In he process of building ARIMA model, i is imporan o deermine he orders of p, d, and q, Seing he orders includes hree major seps: model idenificaion, parameer esimaion and diagnosic checking. In model idenificaion process, one or more model candidaes could be found suiable for he ime series. In such case, auocorrelaion funcion(acf) and parial auocorrelaion funcion(pacf) can be applied o make he firs guess abou he order. Then ypical Akaike s informaion crierion(aic) is adoped o deermine he model orders[3]. AIC crierion funcion is shown in formula (5). The model under minimum AIC value is opimal. Once he model is idenified, he parameers need o be esimaed, and he seleced parameers should generae he lowes residual in principle. The common mehod of esing he residual randomness is Ljung-Box Saisics, and he proposed model is suiable for fiing he hisorical daa when he residuals are uncorrelaed. S AIC S ln ˆ (5) j p Where S is he oal number of unknown parameers in he model, ˆ is he esimaion of variance in some way, and is he sample size. For he firs group of daa, srip hickness ime series is denoed as X, in which he firs 5 daa poins as are used o model for ARIMA. The original ime series is non-saionary shown in Fig.5, hen i is necessary o underake firs order difference processing and obain he series X X. I is obvious ha ACF and PACF are boh railing, so he series ARIMA p d q, in which d. In order o reduce compuaional complexiy produced by he evaluaion parameers, high order AR model fiing is adoped in his paper. Se p among -, X belongs o,, when AIC= -.966, he model is opimal, ha is ARIMA. The fiing equaion is X (9,,), which is used o fi obained and shown in formula (6) : B -.3B B.59B.68B -.456B (6) B.3897B.43B.965B For dynamic rolling forecasing mechanism, L-sep predicion of he model X X X X u is calculaed by he formula (7): Zˆ n L Zn ˆ L Zn ˆ L pzn ˆ L p (7) Where Zˆ n j X j. For he firs group daa, n j he fiing equaion of firs order difference sequence is shown in formula (8): Zn ˆ L.3Zn ˆ L.8333Zn ˆ L.59Zn ˆ L 3 ZnL 4.456Zn ˆ L Zn ˆ L 6 Zn ˆ L 7.43Zn ˆ L 8.965Zn ˆ L 9.68 ˆ.3897 The prediced values of final srip hickness are obained by inverse difference for he prediced resuls of X. -sep predicion resuls are shown in Fig.6 for he firs group of srip hickness daa. Table I records he forecasing performance from -sep o -sep predicion for he firs group of srip hickness daa under ARIMA (9,,) model. 4 5 X (8) Srip hickness Srip hickness Original sequence of srip hickness Sample number Difference sequence of srip hickness Sample number Sample Auocorrelaion Sample Auocorrelaion.5 Sample Auocorrelaion Funcion Lag Sample Auocorrelaion Funcion Lag Sample Parial Auocorrelaions Sample Parial Auocorrelaions Sample Parial Auocorrelaion Funcion Lag Sample Parial Auocorrelaion Funcion Lag Fig.5. ARIMA model deerminaion for he firs group of daa

5 srip hickness(mm) forecased value original value L prediced values. Use he prediced values o updae model coefficiens, hen forecas nex sep predicion. RARIMA forecasing mehod needs wo major seps o implemen srip hickness predicion, including model fiing and exrapolaion predicion. Predicion process of RARIMA model is shown in Fig.7. -sep ahead forecasing resuls of ARIMA and RARIMA are conrased in Fig.8 and Fig9. I is obvious ha RARIMA model has a beer improvemen for -sep ahead predicion of ARIMA model, which verifies he effeciveness of rolling updaing idea srip hickness sampling poin Fig. 6. -sep predicion resuls for he firs group of daa TABLE I THE FORECASTIG PERFORMACE OF -STEP AHEAD FOR THE FIRST GROUP OF DATA ARIMA RMSE MAE EV e I can be seen from Fig.4 ha ARIMA has a good performance for -sep predicion of srip hickness, bu wih he increase of sep lengh, he forecasing accuracy drops and prediced resuls become unsable. Why can appear such resul? Looking bake he process of building ARIMA model, for L-sep ahead predicion, he observed hickness values for he calculaion in nex cycle was inroduced when and only when compleing ieraion calculaion of L ime, which leads ha inermediae process of L-sep forecasing mus be used he prediced value of previous momen. While he model equaion coefficiens were no esimaed again using he prediced value of srip hickness, and he more ieraion number is, he more he model equaion coefficiens