Fault detection of batch process based on multi-way Kernel T-PLS

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1 Avalable nlne Junal f Chemcal and Phamaceutcal Reseach, 04, 6(7): Reseach Atcle SSN : CODEN(USA) : JCPRC5 Fault detectn f batch pcess based n mult-wa Kenel -PLS Zha aqang*, ue Yngfe and Wang a Cllege f Electcal and nfmatn Engneeng, Lanzhu Unvest f echnlg, Lanzhu, Chna ABSRAC Because the dffeent batch f batch pcesses has dffeent aw mateals and changeable cntl cndtns, measuement data ma lead t dft and t s dffcult t btan cmplete samplng data at an tme dung the eactn pcess. S a mult-wa kenel -PLS (MK-PLS) algthm was ppsed t mpve the fault dagnss accuac f batch pcesses. hs algthm fstl unflds thee dmensnal pcess data matx b samplng tme sequence, then flls pcess vaable data accdng t cetan ules t fm cmplete sample f data mssng pblem, s btaned apppate data matx s used t fault detectn b MK-PLS algthm. Smulatn esults f Pensm V.0 smulatn platfm shw that the fault detectn ate f the ppsed algthm s hghe than the the algthm f detectng faults affect the qualt f fnal pducts. hs algthm s me sutable t mnt the eal-tme batch pcess. Ke wds: fault detectn; batch pcess; mult-wa kenel -PLS; Pensm V.0 NRODUCON Mden chemcal pcess especall batch pcess s ve mptant f ndustal pductn. Batch pductn can satsf the dvesfed equement f dffeent custmes and t has hgh flexblt and bette ecnmc effect. n de t mantan batch pcess n nmal cndtn and manufactue qualfed pduct, pcess mntng s necessa and ndspensable. Fault dagnss technlg has been studed b man schlas and expets. hee ae tw man appaches f fault dagnss methds, ncludng fst-pncple mdels and pcess data analss. he mst ppula methd, multvaate statstcal pcess mntng (MSPM), can detect abnmal peatng stuatns and dagnss faults wthut the exact mdelng f the pcess []. MSPM nl needs measued data whch can btan easl b senss n ndustal feld, s t s nt dffcult t meet the equements n mden ndustal pcess. Pncpal cmpnent analss (PCA) [] and patal least squaes (PLS) [3] ae basc pjectn methds f MSPM f cntnuus pcess. he use nmal hst pcess data t buld pedefned mdel, detect fault wth the eal-tme measuement data. he maj advantages f these methds ae the abltes t handle lage numbe f hghl celated vaables, measuement es, and mssng data []. n batch pcess, measuement data s 3-dmensnal fm cntanng the fllwng nfmatn: batch numbe, vaable numbe and sample numbe. Man schlas studed batch pcess and ppsed excellent stateges t slve the pblems, such as mult-wa PCA, mult-wa PLS, mult-stage PCA, mult-stage PLS. Recentl, Zhu [4-6] et al ppsed an mpved stuctue, namel ttal pjectn t latent stuctues (-PLS), f fault dagnss n cntnuus pcess. he make a futhe decmpstn f the PLS mdel whch has bette effect than PCA when detectng qualt-elevant fault. Zha [7] et al gve a sutable extensn f -PLS mdel, sngle space ttal pjectn t latent stuctues (Ss-PLS) and mult space ttal pjectn t latent stuctues (Ms-PLS) wee analzed and cmpaed n the pape. he used -PLS mdel t mnt cntnuus batch pcess and smulatn esults shwed that the new methd s fault detectng ate s hghe than the the s. Hweve, bth Zhu and Zha s -PLS mdels ae lnea mdels. t s dffcult t btan accuate fault dagnss esult f actual ndustal pcess when measuement data have stng nnlnea elatnshp. Kenel functn s a 338

