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TheModeloftheWaterContentoftheDregsinRotaryDryerKilnBasedonSVM

XinWang1,2,ChunhuaYang2,BinQin1

1.DepartmentofElectricalEngineering,HunanUniversityofTechnology,HunanZhuzhou,412008,China

2.SchoolofInformationScienceandEngineering,CentralSouthUniversity,HunanChangsha410083,China

email:

Abstract-Basedonanalysisoftheprocessofrotarydryerkiln,asoft-sensormodelforwatercontentofthedregsbyusingthesupportvectormachines（SVM）isproposed.TheparametersofSVMareoptimizedthroughthehybridoptimizationalgorithmwhichcombinesthegeneticsearchwiththelocalsearch,firstthekernelfunctionandSVMparametersareoptimizedroughlythroughgeneticalgorithm,aftercertaingenerations,thekernelparameterisfineadjustedbylocallinearsearch.Experimentsofacquiringthesampledataaredesignedandthesoft-sensormodelhasbeenobtainedandusedsuccessfullyintheinferencecontrolofrotarydryerkiln.TheproposedmethodcannotonlyovercomethedifficultyindeterminingthestructureandparametersofusingothermodelssuchasRBFmodelbutalsohasbettergeneralizationperformancethanothermodels.

IndexTerms-rotarydryerkiln;watercontentofthedregs;

soft-sensormodel;supportvectormachinesregression;

parameterselection;hybridoptimization

I.INTRODUCTION

Theprocessofrotarydryerkilnisanimportantprocedureforthehydrometallurgyofzinc,andthewatercontentofdregsisthekeyproductionindexforthedryingprocess.Red-raylightmeasurementandneutronmoisturemetersmeasurementarethemainmethodsinactualproductionprocess,however,theformerhasnotbeencompletelymaturedandthelatterisrarelyusedduetoradiationandhighprice.Asaresult,thereisnoonlinemeasurementformostproductionprocessandthewatercontentofdregshastobecontrolledindirectlythroughworkers'experiencewhichishardtomeetthecontrolrequirement.Soitisveryimportanttorealizeonlinemeasurementforthewatercontentofdregsthroughsoft-sensortechnology.

Thedesignofsoft-sensoristoselectagroupofsecond

variables,whicharetightlyrelatedwiththemainvariable

andcanbeeasilymeasured,andtorealizetheonlineestimationofmainvariablebyestablishingsomemathematicmodelbetweenthem[1].TheARMAXandRBFNeuralnetworkmodelhavebeenusedsuccessfullyinthesoft-sensormodelingofwatercontent[2],buttheARMAXmodelisalinearizedmodelaboutacertainworkpointandlargepredictionerrorswillbeproducedifthe

actualworkpointdepartsfromtheoriginalworkpoint,theRBFnetworkmodelisdifficulttodetermineitsstructureandsolvetheover-fittingproblemforthetrainingdataset.SupportvectormachinesintroducedbyVapnik[3]aremachinelearningmethodsbasedonstatistictheory,whichcansolveaboveproblems.InthepresentworkapredictionmodelbasedonSVMhasbeendeveloped,anewhybridoptimizationmethodforparameterselectionofSVMisproposed.Thesoft-sensormodelisobtainedthroughthesampledatesetcollectfromexperiments.

II.FLOWSHEETOFROTARYDRYERKILN

Theflowsheetofrotarydryerkilnisshownasfigure1,whichconsistsofkilnhead,dryerdrum,kilntrailandappenddevices.Thedregswith35-40%watercontentarefedbythecirclefeeder,theexhaustgasisproducedbyburninggasintheheadofkilnandthewatercontentofdregsisdecreasedto15-17%inthedryerdrumthroughheatexchangebetweenexhaustgasanddregswhichismainlyachievedbyconvection,thenthedregsaretransportedtothenextprocedure.Thetaskoftherotarydryerkilncontrolconsistsofthreeparts:

combustion

control,watercontentcontrolandsequencelogiccontrol.Thesoft-sensorofthewatercontentisthekeyfactorforthe

controlsystem.

III.MODELFORTHEWATERCONTENTOFROTARYDRYER

KILNDREGS

A.Supportvectorregression（SVR）

SVMscanbeappliedtoregressionproblemsbytheintroductionofalossfunction[3].Supposethereisagivensetofsamples

SVMregressionmapsthedataintoahigherdimensionalfeaturespaceviaanonlinearmappingф,andthenregresseslinearlyinthisfeaturespace.Anoptimaldecisionfunctioncanbeformulatedas

（1）.

（1）

Wherethevector

andbias

.Sothenonlinearestimationfunctionistranslatedtoalinearestimationfunctioninahigherdimensionalfeaturespace.Byapplyingtheminimizationruleofthestructuralandempiricalrisks,foralinearε-insensitivelossfunction,introducethepositiveslackvariables

andthetaskisthereforechangedinto:

（2）

Where

isthecomplexityofthecontrollingmodel,

Cistheregularizationconstantdeterminingthetrade-off

betweentheempiricalriskandthestructuralrisk.

