Preprints of the 19th World Congress The International Federation of Automatic Control Cape Town, South Africa. August 24-29, 2014

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1 Preprints of the 9th World Congress he International Federation of Automati Control Cape on, South Afria August 4-9, 4 A Step-ise sequential phase partition algorithm ith limited bathes for statistial modeling and online monitoring of multiphase bath proesses Wenqing Li, Chunhui Zhao* State Key Laboratory of Industrial Control ehnology, Department of Control Siene and Engineering, Zhejiang University, Hangzhou, 37, China (orresponding author, hhzhao@zjuedun) Abstrat: For bath proesses, suffiient bathes are in general required for statistial modeling and proess monitoring Hoever, sometimes, it is diffiult and may be impratial to ondut multiple yles and ait until enough bathes are available hus, ho to derive reliable proess information based on limited bathes has been an important question Starting from limited modeling bathes, this artile proposes a phase partition and proess monitoring strategy for multiphase bath proesses First, a stepise sequential phase partition algorithm is developed ith limited bathes here a generalized time-slie is onstruted by ombining several onseutive time-slies ithin a short time region to analyze hanges of proess harateristis Multiple phases are thus identified in sequene along time diretion hih are desribed by different phase models he feasibility and performane of the proposed method for online proess monitoring are illustrated ith experimental data from a typial multiphase bath proess IRODUCIO Bath and semi-bath proesses play a signifiant role in the proessing of speialty hemial, semiondutor, food and biology industries for produing high-value-added produts to meet today s rapidly hanging maret Hene safety and reliability of bath and semi-bath proess is foused on and proper proess monitoring and diagnosis method is of great importane (Kourti et al 995, Kosanovih et al 996, Undey et al ) Multivariate statistial methods suh as Multi-ay priniple omponent analysis (MPCA) and Multi-ay partial least square (MPLS) (omios et al (994, 995b), Wold et al 987) have been suessfully used for bath proesses Hoever, onventional MPCA and MPLS may be diffiult to reveal hanges of proess harateristis along the time diretion sine they treat the entire bath data as a single objet it is also diffiult for online appliation here unnon future data has to be estimated Considering that the multipliity of operation phases is an inherent nature of many bath proesses and eah phase shos different proess variable trajetories, operation modes and harateristis, it is better to develop phase-based models (Undey et al, Wold et al 987) hen eah phase-based model an explain the loal proess behaviors, hih effetively improve monitoring reliability and enhane proess understanding Kosanovih et al (994) and Dong et al (995) developed to MPCA (nonlinear MPCA) models to analyze the phase-speifi nature of a to-phase jaeted exothermi bath hemial reator, Lu et al (4) proposed a phase-based-sub-pca modeling method Sine then, phasebased modeling methods (Zhao et al 7, 8) have been idely developed to handle different problems in bath proesses ith multi-phase harateristis Hoever, they used lustering-based phase partition algorithm to get phase information, hih did not tae the time sequene of operation phases into onsideration So time segments ith similar harateristis at different time may be mixed as a single phase, hih maes the phase division results hard to explain and useless for proess understanding An automati step-ise sequential phase partition (SSPP) algorithm (Zhao et al 3) as developed hih an automatially determine phases in order along time diretion in the bath proess here enhaned proess understanding and superior online monitoring performane have been demonstrated Hoever, as an empirial modeling method, it requires suffiient modeling bathes to over statistially suffiient bath-to-bath variations his is relatively easy for bath proesses ith short duration and that are inexpensive to ondut many trial runs Hoever, for slo bath proesses, suh as bio-related proesses, it taes very long time to omplete a bath yle Also, for those bath proesses hih ost muh to operate a bath yle, it is uneonomi to ondut plenty of experiments herefore, it may be impratial to ait until suffiient bathes are available he insuffiieny of modeling bathes arouses diffiulty for phase analysis and statistial modeling Sometimes, although suffiient bathes annot be obtained, several bathes are often available in pratie Ho to analyze phase nature, extrat proess information and develop monitoring models from limited bathes (ie just several bathes) are important issues, deserving signifiant attention o address the above problems, this artile proposes a phase partition and proess monitoring strategy for multiphase bath proesses starting from limited bathes A step-ise sequential phase partition algorithm is developed ith limited bathes here a generalized time-slie is onstruted by ombining several onseutive time-slies ithin a short time region to analyze hanges of proess harateristis After that, phase-based statistial models are developed ith limited bathes and used for online monitoring he feasibility and performane of the proposed method for online proess monitoring are illustrated ith injetion molding proess Although starting from limited bathes, the proposed method an effiiently extrat proess information for statistial modeling and offer reliable fault Copyright 4 IFAC 746

