New Method for Multivariate Statistical Process Monitoring New Method for Multivariate Statistical Process Monitoring

New Method for Multivariate Statistical Process Monitoring

  • 期刊名字:北京理工大学学报(英文版)
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  • 论文作者:PEI Xu-dong,CHEN Xiang-guang,L
  • 作者单位:School of Chemical Engineering and Environment
  • 更新时间:2020-11-10
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论文简介

Journal of Beijing Instiute of Technology, 2010, Vol. 19, No. 1New Method for Multivariate Statistical Process MonitoringPEI Xu-dong (裴旭东),CHEN Xiang-guang (陈祥光),LIU Chun-tao (刘春涛)( School of Chemical Engineering and Environment, Bijing Institute of Technology. Bejing 100081 , China)Abstract: Aprocess operations more reliably. Fisher discriminant analysis (FDA) is used to derive a feature discriminantdirection ( FDD) belween each normal and fault operations, and each FDD thus decided constructs the featurespace of each fault operation. Individuals control charte ( XmR charts) are used to monitor mulivariale proces-ses using the process data projected onto feature spaces. Upper control limit ( UCL) and lower control limit(LCL) on each feature space from normal process operation are calculated for XmR charts, and are used to dis-tinguish fault from normal. A varialion lrend on an XmR chart reveals the type of relevant fault operation. Ap-plications to Tennessee Eastman simulation processes show that this proposed method can result in better moni-toring performance than principal component analysis ( PCA )-based methods and can better identify step typefaults on XmR charts.Key words: Fisher discriminant analysis; individuals control chart; mulivariate statistical process monitoringCLC number: TP 277Document code: A Article ID: 1004-0579(2010)01-0092-07Multivariate statistical process monitoringcomponents, FDA-based methods aim at determining( MSPM) is an important field of process monitoring forthe optimal discriminant direction which can maximallydynamic,multivariate and nonlinear processes. Krestaseparate fault data from normal ones. Multiway FDAet al. provided the basic idea of using multivariate sla-and improved multi -model FDA are developed to moni-tistical monitoring to control continuous processes'"l.tor batch processes"" -121.He et al. proposed a newThey used principal component analysis ( PCA) tofault-diagnosing method based on fault directions ircompress multivariate information down into a low-di-pairwise FDA and showed that FDA was superior tomensional space which retained most of the informa-PCAIBI. Pei et al. proposed methods of fault detectiontion, and used control charts to monitor the processand identification in chemical processes using FDA andtherein. Later on, many improvements have beencontrol charts, and pointed out their capability ofachieved,such as dynamic PCA ‘2],multi-scaleachieving better performance-18. In this paper, aPCAS-4), and kermel PCA{s-6). In addition, inde-new approach using FDA and individuals control chartspendent component analysis ( ICA),another dimen-(XmR charts) is proposed for monitoring the type ofsionality redution technique, has been used forfaults more reliably. In this method, FDA is used toprocess monitoringderive the feature discriminant direction ( FDD) be- .Fisher discriminant analysis has also been used fortween normal and fault operations. Upper control limitprocess monitoring as a dimensionality reduction tech-(UCL) and lower control limit (LCL) on each XmRnique[10]. Different from PCA- and ICA-based methodschart of relevant FDD are calculated. This new methodwhich deal with information on normal data alone tocan be used to monitor process operations in terms offind the reduced principal components or independentthe variation trend of data projected onto FDD. In ad-中国煤化工Received 2009-01-16Sponsored by the Seientife Research Foundation for Retumed Overseas Chinee.MYHCNMHGChinaBiographyPEI Xu-dong(1975- ), lecturer, Ph. D. . xdpei@ bit. edu. en.