2 Zha aqang et al J. Chem. Pham. Res., 04, 6(7): knd f tls whch have bette effect when dealng wth nnlnea data. S a mult-wa kenel -PLS algthm was ppsed n ths pape. hs algthm use kenel functn t slve the nnlnea pblem f nput data b pjectng them nt featue space fst, and then buld lnea -PLS mdel wth the kenel matx n hgh-dmensnal featue space. Htellng s statstc (ncludng, and ) and Q statstc ae stuctued and calculated n fu dffeent subspace t detect dffeent knd fault espectvel. Because pcess data and qualt data wee pepcessed b kenel functn, qualt-elevant fault detectn ate f mult-wa kenel -PLS algthm s hghe than that f mult-wa -PLS. hs pape s ganzed as fllws. Mult-wa kenel -PLS mdel s ppsed n sectn. hen, qualt-elevant fault dagnss methds based n Mult-wa kenel -PLS mdel s descbed n sectn 3. n sectn 4, a smulatn stud f penclln fementatn pcess based n Pensm V.0 s llustated and esults f Mult-wa kenel -PLS mdel and Mult-wa kenel PLS mdel ae cmpaed. Fnall, cnclusns ae pesented n the last sectn. MUL-WAY KERNEL -PLS(MK-PLS) Smla t the mult-wa pncpal cmpnent analss and mult-wa patal least squaes methd, mult-wa kenel -PLS mdelng cntans thee steps. Fstl, thee dmensnal batch pcess data swtch t tw dmensnal plane data accdng t the de f samplng tme. Secndl, lneaze the pcess data b pjectng them nt hgh dmensnal featue space usng kenel functn. Fnall, buld lnea -PLS mdel n hgh-dmensnal featue space, calculate mntng statstcs and the cespndng cntl lmts, cmpae them detect qualt-elevant fault. Batch Pcess Data Pepcessng Batch pcess measuement data s sted as steescpc data matx, and t cntans the fllwng nfmatn f pcess: batch numbe, measued vaables numbe and samplng numbe. Cmmnl, thee ae tw methds t make the steescpc data matx planazatn. Fst, pattn steescpc matx s detemned accdng t the batch numbe. Secnd, pattn steescpc matx s detemned accdng t the samplng numbe. n ths pape, we chse the secnd methd t pepcess batch measued data. We cut the steescpc matx nt slces n accdance wth the samplng tme sequence fm the fst samplng pnt t the K-th samplng pnt, and then tle them nt a plane data matx del. he schematc plan f batch pcess data pepcess shwed as fg.. * Fg.: Schematc plan f steescpc data matx pepcessng KJ dmensnal data matx can btan fm the abve cmplanatn methd, but t s ve dffcult t use them J K Y M J J K J K mdelng dectl due t ts huge dmensn. Snce the k-th sample f the j-th vaable has been measued tmes ttall and the tmes measuements be cetan statstcal chaactestcs, s t can use the aveage value f weghted mvng wndw xjk = ( x j kλ ) nstead. * KJ dmensnal data matx smplf = t* KJ dmensnal w vect. Pattnng and eaangng the w vect accdng the de J, J,, KJ, new pcess data matx btan as the fllwng fmula. x x L xj xj xj x + + L J = M M M M x( K ) J + x( K ) J + L xkj () 339

3 Zha aqang et al J. Chem. Pham. Res., 04, 6(7): As qualt data can nl be measued at the end f each batch ff-lne, s * M dmensnal data matx Y can be btaned afte batch pductn. Calculate the aveage value f fnal pduct qualt measuements fm fst batch t -th batch b weghted mvng wndw. New qualt data matxy can calculate as the fllwng fmula, whee m = ( mλ ). = [ ] Y = () M t can detect fault f the batch pcess afte stuctung kenel -PLS mdel usng pcess data matx and qualt data matxy. But t s wth ntng that utles exst at each batch pcess, n de t ensue the fault detectn accuac f batch pcess fundamentall, apppate algthms shuld be used t emve utle value. Mult-wa Kenel -PLS Cmpaed wth cntnuus pcess, batch pcess data s sted steescpcall. S t s necessa t planaze the steescpc data befe mdelng. Usng the abve methd btan pcess data matx and qualt data matxy, and then buld MK-PLS mdel wth these matx. Cve theem states that a set f tanng data that s nt lneal sepaable, ne can wth hgh pbablt tansfm t nt a tanng set that s lneal sepaable b pjectng t nt a hghe dmensnal space va sme nn-lnea tansfmatn [8]. Kenel matx K = Φ Φ can btan and be used t buld lnea -PLS mdel f fault dagnss afte pcess data matx mappng t a hgh dmensnal featue space b adal bass functn. Nnlnea mdel MK-PLS between nput-utput space equal t lnea mdel M-PLS between featue-utput space theetcall. Cncete steps t establsh MK-PLS mdel ae as fllws: Step: btan K * J dmensnal pcess data matx and* M dmensnal qualt data matxy usng abve methd; Step: btan pcess data matx ˆ and qualt data matxy ˆ b standadzng andy ; Step3: pject matx ˆ N nt featue space F, Φ : x R Φ( x ) F, stuctue kenel matx K = Φ Φ ; Step4: =, K ˆ = K, Y = Y, extact cnvegent () u equal t a clumn fy andml; t K u t t t () =, / ; (3) q = Y t ; u Y q u u u (4) =, / ; u fmy ; (5)vedct: fu cnvegence, g t Step5;thewse, g t (); Step5: calculate the ladng matx f K : p = K t ; Step6: extact all pncpal cmpnent, calculate, P, U and Q; () K = K + t p, Y = Y + uq ; () cmpnent detemned b css valdatn; = +, epeat Step4 and Step5 untl all pncpal cmpnent have been extacted, the numbe f pncpal = [ t,, t A ], P = [ p,, p A ], U = [ u,, u A ], Q = [ q,, q A ] ; (3) Step7: K = P + E, Y UQ F = + ; Step8: un PCA algthm np, 0 0 Step9: un PCA algthm n E, P = t p + P, the numbe f pncpal cmpnent s A-; E = P + E,the numbe f pncpal cmpnent efe t [9]. Pcess data matx ˆ and qualt data matx ˆ Y f batch pcess can be decmpsed as fllws afte unnng MK-PLS algthm. 340

