Principal-Component-Analysis

ProcessMonitoringMethodBasedOnImprovedDynamicMulti-scalePrincipalComponentAnalysis(1.StateKeyLaboratoryofSyntheticalAutomationforProcessIndustries,NortheasternUniversity,Shenyang,LiaoningProvince,ChinaPR;2.CollegeofInformationScienceandEngineering,NortheasternUniversity,Shenyang,Liaoning110819)Abstract:Aprocessmonitoringapproachbasedonimprovedmulti-scaledynamicprincipalcomponentanalysis(IMSDPCA)isproposedtohandlethemulti-scaleanddynamiccharacteristicsofindustrialprocessdata.Augmenteddatamatrixisstructuredbyusingthe“timelagshift”method,andthenmulti-scalemeasurementcharacteristicsofthewaveletisusedtoanalyzethemeasuringvariableaugmentedmatrixinmultiplicityscale.Sotheproblemthatthemeasuringvariableshavethedynamicandthemulti-scalecharacteristicsofindustrialprocessdataisnotonlyresolved,buttheshortcomingsthatthenumberofprincipalcomponentsistoomuchisovercome,onthebasisofthis,themonitoringindexbasedonT2andSPEisimprovedusing.ThesimulationresultsoftheTEchemicalprocessfaultssimulationandthestripbreakingfaultofrollingprocessbasedonMSDPCAmonitoringmethodshowthattheIMSDPCAalgorithmisfeasibleandeffective,theprocessmonitoringperformanceisimprovedcomparewithPCAandDPCAapproach.Keywords:Processmonitoring,DPCA,Wavelettransform,TEprocess,Faultdiagnosis,Stripbreakingfaultofrollingprocess1.IntroductionInordertoensuretheproductionprocessrunningsafetyandproducehighqualityproducts,allkindsofabnormalconditionswhichmayaffectproductqualityandsafetyequipmentneededforprocessmonitoring.Agreatnumberofhighlycorrelatedvariablesmeasuredexistintheindustrialproductionprocess,thesevariablevaluessampledateachtimeinstantcontainswhetherproductionprocessisnormal,theproductqualityisqualifiedandotherinformation.PCAastherepresentativefortheMultivariatestatisticalmethod,usingthemethodofdimensionreductiontodealwithprocessmeasurementdata,whichdoesnotneedtheaccuratemathematicalmodelandeffectivelyeliminatetheredundantinformationthatexistinprocessdata,Also,PCAreducedthedimensionofthedata.ithasbeenwidelyusedinConditionmonitoringandfaultdiagnosisduringindustrialprocess[1].Asaresultoftheexistenceofvariousrandomnoiseandinterference,intheactualcollectedprocessdata,especiallytheclosed-loopcontrolwillspreadtheeffectofinterferencetoeachinputandoutputvariable,causingprocessvariablecontainsnotonlythestrongmutualcorrelationalsocontainsaselfcorrelation,whichCalleddynamic.ThePCAmethoddoesnotconsiderthecharacteristicsofdynamicdata,Themainelementcannotreflecttherealchangeofcharacteristicdata[2,3].Inordertoovercometheseshortcomings,KuandothersfirstproposedthedynamicPCAmethod,thismethodconstitutethenewaugmenteddatamatrixbyntroducingtheobservationvaluesofprocessvariables,thenthePCAmodelingoftheaugmenteddatamatrix,thusthesequencecorrelationofthedatacanbeextracted.Afterthat,themethodoffaultdiagnosisbasedonDPCAhasbeenwidelyresearchedandused[4,5].ButtheDPCAmethodmakethefirstSmomentsobservationsextendedtotheaugmentedmatrixconstruction,greatlyincreasedthenumberofthemainelement,andreducedthecomputationalefficiency.Inaddition,theindustrialprocessdataismultiscaleInessence，whichmainlyembodiesasfollow:（1）EventsOccurringatdifferentlocation,Withdifferentlocalcharacteristicsintimeandfrequency；（2）Theenergyspectrumofthestochasticprocesschangeswiththetimeorfrequency；（3）Variablesmeasuredwithdifferentsamplingrateorvariablecontainsmissingdata，Nearlyallthedataofactualprocessismultiscale.Inordertomonitorthefaultondifferentscales,Manyscholarshaveputforwardamethodoffaultdetectionanddiagnosisthatbasedonthecombinationofmultiscaleanalysisandmultivariatestatistics[6].Documents[7]Firstproposedthemulti-scalefaultdetectionmethodofwaveletPCA,themethodisbasedonPCAdecompositionofwaveletcoefficientoneverytimescaleandthenintegratedinonescale,thusrealizethefaultdetectionondifferentscales.ThisarticlecombinestheadvantagesofwavelettransformandDPCAmethod,Putforwardaprocessmonitoringmethodbasedonimprovedmultipledynamicprincipalcomponentanalysis(IMSDPCA).Themethodusesanimprovedthresholdfunctionwavelettransformalgorithmtodecomposetheconstructeddynamicaugmenteddatamatrix,reconstructedtheaugmentedmatrix,consideredthedynamicandmultiscalesofthedataofindustrialfield；Newdatamatrixchangedtheinternalstructureoftheaugmentedmatrixofolddata,Alsothemainelementvectorandthenumberofprincipalelementchanged.；Significantlyimproved2TandSPEmonitoringmetrics,2.ThewavelettransformationtheoryandimprovedDPCAmethod2.1wavelettransformationWavelettransformisatime-frequencylocalizationanalysismethodthattimewindowsandfrequencywindowscanbechanged.Becauseofitsgoodtime-frequencylocality,whichcaneffectivelyextractinformationfromsignal,toanalysisfunctionsorsignalsfromMultiscalebytranslationanddilation[8].SetMdimensionalmodel：=,t=1,2,......,n.X(t)f(t)+(t)(1)TheX(t)、f(t)&(t)are1mdimensionvector，and(t)isacentralizedwhitegaussiannoise,covarianceisunknown.f(t)isusefulinformationneedtoberetained.TheelementsofX(t)areasfollows,Amongthem：1im：,t=1,2,......,n.iiiX(t)=f(t)+e(t)Document[9]proposedasimplemethodtoestimatethewaveletcoefficientj,kw,Thethresholdf