2 9th IFAC World Congress Cape on, South Afria August 4-9, 4 detetion performane Considering that it is ommon that suffiient bathes annot be guaranteed for some industrial proesses, the proposed algorithm is signifiantly meaningful for fault detetion in bath proesses From another viepoint, the ase ith suffiient bathes an be regarded as one extreme ase of the onerned problem MEHODOLOGY In this setion, a step-ise generalized time-slie-based sequential phase partition algorithm is developed to solve the problem of phase division based on insuffiient bathes; then phase-based monitoring system is developed here phase models and time-varying onfidene limits are defined For online monitoring appliation, the status of ne samples an be supervised by adopting the orresponding phase models against the predefined onfidene limits Data Arrangement ith limited bathes In eah bath run (bath index i =,,, I ), assume that proess variables are measured online at =,,, K time instanes throughout the operation yle, forming eah regular bath set, denoted as ( K ) In the present or, bathes are of equal length ithout speial delaration so that the speifi time an be used as indiator for data proessing Here the bathes are limited and the data olleted from I bathes are then arranged as a three ay array ( I K ) At eah time, the time-slie an be separated as ( I ) (=,,,K) For limited bathes, information along bath diretion is not suffiient, so the onventional time-slie hih is omposed of bathes at eah time fails to reveal the proess harateristis as ell as the bath-to-bath variations o replae the short timeslies, a ne data unit should be organized before statistial analysis I I 3I K Variable Bath I I I (I K) ime K K KI I I K Fig Illustration v I K of data arrangement for suffiient bathes Generalized time-slie I K I Short time-slie ase and limited bathes As shon in Figure, several onseutive short timeslies are ombined together to onstrut a generalized time-slie ( I ) (=,,,K- +) is the length of K K time region spanned by the generalized time-slie, so I is the number of observations in eah generalized time-slie Without speial delaration, time-slie means onventional time-slie hih only overs bathes at eah time hile generalized time-slie means the reorganized time-slie overing several onventional time-slies he time index is indiated by the speifi proess time orresponding to the middle time ( ) of eah generalized time-slie For the time intervals before the first time index, they are all represented by the first generalized time-slie, for the time interval after the last time index, they are all represented by the last generalized time-slie In this ay, orresponding to eah time, there is a generalized time-slie For eah generalized time-slie, proess variables do not hange signifiantly ithin suh a short time, so the mean and standard deviation an be alulated as the normalization information hih an be used to treat ne samples hus the normalized generalized time-slie data matrix ( I ) (=,,,K) at eah time are prepared for the folloing phase analysis Phase Partition ith Limited Bathes As mentioned above, generalized time-slies have been prepared hey are then analyzed for phase partition he speifi proedure is presented as follos: Step Data preparation Arrange generalized time-slies from onventional time slies and input the normalized generalized time-slie data matrix ( I ) Step Generalized time-slie based PCA modeling Perform PCA algorithm on the normalized generalized time- slie data matries and get the original models R, r, r r P E t p E ( =,,,K) here and P are prinipal omponents(pcs) and orresponding prinipal loadings R is the retained PCs hih is determined to eep most of proess variability (9% here) hen find the number of PCs that ours most throughout the bath proess and set it as the unified dimension of timeslie PCA models hus PCA models for eah generalized time-slie have the same dimension Step 3 Confidene limit for time-slie model Calulate the monitoring statisti value of squared predition errors () of eah PCA model, e e ; hen, onfidene limit termed C tr is, i, i, i determined by a eighted Chi-squared distribution (Lory et al 995) Step 4 ime-segment based PCA modeling From the beginning of proess, add next generalized timeslie to the former ones and variable-unfold them, ( I ) Perform PCA on the rearranged matrix to get v, the time segment PCA model up to the urrent time, 747