4 Zha aqang et al J. Chem. Pham. Res., 04, 6(7): ˆ 0 0 = t p + P + P + E (3) Yˆ = t + F (4) E = E( P P ) (5) Whee t, 0 and ae sce vects f dffeent subspaces, decmpstn f MK-PLS mdel s shwn n fg.. E s fnal esdual that epesents nse. he ˆ Fg.: Decmpstn stuctue f MK-PLS mdel FAUL DEECON SEPS BASED ON MK-PLS Fault detectn based MK-PLS mdel ncludes tw steps: fst, establsh MK-PLS mdel usng nmal hstcal fflne data, cmpute mntng statstcs and detemne the cespndng cntl lmts; Secnd, calculate D and Q statstc usng nlne measued data, detectng qualt-elevant fault n eal tme b cmpang statstc and ts cntl lmt. Data Supplement Because batch pcess measuement data s sted as whle, t s had t get the whle sample untl the batch pductn pcess fnsh. hs s a dsadvantage f eal-tme mntng f batch pcess. Hweve, nl detectng fault n tme and takng apppate actns can avd unnecessa lsses n actual ndustal pductn pcess. n de t slve ths pblem, Nmks et al[0] ppsed the fllwng thee fllng algthm t pedct defaults fm cuent tme t the end f ente batch pcess. ()0 value fll methd, the data f futue s cnsdeed nt devatng fm the aveage taject; ()cuent value fll methd, the data f futue s cnsdeed have the same devatn fm the aveage taject; (3) pjectn methd, the data f futue s detemned b the cuent value pjected nt a patcula space. hs pape chse the thd methd t fll the unsampled data * f the pcess vaable data matx fault detectn. x x L xj M M M M = xkj + xkj + L x( k + ) J * * L *, s as t btan a cmplete sample f batch pcess f Statstcs And Cntl Lmts F batch pcess, thee ae man dffeences between each batch, such as dffeent aw mateals, changed pductn envnment, peatng pnt dft f equpments. All f these shuld be cnsdeed caefull befe establshng MK-PLS mdel. Weghted mvng wndw was used t btan the latest nmal batch pcess weghted aveage measuement data matx, and then t was mapped t featue space nn-lneal btan kenel matx K, sce and esdual vect f K ae as the fllwng fmula. 34