are no suiable for new sequence characerisics, so he accuracy becomes lower. In pracical engineering, he less sep ahead hickness predicion can no provide enough ime for rolling equipmen parameers o imely adjus o achieve accurae conrol of srip hickness, so i is necessary o increase forecasing sep lengh and mainain or improve he sabiliy of he ARIMA model predicion accuracy and predicion resuls. C. RARIMA forecasing model In view of ARIMA model problem, namely significan reducion in he muli-sep predicion accuracy, his paper pus forward rolling updae parameer hough: in he process of muli-sep ahead predicion calculaion, forecasing value a momen is go hrough ieraion, which is aken advanage of re-esimaing he model parameers in order o ge new model equaion, including he prediced informaion, hen underake he predicion a momen. Afer compleing L-sep in advance, inroduce measured values o correcion model parameers and underake nex cycle of muli-sep predicion calculaion. amely, for L-sep predicion, i involves M L pracical values and Fig.7. Flowchar of RARIMA modeling for srip hickness predicion srip hickness(mm) srip hickness(mm) sep ahead forecasing of ARIMA(9,,) forecased value original value srip hickness sampling poin Fig.8. -sep ahead predicion of ARIMA -sep ahead forecasing of RARIMA(9,,) forecased value original value srip hickness sampling poin Fig.9. -sep ahead predicion of RARIMA

6 IV. RARIMABP HYBRID DYAMIC PREDICTIO A. RBP forecasing mehod As is known o all ha BP neural nework(bp) is a nonlinear model[33]. I is one of he mos popular neural nework models in business applicaions, especially for ime series predicion. BP is used as he seleced nonlinear models o combine wih he linear ones fied by ARIMA model. The key moivaion for doing so is due o he ruh ha BP do no make any assumpion abou he daa[34]. Insead, hey ry o learn he funcional form of rue model from he daa iself. For BP, i ypically employs hree or more layers of processing elemens: an inpu layer, an oupu layer, and a leas one hidden layer. In order o achieve hybrid dynamic muli-sep predicion of srip hickness, i is necessary o build BP neural nework wih rolling forecas performance. In general, here are wo schemes o achieve his goal: he one is o se oupu layer node equal o forecasing sep lengh. Due o simple hough, he presen sudies mosly adop his way of nework build[35-37]. While his sraegy need renew ne and rain a every ime of changing forecasing lengh, boh ime and space complexiy significanly increases; anoher sraegy is o se oupu node as. According o rolling dynamic predicion idea, rolling forecas mechanism[38-39] avoids renewing he ne. I has been proved in heory ha wihou limiing he number of hidden layer nodes, hree layers (only one hidden layer) of he BP nework can achieve arbirary nonlinear mapping, in addiion, residual of he model is small daa, herefore, as a kind of error compensaion model, i is no necessary o build complex nework srucure and spend a lo of ime and space. As demonsraed in lieraure [4] ha he parameer p of ARIMA model is consisence o he number of inpu layer nodes in BP. Therefore, se inpu layer node number as 9, and implici layer node number according o he empirical formula n n m a, in which m refers o oupu node number, n is inpu node number, and a is consan ha is an ineger from o. The experimen verifies ha implici layer node number is under opimal performance. Oupu node number is. This paper adops he second sraegy o achieve hybrid dynamic muli-sep predicion of srip hickness. The residual of RARIMA(9,,) model for he firs group of srip hickness is denoed as R,,,,. RBP neural nework is buil as hree layer ne srucure (9,,), in which learning facor is.8 and exciaion funcion is S logarihmic funcion. For insance he firs group of daa, rolling muli-sep predicion sraegy of RBP neural nework is shown in Fig.. B. RARIMABP srip hickness forecas Specifically, RARIMABP predicion mehod includes he following six seps: ()Fi ARIMA model using hisorical srip hickness daa o ge he coefficiens of he model equaion; ()Compare o he original srip hickness wih he observed value and obaining he residual of ARIMA model, build and rain rolling BP neural nework. (3)Deermine wheher reaching he predicion sep lengh, if less han he predicion sep lengh, using he prediced values o updae ARIMA model