-92-PEI Xu-dong (裴旭东) et al.1 New Method for Muliariale Saistical Process Monioringdition, it has been applied to Tenessee Eastman simu-w'(m,-m.)(m, -m;)'w=w'S,w,(6)lation processes, with comparisons to conventionalwhere S, is the between-class scatter matrix, which isPCA-based methods conducted.defined as1 MethodS。=(m, -m,)(m,-m,)'.(7)Similarly , the two scatters satistyThe proposed method is based on data sets of nor-mal and various kinds of fault operations. It consists of弓+弓=w's.w.(8)derivation of FDD and projected trend monitoringwhereS. is the within-class scatter matrix, with the(PTM) along FDD using XmR charts.following definition:1.1 Fisher Discriminant Directions.= En, (x-m,)(x-m,)T. (9)Fisher discriminant analysis is a linear dimension-Now Fisher criterion function can be rewritten inality reduction technique for finding a direction alongwhich data are optimally grouped into two classes. Theterms ofS, and S.:process is called derivation of Fisher discriminant diJ(w) =w"'S,w(10)rection. The optimal discriminant direction is deter-w'S.wmined by maximizing the satter between different clas-To maximize J(),the direction w should beses while minimizing the dispersion degree within eachidentical to the eigenvector corresponding to the largestone.eigenvalue in the generalized eigenvalue issue:Le's divide a given set of n d-dimensional sam-S,w=λS.w.(11)ples x1,*,"",*。into two subsets, X and xz,whichIfS. is nonsingular, Eq. (11) can be reriten inhaven and n2 samples (n +m2 =n) respectively.the conventional way, i.e. ,The mean of a subset of d-dimensional samples is de-s.'Ss,w=λw.(12)fined asThe discriminant direction w of the maximingm.=一Ex,i=1,2.(1)function J(.) is the searched Fisher discriminant di-rection.If there is a one-dimensional projection direction1.2 Projected Trend Monitoring Along FDDw, the projection of sample vectorx; on w is given byUsing XmR Chartsy二wx,j=1,2.,*,n.(2)XmR control charts are useful in monitoring uni-All n proections y ,2,.. ,y。are grouped into thevariate aystems. However, when applied to a mulivari-subsets Yi and Y2x- The means for the projections of theate system in which a chart is given to each variable,two subsets are denoted by m and m2, then we havemonitoring will become complicated and time .consu-ming, therefore no longer practical.m,=w'm,,i=1,2.(3 )For multivariate processes, any two elasses of dataThe scatter of projected samples is defined ascan be optimally grouped along a certain FDD. Projec-不式S (y-m).ted trends of these data along these directions can beFisher discriminant analysis takes up the projec-monitored using XmR charts. Given a set of n projec-tion direction w which maximizes the following objec-ted datax,x.,"",*n, the moving range is defined astive function:the absolute diference between two successive projec-tions(m, -m)'(5 )M.=lx.一x,(13)引+号中国煤化工change between theThe separation of the two projected means obeys::YHCNMH G(m, -m)'=(w'm, -w'm,)'=Letx be the average of all projections, and M, be-93-Journal of Beijing Institute of Technology, 2010, Vol. 19, No. 1the average moving range, then UCL and LCL are de-from a fault operation and denoted by triangles. Thefined astrends of variable U and U2 on XmR charts are shown inUcL =x+2.660 M,(14)Fig.1c and Fig. 1d respectively, each with its corre-Lc=x-2.660 M,,(15)sponding control limits. The trends of D. clearly distin-where 2.660 is the XmR chart constant. If a fault isguish the fault data from the normal ones, but thedetected in the process by using Eqs. (14)(15), type .trends of U2 do not. Fig. le and Fig. 1f show the trendsof the fault can be traced in terms of the trend of pro-of principal components PCI and PC2 with control lim-jected data along FDD.its. The trends of PC2 clearly distinguish the fault dataWhen there is a fault process, the optimal separa-from the normal data, but the trends of PC1 do not.tion between normal and fault data along FDD makes itThe first princeipal component is