联合估计异常检测方法的水处理控制pdf.docx

联合估计异常检测方法的水处理控制pdf.docx

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联合估计异常检测方法的水处理控制pdf

EnvironmentalModelingandAssessment6:

77–82,2001.

2001KluwerAcademicPublishers.PrintedintheNetherlands.

Watertreatmentcontrolusingthejointestimationoutlierdetectionmethod

ChristineWrighta,∗andDavidBoothb

aDepartmentofManagement,WesternCarolinaUniversity,Cullowhee,NC28723,USA

E-mail:

cwright@email.wcu.edu

bAdministrativeSciencesDepartment,KentStateUniversity,Kent,OH44242,USA

Thelossofcontaminatedwastewaterintotheenvironmentbyleakageorothermeansisaseriousproblem.Thisproblemisessentiallythesameastrueofthelossofchemicalreagentsfromachemicalproductionorpurificationprocess.Thepresentarticleshowshowthejointestimationmethod,anoutlierdetectionmethodfortimeseriesanalysis,canbeusedbyafacilitymanagertodealwiththeseproblems.

Keywords:

jointestimation,outlierdetection,processcontrol,wastewatercontrol

1.Introduction

Inmanyindustries,itisimportanttodeterminewhentheprocessisout-of-control,（i.e.,whensignificantadverseprocesschangesoccur）.Theideaistodiscoverthesead-verseprocesschangeswhiletheyarestillrelativelyminor,beforesubstandardproductorsignificantpollutionispro-duced.Oneexampleofanimportantchemicalprocesscon-trolproblemiswastewatertreatment.Thispaperdiscussestheuseofaprocesscontrolmethodforthepurposeofmonitoringwastewaterdata.Theobjectiveoftheresearchwastodetermineiftheout-of-controlobservations（i.e.,abnormalstates）couldbedetectedbyJEintheperiodwhentheyfirstoccurred.Theprocesscontrolmethodreportedhereincanbeusedforanycompoundforwhichananalyticalchemicaldetectionmethodexists.Themethodthatweconsider,JointEstimation（JE）,hasthepotentialtobeextremelyimportanttobothgeneralpollutioncontrolandstatisticalprocesscon-trol.

2.Background

Ithasbeenpreviouslyshownthatpollutionproducingsituationsmayberecognizedthroughthedetectionofstatisticaloutliers[1–14].Anoutlierisanypointthatdeviatessignificantlyfromtheunderlyingprocessmodelortimeseriespattern,indicatingachangeintheprocessandthusanout-of-controlsituationwithrespecttotheprocessmodel.Pointsoutsideofthreestandarddeviationsofthetargetedprocessmeanareusuallyconsideredtobeoutliers.Suchapointcanbeidentifiedusingstatisticalmethods.Ifsuchexist,theprocessissaidtobe“outofcontrol”（i.e.,thereisasignificantadverseprocesschangeduetoanassignablecausewhichisacausethatcanbeidentified）.Otherwisetheprocessissaidtobe“incontrol”（i.e.,onlyrandomvariationsofoutputexistwithincertaincontrollimits）.

Traditionalstatisticalprocesscontrolchartsaswellasmostoftheothermethodscurrentlyusedarebasedupontheassumptionthattheobservationsintheprocesstimeseriesareindependentandidenticallydistributed（IID）aboutthetargetedprocessmeanortargetedvalueatanytimetandthatthedistributionisnormalwhentheprocessisinstatisticalcontrol.Independenceimpliesthatthereisnoparticularpatterninthedata.

Unfortunately,muchofthedatausedinstatisticalprocesscontrolisnon-IID[15].AlwanandRadson[15]alsonotethatbecauseoftheeffortsofG.E.P.Box,thechemicalindustryhasrecognizedformanyyearsthatautocorrelation（i.e.,relationshipsacrosstime）existintheirprocesses.Bax-ley[16],Berthouexetal.[17],Emeretal.[18],HarrisandRoss[19],andHunter[20]havenotedthatcontinuousprocessindustries,suchaswastewaterplants,oftenhaveautocorrelatedprocessdata.

3.ApproachestoSPCwhenstandardmethodsarenotappropriate

Processmeasuresovertimeareofteninterdependent（i.e.,theobservationsareautocorrelated）.Further,manyprocesstimeseriesexhibitacharacteristicallyrepetitivepattern,whichcanbemathematicallymodeledbyanAutoregressiveMovingAverage[ARMA（p,q）]model.Forexample,ARMA（1,1）andothertimeseriesmodelshavebeenempiricallyfoundinsomecasestobeappropriateformodelingaprocesstimeseries[21].Undersuchconditions,traditionalSPCproceduresmaybeineffectiveandinappropriateformonitoringandcontrollingtheprocess,perhapsevenerroneouslyindicatinganout-of-controlsituationwhenthecriteriaofthetraditionalcontrolchartareapplied[15].Inotherwords,theyarenotaseffectiveastheyshouldbeindetecting,forexample,theescapeofpollutantsintotheenvironment.Thus,iftheprocessbeingcontrolledisonethatproducespollutants,thesecompoundsmaybeintroducedintotheenvironmentwithouttheproducer’sknowledge.Useoftimeseriesbasedprocesscontrolmethods,ratherthanstandardstatisticalprocesscontrolmethods,isappropriatewhendataisnon-IIDorwhenoutlyingobservationsmayexistinthedata,suchaswhenthematerialsareparticularlyvaluableorinvolvecriticalsafetyconcerns.