5 Zha aqang et al J. Chem. Pham. Res., 04, 6(7): t = qr K R t = P ( P p q) R K R A t = P ( PR ) K R A E = ( P P )( PR ) R m (6) MK-PLS mdel s statstcs,, and Q ae calculated usng the weghted aveage value f nmal batch hst data. f the measued vaables cnfm t nmal dstbutn, statstcs and ts cespndng cntl lmts ae shwn n able.. able.: Statstcs and ts cespndng cntl lmts Statstc cmputatnal fmula cntl lmts fmula Statstc cmputatnal fmula cntl lmts fmula n t Λ t + F A ( n ), n, α t Λ t F A, n A, α n n( n A ) ( A + )( n ) t Λ t F A, n A+, α Q E gχ h, α n( n A + ) Off-lne Mdelng MK-PLS algthm calculates fu statstcs and the cespndng cntl lmts n dffeent sub-space t mnt the batch pcess, detect fault b analzng and cmpang them n sub-space mntng chat. Smla t -PLS algthm, the man vaatn f pcess uses Mahalanbs dstance t measue whle the esdual pat f pcess uses Eucldean dstance. he detaled steps f mdelng fflne based n MK-PLS algthm ae as fllwng. Step: btan the latest batch pcess data matx and qualt data matxy usng abve methd; Step: btan pcess data matx ˆ and qualt data matxy ˆ b standadzng andy ; Step3: pject matx ˆ nt featue space F nn-lneal, stuctue kenel matx K = Φ Φ ; Step4: decmpse kenel matx K, calculate t, p,, P,, P, E, u, q, F ; Step5:stuctue statstcs,, and Q, chse the cespndng cntl lmts accdng table. wth sutable degees f feedm and cnfdence. On-lne Detectn Snce the cmplete samplng f batch pcess can t btan untl the whle eactn fnshed, n de t ealze eal-tme mntng, unsampled values must be flled as the abve methd befe detectng fault. MK-PLS mdel uses the cmplete sample matx whch has been flled wth apppate data as nput, calculates mntng statstcs n fu specfc sub-space, cmpaes them wth the cespndng cntl lmts t detect fault. he cncete steps f n-lne detectn ae as fllws: Step: pject the measued value[,,, k ] f sample tme,,,( k ), k nt a specal space, btan the value [ k+,, K ] f sample tme ( k + ),, K. he cmplete matx new =[,,, k, k +,, K ] has btaned, the cncete algthm can efe t [65]; Step: standadze pcess vaable matx new t ˆ new ; Step3: use ˆ new as MK-PLS mdel s nput, calculate the fllwng value t, p,, P,, P, E, u, q, F espectvel,,,,,,,, Step4: calculate statstcs, new new new new new new new new new new ;,new,,new,,new and Q, new Step5: detect qualt-elevant fault: f statstcs,new and Q, can affect fnal pduct s qualt; espectvel; new bend the cespndng cntl lmts,the fault 34

6 Zha aqang et al J. Chem. Pham. Res., 04, 6(7): f statstcs,new and,new bend the cespndng cntl lmts,the fault can t affect fnal pduct s qualt; SMULAON RESULS AND ANALYSS Penclln fementatn pcess s a tpcal batch pductn pcess, whch s wdel used t evaluate the cntl stateges and algthms f batch pcess. hs batch pcess cmpses nne vaables (ventlatn ate, stng pwe, acceleatn f the bttm steam, tempeatue f the fementatn vessel, ph, acceleatn f the clng wate flw, medum vlume, xgen satuatn and cabn dxde cncentatn) and fu qualt vaables (penclln cncentatn, substate cncentatn, bmass cncentatn and eactn heat). hs pape uses Pensm V.0 smulatn sftwae f testng, whch was develped b Pfess Cna and hs eseach team f llns nsttute f echnlg fm 998 t 00 [], Pensm V.0 smulatn sftwae has hgh pactcal value. t can nt nl smulate penclln fementatn pcess ealstcall, but als btan a sees f paametes f the fementatn pcess easl. Pensm V.0 has becme an useful tls t valdate scentfc appach based n data-dven f dagnse fault and mnt batch pcess[-4]. ntalzatn elevant paametes shuld be executed befe smulatng penclln fementatn pcess usng Pensm V.0 sftwae. he default values and the ange f elevant paametes ae shwn n able. and able.3. able.: Default value and value ange f Pensm V.0 Vaable name Unt Default value Value ange substate cncentatn G/L xgen cncentatn G/L.6 -. bmass cncentatn G/L 0. 0 penclln cncentatn G/L 0 0 medum vlume L cabn dxde cncentatn G/L hdgen n cncentatn MOL/L 0-5. ph tempeatue f the fementatn vessel K able.3: Cntl paamete f Pensm V.0 Vaable name Unt Default value Range ventlatn ate L/H stng pwe W acceleatn f the bttm steam L/H substate heat K ph eactn heat K Penclln fementatn pcess smulatn stud base n Pensm V.0 cntans thse steps: set the ntal values f vaables and paametes, set the cntlle f tempeatue and ph, set eactn cndtns (nmal/fault), expt eal-tme mnt plt f each pcess vaable, expt sample data matx f each pcess vaable. he detaled steps see Fg.3. Fg.3: Flw chat f Penclln fementatn pcess based n Pensm V.0 343