3 9th IFAC World Congress Cape on, South Afria August 4-9, 4 R v, v, v, v, v, v,, r v,, r v, r P E t p E Calulate values for eah generalized time-slie data matrix by using the time segment model P hen the onfidene limit v, Ctr is determined by a eighted Chi-squared distribution v, (Lory et al 995) Step 5 Compare model auray Compare Ctr ith C tr for eah generalized time-slie v, ithin the onerned time region If there exist onseutive three samples revealing Ctr >α* C tr, it means that the v, urrent generated time-slie has different variable orrelations in omparison ith the existing ones he predefined parameter α alled relaxing fator (Zhao et al 3) determines ho muh the time segment PCA model is permitted to be less representative than generalized timeslie model hen the time slies before * are denoted as one sub-phase Step 6 Update data for reursive implementation Remove the first sub-phase, then the remaining bath proess data are employed as the ne input data in the 4th step Reursively repeat step 4~5 to determine the folloing sub-phases Using the above partition proedure, different phases are automatially identified in sequene along time diretion to apture different operation statuses, hih an guarantee similar harateristis ithin the same phase 3 Sub-phase modeling ith limited bathes he sub-phase data ( I K ) are arranged by variable-ise unfolding the generalized time-slies ( I )(,,, K ) ithin the same phase hen PCA is performed on it and e an get the similar underlying harateristis in eah phase: here R, r, r r P E t p E P P P P E () K is the duration of the urrent loal time region, ( I K R ) denote the priniple omponents, P ( R ) are the sub-phase loadings and they reveal the major variation diretions in the urrent time region, R is the number of retained PCs to eep the most variations in eah sub-phase In this ay, the systemati variation in is desribed by, and the residuals E are deemed as noises he subspaes spanned by P ( R ) and E are alled systemati subspae and residual subspae respetively In systemati subspae, monitoring statisti is alulated at eah time, hile in residual subspae e an get Q- statisti() from residuals at eah time: t t S ( ) ( t t ) e e here t ( R ) is the PC vetor separated from, and t is the mean vetor of ( I R ) hih are separated from ; () represents the systemati variations in eah sub- phase for training data S denotes ovariane matrixes for eah phase e ( ) is the PCA residual vetor hih is obtained from the ro vetor in residual matrix E ( I K ) In this or, data of time diretion and bath diretion are mixed at eah time for generalized time-slie, hose variation of normal measurement samples do not follo a multivariate Gaussian distribution, so ontrol limits annot be determined by a F-distribution and a eighted hisquared distribution(lory et al 995) respetively Here, the onfidene limits are defined empirially based on the modeling data We arrange the values of eah monitoring index in a desending order at eah time and hoose the values at 95% perentile of the sorted data A oeffiient is also used to relax the values and the enlarged values are defined as the ontrol limits 4 Online monitoring strategy When ne observing data x ( ) is oming, it is first ne normalized by the mean and variane of orresponding time Based on the monitoring system P, the proess status at eah time an be heed by projeting the urrent measurements onto it: he ne alulated as: ne ne t x P ne ne ne e x t P (3) -statisti and ne -statisti are then ne ne ne ( t t ) S ( t t ) e e ne ne ne Proess status is thus heed by ontinuously omparing the to monitoring statistis ith predefined onfidene limits Here, to evaluation indexes for the performane of monitoring system an be defined by alulating False Alarming Ratio (FAR) and Missing Alarming Ratio (MAR): f m FAR %, M AR % (5) here is the total number of samples, FAR is used to evaluate the monitoring performane for normal ase here if three onseutive samples go out of ontrol, it is deem that false alarming is falsely issued and is the ourrene number of those three onseutive samples Similarly, MAR is utilized for evaluation of monitoring performane for fault ase, if three onseutive samples stay ell in onfidene f (4) 748