4.Jointestimationmethod

Themethodconsideredissuccessfulinhandlingtheproblemsofgeneralstatisticalprocessandpollutioncon-trol[12,14].JointEstimation（JE）,atimeseriesprocedure,developedbyChenandLiu[22]hasbeenappliedtootherenvironmentalpollutionsituations[12].ThismethodissuperiortotheoneusedearlierbyPrasad[23]inthat（a）outliersareobtainediteratively,basedontheadjustedresidualsandobservations,（b）theproceduredoesnotrequireinterventionmodelstobeestimatedtoaccommodatetheoutliers，（c）theidentificationandlocationofoutliersarebasedonrobustparameterestimates,（d）theoutliereffectsarejointlyestimatedusingmultipleregression,and（e）theproceduredifferentiatesbetweenandaccommodatesforfourformsofoutliers:

InnovationalOutliers（IO）,AdditiveOutliers（AO）,LevelShifts（LS）,andTemporaryChanges（TC）.Thesefourtypesofoutliersrangebetweentheextremesofaone-timechange（AO）,apermanentshiftinthelevelofaprocess（LS）andtwodecayingpatternsaftertheinitialimpact（IOandTC）.Thismethodisproprietary;thedetailsofitsalgorithmsarelimited.TheJEsubroutineisavailableontheXUTSSoftwarefromScientificComputingAssociates（SCA）,OakBrook,IL.Themethodisdescribedinappendix.Inaddition,figure1depictsallfourtypesforanARMA（1,0）model.

TheinformationprovidedbytheJEmethodwithregardtothelocationoftheoutliercanincreasetheeffectivenessofdetectingthelossofpollutantsintotheenvironment.ThismethodwastestedbyPrasadetal.andfoundtobeverysuccessfulwithnuclearinventorydataaswellasgeneralSPCdata[2,3].Wright[14]andWrightetal.[24]showthatthismethodcaneffectivelylocateoutliersinatimeserieswithasfewas9observationswheretheoutlieristhelastobservationinthetimeseries.AlloutliersareidentifiedasAOwhentheyfirstoccur,thiscanbeseeninfigure1.Furthermore,thismethodhasconsiderablyfewerfalsealarmsthantheExponentiallyWeightedMovingAverage（EWMA）model[12,14,24].

Figure1.AO,TC,LSandIOforanARMA（1,0）model.

5.Researchmethod

Weutilizethejointestimation（JE）outlierdetectionmethodofChenandLiu[22]todetectoutliers（i.e.,out-of-controlobservations）inwastewatertreatmentdata.Thisdataconsistsof527dailymeasurementsof38differentsensorreadings（variables）.Thesevariablesareshownintable1.Thewastewaterplantmanageridentified13differentstatesofperformance;theseareshownintable2andincludesuchconditionsasnormaloperations,storms,solidsoverload,etc.Ofthesestates,onlystates1,5,9and11arenormal.Theobjectiveoftheresearchwastodetermineiftheout-of-controlobservations（i.e.,abnormalstates）couldbedetectedbyJEintheperiodwhentheyfirstoccurred.Itisofconsiderableimportancetodeterminethatanout-of-controlsituationexistsonthedaywhenitfirstoccursratherthanseveraldayslater.Clearlytheenvironmentalandhealthrisksinvolvednecessitateearlydetection,perhapsevenatthecostofsomefalsealarms.

Thejointestimationmethodisappealingbecauseitperformswelloverawidevarietyofbothseasonalandnon-seasonalARIMAmodels.TheusermustspecifythemodeltypefortheseriespriortousingtheJEroutine.Thismethodisproprietary,thedetailsofitsalgorithmsarelimited.TheJEsubroutineisavailableontheXUTSSoftwarefromScientificComputingAssociates（SCA）,OakBrook,IL.Inaddition,itispossibletousetheJEmethodasanonlineprocesscontroltechniquethroughacommunicationprotocoldevelopedbetweentheonlinedatacollectionunitandtheSCAsystem.Wrightetal.[24]describethemethodindetail.Abriefsummaryofthemethodisincludedhere.

Thejointestimationmethodinvolvesthreestages.Thefirststageobtainsmaximumlikelihoodestimatesofparametersandresiduals.Then,outliersaresoughtandtheireffectsareremovedfromtheresiduals.Afteralloutliershavebeendetected,modelparameterestimatesarerevised.Inthesecondstage,multipleregressionisutilizedtojointlyestimatetheeffectoftheoutliersandmodelparameters.Thentheestimatedt-valuesarecomparedwiththecriticalvalue,C.Ifthet-valueofasuspectedoutlierissmallerthanC,theoutlierisdeemednotsignificant.Next,anadjustedseriesisobtainedbyremovingsignificantoutliereffects.Maximumlikelihoodestimatesofmodelparametersarefoundbasedontheadjustedseries.Inthethirdstage,outliersaresoughtbasedonfinalparameterestimatesfoundinstagetwo.Residualsarecomputedusingtheseestimates.Theseresidualsareusedastheprocedureiteratesthroughthefirsttwostages.

ChenandLiu[22]haveshownthattheJEmethodisextremelyeffectivefordetectingoutliersinautoco