equaion coefficiens, oherwise, updae he ARIMA model coefficiens wih he observed srip hickness values; (4)Use RARIMA model o ge linear par predicion of srip hickness; (5)Apply he rained RBP o obain he residual predicion, and among hem, L is lagging sep lengh; (6)Summing ŷ and Rˆ, and he final srip hickness values are obained, denoed as f, in which f yˆ Rˆ. C. Experimen and resul analysis Experimen In order o esimae he conribuion of modeling srip hickness of ho rolling using RARIMABP model, he laer is compared o he models of basic ARIMA, RARIMA and RBP using wo groups of ho rolling ime series and hree esimaion indexes. Table Ⅱ shows he forecasing performance in advance, 3, 5, 7 and 9 seps for he firs group of srip hickness. Fig.. Rolling muli-sep predicion sraegy of RBP

7 TABLE Ⅱ MULTI-STEP FORECASTIG PERFORMACE FOR THE FIRST GROUP OF DATA Sep Evaluaion indicaors ARIMA RARIMA RBP RARIMA- BP lengh RMSE MAE EV I can also be observed ha depending on forecasing horizon, hybrid mehod ouperforms he oher single model approaches, namely, ARIMA, RARIMA, RBP. Rolling updaing sraegy has obvious improving effec on basic ARIMA; RBP has a grea advanage in aspec of forecasing sabiliy, and he advanage of RARIMABP model is obvious wih forecasing sep lengh increasing. Experimen The second group of srip hickness daa applies he same process o model wih he firs group of daa. The model of opimal performance is ARIMA(5,,), and fiing equaion is shown in formula (9): Zn L Zn L Zn L Zn L (9).34 ZnL4.874 ZnL5 In he same way, RBP is used o forecas he residual from he second group of srip hickness, he bes nework srucure is hree layer srucure (5,,). Table Ⅲ shows he forecasing resuls, 3, 5, 7 and 9 seps in advance for he second group of srip hickness. TABLE Ⅲ MULTI-STEP FORECASTIG PERFORMACE FOR THE FIRST GROUP OF DATA Evaluaion indicaors Sep lengh ARIMA RARIMA RBP RARIMA- BP RMSE MAE e EV e e e RBP sill has good predicion sabiliy for he second group of srip hickness daa, bu he model predicion accuracy is relaively lower. The second group of daa furher verifies ha he rolling updaing sraegy has obvious improvemen in predicion performance for basic ARIMA model. ARIMA is an effecive forecasing mehod wih high forecasing accuracy in -sep ahead predicion, bu he informaion is progressively los in ieraive muli-sep forecas. The advanages of he rolling updaing sraegy proposed in his paper increases less compuaional complexiy and space complexiy. Also, being a linear model, daa dynamics rend is preserved and predicion accuracy and sabiliy are high. RBP has a grea advanage in boh forecasing accuracy and sabiliy, which furher illusraes ha dynamic rolling forecas mechanism in muli-sep predicion plays an imporan role, and he advanages of RARIMABP model are obvious wih forecasing sep lengh increasing. In addiion, higher predicion accuracy can be go only using one dimensional ime series, which reduced he demand for raining daa wih higher imeliness of predicion algorihm. V. THE SELECTIO OF FORECASTIG STEP LEGTH In he engineering, srip hickness conrol sysem is consruced by process compuer, AGC conroller, hydraulic screwdown, finishing mill and hickness gauge conroller as shown in Fig.. Fig.. Srip hickness conrol sysem srucure The monior AGC is a gauge conrol mehod which is in common used in srip rolling processing; exi srip hickness is measured by gauge meer, and hen hickness feedback conrol will be carried ou by adjusing roll gap[4]. As gauge meer is insalled a -5 m behind mill sand usually, a delay ime exiss in hickness measuremen, so monior AGC sysem is a pure ime delay sysem. The ime-delay of conrol objec will reduce sysem sabiliy and deeriorae ransiion characerisic. Srip hickness predicion conrol is o add a predicion model in he feedback loop, which uses m consecuive sampling daa before he curren ime k o obain he prediced value a he momen k m hrough cerain predicion algorihm, in which he predicion error e r k y k m replaces curren measuremen error p =

