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1、Computerschem.EngngVol.22,No.4/5,pp.503-514,1998©1998ElsevierScienceLtd.AllrightsreservedPergamonPrintedinGreatBritainPII:S0098-1354(97)00262-70098-1354/98$19.00+0.00RecursivePLSalgorithmsforadaptivedatamodelingS.JoeQin*DepartmentofChemicalEngineering,TheUniversityofTexa
2、satAustin,Austin,Texas78712,U.S.A.(Received17June1996;revised25September1997)AbstractPartialleastsquares(PLS)regressioniseffectivelyusedinprocessmodelingandmonitoringtodealwithalargenumberofvariableswithcollinearity.Inthispaper,severalreeursivepartialleastsquares(RPLS)al
3、gorithmsareproposedforon-lineprocessmodelingtoadaptprocesschangesandoff-linemodelingtodealwithalargenumberofdatasamples.Ablock-wiseRPLSalgorithmisproposedwithamovingwindowandforgettingfactoradaptationschemes.Theblock-wiseRPLSalgorithmisalsousedoff-linetoreducecomputation
4、timeandcomputermemoryusageinPLSregressionandcross-validation.Asanaturalextension,therecursivealgorithmisextendedtodynamicmodelingandnonlinearmodeling.AnapplicationoftheblockrecursivePLSalgorithmtoacatalyticreformerispresentedtoadaptthemodelbasedonnewdata.©1998ElsevierSci
5、enceLtd.AllrightsreservedKeywords:Partialleastsquares;recursivePLS;cross-validation;forgettingfactors;chemicalprocessmodeling;dynamicmodelingNOMENCLATUREqi[Rp,loadingvectorforYAicoefficientmatrixinanARXmodelri~n,residualsfrominnermodelsaj,buquadraticVolterramodelcoeffici
6、entsrrankoftheinputdatamatrixBdiagonalmatrixofinnermodelcoefficientsBicoefficientmatrixinanFIRorARXmodelsnumberofdatablocks~n×o,scorematrixforXblinnermodelcoefficientTCE~mxp,modelcoefficientmatrixt~~n,scorevectorforXCpLsefltmXp,regressioncoefficientmatrixfromuj~",scoreve
7、ctorforYPLSu(k)inputvectorinanAR.XorFIRmodelCPLSnew,fitn,×p,updatedregressioncoefficientVnoisematrixmatrixfromPLSv(k)noisevectorEi~"×m,residualmatrixforXWfitm×a,weightingmatrixinPLSFi~"×p,residualmatrixforYw~Efitm,weightingvectorinPLSJobjectivefunctioninPLSwwindowsizeofa
8、movingwindowmnumberofinputsinXX~fft"×m,inputdatamatrixnnumberofsamplesinXandYx(k)samplevectorforinputsn