4 9th IFAC World Congress Cape on, South Afria August 4-9, 4 limit for issued and -statisti or -statisti, missing alarming is is the number of those issues m In this or, ho to better derive phase information and models from limited bathes for online monitoring is foused on herefore, the performane of monitoring models developed from limited normal bathes is the major onern Here, bath-ise stepping model updating is simply used Whenever one ne normal bath is available, it is inluded into the modeling bathes of normal ase Phases, data renormalization and monitoring models are then updated based on ne information With the supplementation of ne normal bathes, the time length of eah generalized time-slie ( ) ill derease so that the generalized time-slie an more fous on the bath-ise variation 3 SIMULAIO AD CASE SUDY In this setion, a typial multiphase bath proess, the injetion molding, is used to illustrate the performane of the proposed method he effetiveness of the proposed algorithm is demonstrated ompared ith the SSPP algorithm ith suffiient bathes Injetion molding proess, hih is onsisted of three major phases, is a typial multiphase bath proess and has been idely used in previous or for proess monitoring ine proess variables are seleted for modeling, six normal bath runs are onduted under normal operation onditions and are used to develop the PCA monitoring system Besides, four types of fault are onsidered All bathes are unified to have even duration (56 samples in this experiment), hih thus results in three-ay ( I 9 56) here I denotes the number of bathes for both normal and fault ases Six normal bathes are used for modeling and the other ten bathes are utilized for model testing For eah fault ase, ten bathes are used for testing First, the training data (6 9 56) should be variableise unfolded; hen, generalized time-slie ith the length of is determined to be four hus the atual length of generalized time-slie I is about three times of the number of variables (ohnson et al ) Subsequently, PCA is performed on eah normal generalized time-slie data, the number of PCs for eah generalized time-slie is determined to eep 9% variability he unified PC number used for the proposed phase partition algorithm is three he phase partition results are shon in Figure for different values of parameter α in omparison ith the results from SSPP algorithm hih is used at the ondition of suffiient bathes he relaxing fator α used in the proposed algorithm is omparatively larger than that of SSPP algorithm, hat s more, a larger relaxing fator ill result in feer phases Although the proposed algorithm shos different phase division results from SSPP algorithm, they present similar onvergene trend as α hanges Moreover, by using the proposed algorithm, the hole bath proess is automatially partitioned into different time segments in time order based on limited bathes, no extra postproessing has to be arried and division result is more diretly and easy to understand, hih is similar to the that of SSPP algorithm ith suffiient bathes Based on the phase partition result using the proposed algorithm, different PCA monitoring models are developed for eah phase by variable-unfolding data matries ithin the same affiliation, here the oeffiient used to relax ontrol limits is set to be to hen online monitoring is arried on starting from the initial monitoring system able presents the monitoring performane after updating regarding six values of α assessed by FAR for ten normal bathes, the mean and mean absolute deviation (MAD) values of FAR index are alulated Compared ith, monitoring results are more seriously influened by α It is beause that phase partition is implemented based on the evaluation of With α inreases, it is noted that results first derease and then inrease, and the monitoring performane has the same trend able also shos the fault detetion performane after model updating onerning six values of α he results are evaluated by MAR for 4 fault bathes (ten for eah fault ase) It is noted that MAR index indiates similar results ith those by FAR = 4 5 = 4 3 =3 4 5 = 4 =6 4 = 5 4 (a) 4 =3 4 5 =5 4 =5 4 4 =4 4 =8 4 =6 4 (b) Fig Phase partition results for IM proess using (a) SSPP algorithm ith suffiient bathes (b) the proposed algorithm ith limited bathes 749

5 9th IFAC World Congress Cape on, South Afria August 4-9, (b) Fig 3 Online monitoring results for (a) a normal bath (b) a fault bath using the proposed method before updating (a) (a) Fig 4 Online monitoring results for (a) a normal bath (b) a fault bath using the proposed method after updating Considering model auray and model omplexity refleted by Figure and able, the value of α an be set to 8 hen as shon in Figure 3, ithout updating the monitoring model, the online monitoring results for one normal bath hih is operated right after six normal bathes and one fault bath are presented using the proposed algorithm ith the parameter α=8 It is noted that no obvious false alarms are issued for normal ase, indiating loer FAR values For fault ases, there are no signifiant missing alarms for Reliability of the original monitoring model before updating is demonstrated by the above results Sine the monitoring models are developed from limited normal bathes, model updating may be needed as ne normal bathes are available