8 ek r k y k, among hem, r k is he desired hickness sequence[4]. This kind of conrol srucure is shown in Fig.. Fig.. Srip hickness conrol srucure based on predicion Sep lengh of srip hickness predicion is closely relaed o ime-delay of srip hickness sysem. Minimum predicion sep is usually, however, when ime-delay of he sysem is as known, minimum predicion sep should be / T, where, T is he sampling ime. In heory, he ime-delay is = l, where, l is he disance beween he hickness gauge v and es poins, and v is rolling speed, bu he speed is a ransformaion, which is gradually from zero o maximum rolling speed, herefore he measured lag ime is usually greaer han he minimum delay ime = l. The maximum v predicion sep lengh is usually closer o he general sysem rising ime, and i is necessary o make rolling opimizaion meaningful, which should include he conrolled objec's dynamic secion. VI. COCLUSIO Shor-erm forecasing of srip hickness is criical o rolling echnology so ha dynamic conrol can be accomplished o increase producion and improve produc qualiy. Srip hickness predicion behavior of ho roll possess dynamic and highly nonlinear characerisics, and "once and for all" daa-driven predicion mehod in he pas is inerval or saic predicion essenially, in order o imely conrol srip hickness of ho rolling, saving daa rend is necessary, namely, implemen muli-sep predicion wih higher predicion accuracy and sabiliy. According o curren research siuaion, his paper presens a hybrid RARIMA- BP predicion mehod. In order o verify he effeciveness of RARIMABP, he prediced resuls are underaken wih wo daa ses from 6mm srip finishing mill group of ho rolling wih nine racks and he comparaive sudies of muliple predicion mehods are presened. In comparison o he previous works above, our research has some advanages: ()The performance of he proposed mehod is compared wih oher models under hree indexes, in which he firs wo are widely used o evaluae predicion accuracy of model, he hird evaluaion index is pu forward o access he sabiliy of he model called he error variance and denoed as EV, and i has been proved ha EV can reveal he sabiliy degree under differen forecasing seps and mehods. () I can be seen from Fig.4 and TableⅠ, ARIMA mehod is an effecive forecasing mehod wih high forecasing accuracy in -sep ahead predicion, bu he informaion is progressively los in he ieraive muli-sep forecas. max (3)ARIMA model is used o fi hisorical daa model equaion, and rolling updaing equaion parameers sraegy is applied in he fuure predicion aiming a reaining more srip hickness rend informaion, which develops rolling ARIMA model. Through experimenal analysis from Table Ⅱ and Table Ⅲ, i can be seen ha RARIMA has an average of % improvemen han ARIMA model in aspec of he forecasing accuracy under he same good sabiliy. Rolling updaing sraegy proposed in his paper increases less compuaional complexiy and space complexiy. Also, being a linear model, daa dynamics rend is preserved and he predicion accuracy and sabiliy are high. (4)From he fifh column in Table Ⅱ and Table Ⅲ, i can be seen ha RBP has good advanage in boh forecasing accuracy and sabiliy, which furher illusraes ha dynamic rolling forecasing mechanism in muli-sep predicion plays an imporan role. (5)ARIMABP model akes advanages of RARIMA wih good linear performance and RBP wih high nonlinear performance, and he sum of he prediced resuls from wo par is regarded as final prediced resuls of srip hickness. Through wo groups of experimens, i is concluded ha he advanages of RARIMABP model is obvious wih forecasing sep lengh increasing. In addiion, higher predicion accuracy can be go only using one dimensional ime series, which reduced he demand for raining daa wih higher imeliness of predicion algorihm. (6)This program also provides a new idea o conrol delay problem in oher areas. (7)Generally, he greaer he sysem lag, he greaer he predicion sep lengh. Wih predicion sep lengh increasing, he predicion accuracy will decrease, which is caused by unknown facors, so dynamic updaing sraegy has a demonsrable effec for muli-sep predicion performance. To sum up, he research has obained cerain achievemen in srip hickness predicion of ho rolling. Our fuure work will be o use he proposed model as inernal model of he model predicive conroller aiming a conrolling srip hickness of ho rolling wih high accuracy. ACKOWLEDGEMET This work was suppored by he aional High-ech Research and Developmen Projec(863) of China (4AA48). REFERECES [] J.J. Zhang, Coninuous srip producion. Beijing: Meallurgical Indusry Press,. [] E. G. D. 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