Withconstraints:

Afterkernelsubstitutionthedualobjectivefunctionis:

（3）

Ontheconditionsthat:

And

Where

aretheintroducedLagrangemultipliers,andK（

）isthekernelfunctionwhichsatisfiestheMercercondition.ChoosedifferenttypeofkernelfunctionsanddifferentSVMscanbeconstructed.InthisresearchweusetheGaussiankernel

Thequadraticprogrammingproblem（3）canbesolvedthroughsequentialminimaloptimization（SMO）[4]andderivativesdecompositionmethods[5].Onlysomecoefficients（

-

）willbenonzero,andthedatapointsassociatedwiththemrefertosupportvectors（SVs）.Giventhenumberofsupportvectorm,thefunctionmodelingdataisthen:

（4）

Thebias,b,canbecalculatedbyconsideringKurash-Kuhn-Tucker（KIKT）conditionsforregression.

B.Structureofthemodelandselectionofthesecondvariables

ThestructureofthepredictionmodelbasedonSVMisshownasFig.2,ithasthreelayers,aGaussiankernelisusedinthemiddlelayerandthenodesinmiddlelayersareformedbySVRautomatically.Theoutputrepresentsthepredictionvalueofthewatercontentofrotarykilndregs.

Selectingtheinputvariablesfromallpossibleinputvariablesisimportantforsystemmodeling.Basedonthemodeloftechnology,experimentsandanalysisoftherelativitybetweenthesecondvariablesandthemainvariable,wehaveselectedthefuelflowmass

differenceoftemperaturesbetweenkilnheadandtrail

temperatureinthemiddleofdrumTm,thespeedofdrumVetcasthesecondvariables,andthewatercontentofrotarykilndregsMsastheoutputvariable.

C.HybridoptimizationofSVMParameters

ItiswellknownthatSVMgeneralizationperformance（estimationaccuracy）dependsonagoodsettingofparameterssuchasregularizationconstantC,insensitivecoefficientεandthekernelparameters.GenerallytheempiricalerrorwilldecreasemonotonouslywithCandcometoremainconstantwhenCisbigenough.ThegeneralizationerroronthetestwillfirstdecreaseimmonotonouslywithC,cometoanalmostconstantvalueasCchangesinacertainzone,andthenincreasewhenCgoesbeyondacertainvalue.TrainingtimewillincreasewhenCincreases.Parameterεcontrolsthewidthoftheε-insensitivezoneusedtofitthetrainingdata.ThevalueofεcanaffectthenumberofSVMsusedtoconstructtheregressionfunction.Largerε-valueresultsinfewer

selectedSVMs,lesscomplexregressionestimationandlesstrainingtime.Kernelfunctiontypeandparameter（σandd）thatimplicitlydefinesthenonlinearmappingfrominputspacetosomehigherdimensionalfeaturespacearealsoveryimportanttotheperformanceofSVM.AlargeamountofexperimentshavedemonstratedthatthewidthparameterσintheGaussiankernelfunctionstronglyaffectsgeneralizationperformanceofSVM[6].Itiswell-knownthatthevalueofεshouldbeproportionaltotheinputnoiselevel,thatisε∝

.ExperimentsshowthattheRMSEonthetrainingsetincreaseswithσ.Ontheotherhand,theRMSEonthetestsetdecreasesinitiallybutincreasessubsequentlyasσincreases.Thisindicatesthattoosmalla

valuecausesSVManover-fitwhiletoolargeavaluecauses

anunder-fitofthetrainingdata.Anappropriatevalueforσ

canonlybeobtainedinacertainzone[7].

InthispaperahybridoptimizationalgorithmforSVM

parameterselectionisproposed,firstanevolutionarySVM

isusedtosearchthekernelfunctionanditstraining

parameterswiththetrainingsampleset,andaftercertain

generationsthekernelparameterisfineadjustedbylocal

search.ThetentativeSVMsaretestedbythevalidationsampleset.ThetrainingprocessoftheSVMwillbecompletedwhentheidentifiedSVMcangivegoodgeneralizedpredictionsforvalidationsamples.ThealgorithmcombinestheabilityofGAwhichwidelysampleasearchspacewiththeacceleratingsearchabilityoflocalsearch.Tofindtheglobaloptimumthehybridoptimizationalgorithminvolvesfivemainparts.

1）Performancecriterion

Cross-validationisapopulartechniqueforestimating

generalizationerrorandthereareseveralversions.Ink-fold

cross-validation,thetrainingdataisrandomlysplitintokmutuallyexclusivesubsets（thefolds）ofapproximatelyequalsize.Inthisstudy,inordertosimplifythealgorithm,wedividethesampledatasetintothreefolds,onefortraining,oneforvalidation（calculatingtheperformancefitnessofthemodel）andonefortesting.

2）Chromosomerepresentation

Basedonanalysisabove,theconstantCandεhavelessinfluenceonthegeneralizationerrorthankernelparameter,andthekernelparameterwillbefineadjustedlater,soabinarycodeformisadoptedtodecreasethecomputationcost.Adirectcodeisusedtocodetheparameterε,alogarithmmappingisusedbeforecodingthevalueofCandtheGaussiankernelwidthσ.Therangeoftheparameterscanbeestimatedthroughthemethodsproposedin[6]orpriork