7 Zha aqang et al J. Chem. Pham. Res., 04, 6(7): he actual penclln fementatn pcess ften ccu valve leakage pump falue, Pensm V.0 smulate thee tpes f falues dung the actual fementatn pcess. he fault s ntductn tme and end tme can be set atfcall, step and amp sgnal can be set as the fault tpe, the default faults f Pensm V.0 ae descbed n able 4. able 4 he Default fault f Pensm V.0 Fault Numbe Fault Descptn Fault tpe Fault Aeatn Rate Fault Step / Ramp Fault Agtat Pwe Fault Step / Ramp Fault 3 Substate Feed Rate Fault Step / Ramp n de t btan dffeent batch s pcess vaables, 0 batches f nmal penclln fementatn pcess smulatn have been dne b adjustng the value f each paamete n able. and able.3. Fg.4 shws the taject f each pcess vaable f penclln fementatn pcess n nmal cndtn based n Pensm V.0. Fg.4 :aject f each pcess vaable f penclln fementatn pcess (nmal cndtn) he 0 batches nmal pcess data wee used t buld ff-lne mdelng, and cntl lmt f each mntng statstc detemned as sectn 3.3. n de t btan fault samples, fault ntduce tme, fault end tme, fault tpe, fault ampltude shuld be set n tpe 9 f Pensm V.0 ntalzatn. hs pape set smulatn tme: 400h, samplng tme: 0.h, fault ntduce tme: 00h, fault end tme: 400h, fault tpe: step, fault ampltude: *8 dmensnal fault sample data matx can btan afte the whle pcess fnshed. aject f each pcess vaable f penclln fementatn pcess n fault 3 cndtn based n Pensm V.0 ae shwed n Fg

8 Zha aqang et al J. Chem. Pham. Res., 04, 6(7): Fg.5: aject f each pcess vaable f penclln fementatn pcess (fault 3 cndtn) Use the abve fault data matx as MK-PLS mdel s nput, pcess mnt dagam based n MK-PLS s shwed n Fg.6. n de t hghlght the supet f ppsed methd, cmpasn algthm was un wth the same nput. Fg.7 s pcess mnt dagam based n MKPLS Q Q Samples Samples (a) (b) Fg.6: Mnt dagam based n MK-PLS Samples Samples (a) (b) Fg.7: Mnt dagam based n MKPLS 345

9 Zha aqang et al J. Chem. Pham. Res., 04, 6(7): Obvusl, fault detectn ate f MK-PLS mdel s hghe than that f MKPLS mdel, because MK-PLS mdel decmpse the thgnal ptn f vaatn fm pjectn subspace and btan eal nse n esdual subspace. CONCLUSON hs pape ppsed a sutable mdel, MK-PLS whch s an apppate extended f K-PLS algthm, t detect fault f batch pcess. Fault dagnss based n MK-PLS must btan apppate data matx fst, s sme data pepcess methd was ntduced and used. What s me, due t the shtcmng that cmplete sample can t btan untl whle pcess fnsh, supplementa data technque was used t fll the blank. Smulatn esults f penclln fementatn pcess shw that, MK-PLS algthm has hghe fault detectn ate, whch means that t s me sutable t detect qualt-elevant fault and mnt batch pcess eal-tme. Acknwledgments he auths wsh t thank the Natnal Natual Scence Fundatn f Chna f cntact and663003, the unvest basc scentfc eseach pject f Gansu pvnce f cntact 03ZC06. REFERENCES [] Dnghua Zhu, Gang L. AChE Junal, 00, 56, [] Nngun Lu, Yuan Ya, Fung Ga, Ful Wang. AChE Junal, 005, 5, [3] Yngwe Zhang, Zhng Hu. AChE Junal, 0, 89, [4] Gang L, S. Je Qn, Yndng J, Dnghua Zhu. Acta Autmatca Snca, 009, 35, [5] Gang L, Dnghua Zhu, S. Je Qn. Output-elevant fault ecnstuctn based n ttal PLS. n: Pceedngs f the 8th Wld cngess n ntellgent Cntl and Autmatn (WCCA). Jnan, Chna, 00, [6] Gang L, S Je Qn, Dnghua Zhu. ndustal and Engneeng Chemst Reseach, 00, 49, [7] C Zha, Y Sun. he mult-space genealzatn f ttal pjectn t latent stuctues (Ms-PLS) and ts applcatn t nlne pcess mntng. 03 0th EEE ntenatnal Cnfeence n Cntl and Autmatn (CCA), Hangzhu, Chna, 03, [8]. M. Cve. EEE ansactns n Electnc Cmputes, 965, 4(3), [9] S. Je Qn, Duna R. Junal f Pcess Cntl, 000, 0(), [0] Nmks Paul, Geg Jhn F. echnmetcs, 995, 37(), [] Gulnu Bl, Cenk Unde, Al Cna. Cmputes and Chemcal Engneeng, 00, 6(), [] Yew Seng Ng, Rajagpalan Snvasan. Cmputes and Chemcal Engneeng, 009, 33(4), [3] ang Ga, Wenfeng Y, Yume Sun. Scentfc Junal f Cntl Engneeng, 03, 3(6), [4] Shalln Stubbs, Je Zhang, Julan Ms. nd. Eng. Chem. Res., 03, 5(35),