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1、JOURNALOFCHEMOMETRICSJ.Chemometrics2005;19:427438Publishedonline5January2006inWileyInterScience(www.interscience.wiley.com).DOI:10.1002/cem.945Clusteringmultivariatetime-seriesdata12AshishSinghal*andDaleE.Seborg1JohnsonControls,Inc.507E.MichiganStreet,Milwaukee,WI53202,USA2DepartmentofCh
2、emicalEngineering,UniversityofCalifornia,SantaBarbara,CA93106,USAReceived9December2004;Revised22August2005;Accepted25August2005Anewmethodologyforclusteringmultivariatetime-seriesdataisproposed.Thenewmethodologyisbasedoncalculatingthedegreeofsimilaritybetweenmultivariatetime-seriesdataset
3、susingtwosimilarityfactors.OnesimilarityfactorisbasedonprincipalcomponentanalysisandtheanglesbetweentheprincipalcomponentsubspaceswhiletheotherisbasedontheMahalanobisdistancebetweenthedatasets.ThestandardK-meansclusteringalgorithmismodifiedtoclustermultivariatetime-seriesdatasetsusingsimi
4、larityfactors.Simulationdatafromtwononlineardynamicsystems:abatchfermentationandacontinuousexothermicchemicalreactor,areclusteredtodemonstratetheeffectivenessoftheproposedtechnique.Comparisonswithexistingclusteringmethodsshowseveraladvantagesoftheproposedmethod.Copyright#2006JohnWiley&So
5、ns,Ltd.KEYWORDS:clustering;similarityfactor;faultdiagnosis;processmonitoring1.INTRODUCTIONInthispaper,anewclusteringmethodologyforprocessdata,particularlymultivariatetime-seriesdata,ispresented.Clusteranalysisistheartoffindinggroupsindata.BecauseItisassumedthatthedatabasecontainssetsofmul
6、tivariatelivingbeings,objectandeventsencounteredineverydaylifetime-seriesdata,whichcorrespondtodifferentperiodsofaretoonumerousforprocessingasindividualentities,theyareprocessoperation,forexampledifferentbatchesproducedusuallygropedonthebasisofthesimilarityoftheirfeaturesbyabatchprocess.
7、Theclusteringmethodologyisbasedonintocategories.Arelatedterm,classification,istheprocessorcalculatingthedegreeofsimilarityusingprincipalcompo-actofassigninganewitemorobservationtoitsproperplaceinnentanalysis(PCA)anddistancesimilarityfactors.anestablishedsetofcategoriesorcl