hose proess harateristis more or less different from those for model development Figure 4 shos the online results for one normal ase and one fault ase after updating the monitoring model, here the value of α is also eight It is noted that the updated model an better aommodate the normal variations and an better detet faults than initial monitoring models For the onerned normal ase and four fault ases, the monitoring results are summarized in able for ten testing bathes he mean and mean absolute deviation of FAR% and MAR% are alulated he proposed modeling method hih is based on limited bathes and bath-ise stepping model updating is ompared ith SSPP modeling method ith suffiient bathes For omparison, ith suffiient bathes (3 bathes here), phase partition and statistial models are also developed here generalized time-slies in fat onverge to bath-ise observations at eah time For a fair omparison, best monitoring results are presented for eah method ith the parameter α=8 (for limited bathes) and α=3 (for suffiient bathes) respetively From the results shon in able, starting from limited bathes and using stepping model updating, the values of FAR and MAR are generally loer than 8% Hene, its monitoring performane is in general omparable ith that using models developed from suffiient bathes he results sho that for limited bathes, the phase information an be effetively explored for model development and thus reliable online monitoring performane is obtained using the proposed algorithm 4 COCLUSIO (b) 75 In this or, a sequential phase partition algorithm and modeling method is proposed ith limited bathes to apture the time-varying proess harateristis for multiphase bath proess By rearranging generalized time-slie as ne analysis unit, hanges of variable orrelations are aptured for phase partition hen, based on the phase partition results, PCA monitoring system is set up for online monitoring Simple stepping model updating is implemented to inlude ne normal bath information and improve the monitoring performane he ase study on injetion molding shos the

6 9th IFAC World Congress Cape on, South Afria August 4-9, 4 feasibility of the proposed method for both proess understanding and online monitoring ACKOWLEDGME his or is supported by Program for e Century Exellent alents in University (CE--49), Zhejiang Provinial atural Siene Foundation of China (LR3F3), the Sientifi Researh Foundation for the Returned Overseas Chinese Sholars, State Eduation Ministry and Open Researh Projet of the State Key Laboratory of Industrial Control ehnology, Zhejiang University, China (o IC3) REFERECES Kourti, MaGregor F, (995) Proess analysis, monitoring and diagnosis, using multivariate projetion methods, Chemom Intell Lab Syst, 8, 3 Kosanovih KA, Dahl KS, Piovoso M, (996) Improved proess understanding using multiay prinipal omponent analysis, Ind Eng Chem Res, 35, Undey C, Cinar A, () Statistial monitoring of multistage, multiphase bath proesses, IEEE Control Syst Mag,, 4 5 omios P, MaGregor F, (994) Monitoring of bath proesses using multi-ay priniple omponent analysis, AICHE, 4, Wold S, Esbensen K, Geladi P, (987) Priniple Component Analy-sis, Chemom Intell Lab Syst,, 37 5 omios P, MaGregor F, (995b) Multiay partial least squares in monitoring bath proesses, Chemom Intell Lab Syst, 3, 97 8 Kosanovih KA, Piovos M, Dahl DS, (994) Multiay PCA Applied to an Industrial Bath Proess, Proess of ACC, Dong D, MAvoy, (995) Multi-stage Bath Proess Monitoring, Press of ACC, Lu Y, Gao FR, Wang FL, (4) A sub-pca modeling and on-line monitoring strategy for bath proesses, AIChE, 5, Zhao CH, Wang FL, Mao ZZ, Lu Y, ia M, (8) Improved bath proess monitoring and quality predition based on multiphase statistial analysis, Ind Eng Chem Res, 47, Zhao CH, Wang FL, Gao FR, Lu Y, ia M, (7) Adaptive Monitoring Method for Bath Proesses Based on Phase Dissimilarity Updating ith Limited Modeling Data, Ind Eng Chem Res, 46, Zhao CH, Wang FL, Lu Y, ia M, (7) Stagebased soft-transition multiple PCA modeling and on-line monitoring strategy for bath proesses, Proess Control, 7, Zhao CH, et al, (3) Step-ise sequential phase partition(sspp) algorithm based statistial modeling and online proess monitoring, Chemom Intell Lab Syst 5, 9- ohnson RA, Wihern DW, () Applied multivariate statistial analysis, M, e ersey, Pretene Hall Lory CA, Montgomery DC, (995) A revie of multivariate ontrol harts, IIE rans, 7, 8 8 able Monitoring performane regarding different α values (FAR% (Mean MAD) for normal ase and MAR% (Mean MAD) for fault ases) α FAR% MAR% able Comparison of online monitoring performane (FAR% (Mean MAD) for normal ase and MAR% (Mean MAD) for fault ases) for testing bathes beteen to methods Methods Limited bathes Suffiient bathes Case =8 a =3 b normal fault a It shos the best monitoring results for limited bathes b It shos the best monitoring results for suffiient bathes 75