less satisfactory thansimpler and more efficient to monitor the projected datathe second one. Therefore, it is necessary to select ap-instead of either the original data or their principalpropriate principal components for quick and accuratecomponents. Fig. 1 shows an example of trend compar-monitoring when PCA -based methods are used. Fig. lbisons among projected data along FDD, the measure-shows the trends of Fisher component ( FC) along FDDment results and the projected data on principal compo-with control limits. These trends can clearly distinguishnents. Fig. 1a shows two classes, I and I,of two- .fault data from normal ones. This example shows thevariable data, U and D2; Class I data are from a nor-advantage of monitoring projected trends by FDD overmal operation and marked by ecircles while Class Ithe other two approaches.150LCLUGL0.ela I= -501.CI.C..-150-0.4-_-250 -200-150-100-50 0 50 T00020406080100204060801o0(细) original data(b) trend by FDA(c) trend ofu,1.5-10_UCI.huca.。-10CL-.s-2-20-(L.-.5 却- 4068010020406080100(d) lendoror,(e) trendof PCI()trend. of PC2Fig. 1 Trende comarionproducts, G and H, from four reactants, A, C, D and2 ApplicationE through the following reactions2.1 Tennessee Eastman ProcessA(g) +C(g) +D(g)- +G( liq),The proposed method is applied to TennesseeA(g) +C(g) + E(g)-→H( liq).Eastman (TE) simulation processes. Fig. 2 shows aMcAvoy and Ye present a multi-oop single-input-schematic diagram of a typical TE plant. Five major single-out2wt mntrml atntureplotted by dottedoperation units are included in this plant: reactor, lines中国煤化工_3ses for the base op-product condenser, vapor-liquid separator, a recycleeratifHC N M H Gtrol system stisfiescompressor and a product stripper. It produces twolI the specifications and is able to deal with 20- 94-PEI Xu-dong (裴旭东) et al. / New Mehod for Mulivariase Staistical Process Monitoring四hrimqpray良0-四Crondenuer rolingr[cundenspr四-四13.良。-四- -四⑦⊥良2四1上四0-Oreactor coolingED-(C良10]民了T2品。↑slram团h-0-T @-@-@-cI良_produrt ,岗Fig.2 Tennessee Easlman challenge procese witb base controldifferent types of disturbances.Tab.2 Faults2.2 Process Monitoringnumberprocess variabletypeIn this study, twenty-two continuous-measurementIDV(1)A/C feed ratioslepvariables are used, as listed in Tab. 1. The right sideIDV(2)B compositionstepIDV(3)D feed temperaturecolumn shows where and what to measure. For exam-IDV(4) .reactor cooling waler inlet tlemperatureple, XMEAS(1) measures the feed flowrate of reactantIDV(5)condenser cooling water inlet temperatureA. Seven faults, all of step type, designed in the TEIDV(6)A feed losselepsimulator are listed in Tab. 2 and used to evaluate theIDV(7)c header pressure lossproposed method.Tab.1 Continuous process measurementsTennessee Eastman process control test program(TEPCTP) coded in FORTRAN by Downs and VogelmeasurementdeseriptionXMEAS(1)A feed flowratecan be used to simulate normal as well as all types ofXMEAS(2)D feed lowrateXMEAS(3)E feed flowratefault operations. 100 normal data and 100 fault dataXMEAS(4)A and C feed flowratewill be generated from TEPCTP for each fault. ByXMEAS(5)recycle 0lowraleusing these dala, the optimal discriminant directionXMEAS(6)reactor feed raleXMEAS(7)reactor pressurecorresponding to each fault is determined. The controlXMEAS(8)reactor levelcharts of the projected trends of each fault are shown inXMEAS(9)reaclor LemperatureXMEAS( 10)purge rateFigs.3 -9. Projected trends of normal data are markedXMEAS(11)product separator temperalureby dots, and projected trends of each fault are speci-XMEAS(12)product separalor pessurefied by asterisks. These seven figures indicate the stepXMEAS(14)produet separator underlowchanges of the 7 faults from normal operation.XMEAS(15)stripper levelXMEAS(16)stripper pressurePerformance of this process monitoring is relatedXMEAS(17)stripprr underlowto the locations of measurement variables and types ofXMEAS( 18)stripper temperatureXMEAS( 19)faults. If detected faults are strongly connected toXMEAS(20)compreesor workmeas中国煤化工ts can show notie-XMEAS(21)reactor cooling waler outlet temperatureXMEAS(22)condenser cooling waler oulet temperatureableMYHC N M H Gotherwise the efetof faults on measurement variables may weaken. For一95一Journal of Beijing Insitute of Technology, 2010, Vol.19, No. 1fault number IDV(1) or IDV(2), a transient responsements are strongly connected to the root causes, and ais clear. The first reason is that TE process does notclear step change appears in all relevant projecteddirectly measure the A/C feed ratio and B composi-trends. Therefore, the proposed PTM gives accuratetion, the two root causes. The second reason is that thefeature description of faults.effects of these two faults are measured through otherFor comparison reasons, control charts of eachvariables which are dynamically regulated by control-fault on the first and the second principal componentslers.extracted from normal data are also shown in Figs. 3 -For IDV(3), blending of D feed with A feed and9. The dots are projections of normal data, and the as-E feed before it enters reactor weakens the infuence ofterisks are those of the fault. The projected trends ofD feed temperature on the temperature measurementthese fault data did not clearly indicate the step chan-variables. The projected trend of fault IDV(3) showsges occurred in the TE process. This result shows thatsmall changes from the projected trend of the normalthe PTM is better than PCA-based methods for featuredata.identification of faults.For the other 4 faults, the 22 continuous measure-1000.02_ TCL..-100--0.02L.L-50-出-0.06-”-150-0.10-200-700--0.14 4030 120 160 200040801201602004(80 120 160 200(a) pieee trends on FDD(h) pmrererd lrenda of PCI(c) prieeted trends of PC2Fig.3 Prieeted trends of IDV(1)2(s面0.05--20皇0.02-2 -15-0.011-20--80--25--1205040~8012016020040 80 120 160 20040(回) pieeed lrende on FDD() pripeted trndw of PCI() pieted trends ofPC2Fig.4 Projected trends of IDV(2)sF4-03|LCL20.0h豆0.0110-0.030120 160 200(a) piered rnrdrs on FDD叫pjerir trnda中国煤化bsd2Fig.5 Prijected trends of:YHCNMHG- 96-PEI Xu-dong (裴旭东) et al. / New Method for Mulivariate Statistical Process Monitoring0.s5厂0.2525-0-0.20ucL20-。0.15至15t205IaL.0.100.0510-LCLICI.0-0.05 40 0201602000 80120 160 2000一 4080120160 20(细) pojered trends on FDD(h) pjeee trends of PCI(0) pmjeled trends nf PC2Fig.6 Prijeted trends of IDV(4)0.1212-6CL0.08-器0.04uCL.空-10-12-da.-0.04E14040801201602000 40 80120 160 200(间) pojerted trndo on FDD() prerterdl trends of PCI(c) prijected trends of PC2Fig.7 Projected trends of IDV(5)00-o- -0.05-20-0.10-空呈0.15-100-0.20-04030 120 160 200(细) prijerted trends on FDD(h) prmjerted trends of PCI(c) pmjeetedd trenda of PC2Fig.8 Prijeced trende of IDV(6)1.0F400-700F600-0.8-00500-4000.4-t 300100-200-0.2-.1..040801201602080 120 160 200o4080120160200(a) pripetred trende on FDD6) pjprtred trends of PCI(c) poeted lrende of PC2Fig.9 Projeced trends of IDV(7)inant direction. By using this method the inapplicabili-Conclusionty of univariate SPM methorls tn multivariate processesIn this paper, a new method for multivariate sta-can I中国煤化工oitoring projecredetistical process monitoring was proposed using XmRtrendsC N M H Gparisons to monito-charts to monitor projected trends along Fisher discrim-ring original variables and to monitoring projected- 97-Journal of Beijing Instiute of Technology, 2010, Vol. 19, No. 1trends on principal components. An application to TE[9] Lee」 M, QinSJ, Lee I B. Fault delection and diagnosisprocess has also showed that the proposed method maybased on modified independent component analysis[J].AIChE Jourmal, 2006, 52( 10): 3501 - 3514.result in fealure idenification of faults better than PCA-[10] ChiangLH, Rusell E L, Braalz R D. Fault diagnosisbased methods.in chemical processes using Fisher discriminant analy-sis, discriminant partial least squares, and principalReferences :component analysis [J]. 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