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Detection

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DetectionDetect

    Detection

;CHINESEJOURNALOFMECHANICALENGEERING

    ;‘76’Vo1.21,No.6,2008

    ;DOI:10.3901/CJME.2008.06.076,availableonlineatvc~vv~.cjmenetcom;www.cjmenet.corn.cn

    ;LIUPengfei

    ;LuoyangShipMaterialResearchInstitute,

    ;Luoyang471039.China

    ;SHANPing

    ;LUOZhen

    ;SHENJunqi

    ;SchooIofMaterialScienceand

    ;Engineering,

    ;TianjinUniversity

    ;Tianjin300072,China

    ;QINHede

    ;SchoolofXinxiangEtectromechanical

    ;Engineering,

    ;Xinxiang453000,China

    ;OINTRoDUCTloN

    ;DETECTIONMETHODOFSPOT

    ;WELDlNGBASEDONMULT1.1NFOR.

    ;MATIONFUSIONANDFRACTAL

    ;Abstract:Anove1detectionmethodofsuppo~vectormachine(SVM)basedoilfracta1dimensionof

    ;signalsispresented.AndmodelsofSVMaremadebasedonnuggetsizedefectsofspotwelding.

    ;ClassificationusingthesetrainedSVMmodelsisdonetosignalsofspotwelding.Itisshownfrom

    ;e

    :ctOfdifrerentSVMmodelsthatthesemodelswithdirentinputs.Indetectionofdefects,these

    ;modelswithinputsincludingsoundsignalhaveahighpercentageofaccuracv.thedetectionaccuracy

    ;ofthesemodelswithinputsincludingvoltagesignalwillreduce.SotheSVMmodelsbasedonfractal

    ;dimensionsofsoundaresomeoptimalnondestructivedetectionones.Atlastacomparisonbetween

    ;SVMdetectionmodelandANNSdetectionmode1isresearchedwhichindicatesthatSVMi

samore

    ;effectivemeasurethanArtificialneuralnetworksindetectionofnuggetsizedefectsdurings

    pot

    ;welding.

    ;Keywords:Multi-informationfusionSupportvectormachineBoxcountingdimensionDe

    tection

    ;Spotwelding

    ;Spotweldingisoneofconventiona1methodsforaluminum ;alloyssheetipints,itisappliedinmanyindustria1~ades, ;especiallyinautomobilemanufacturet.andsotheresearchon ;thenondestructivedetectionofspotweldingbecomesmore ;necessary.Duetothecharacteristicsofhighnonlinearand ;multi-variablecouplingintheprocessofspotwelding.itisvery ;difficulttodonondestructivedetectiontoweldingspot.Withthe ;developmentofdataminingandpatternRecognition,some ;methodsbasedondatalearning.suchaswavelettransformand ;NeuralNetworks,areappliedinqual!tydetectionofspotwelding. ;Becauseitisdifficulttocollectenoughdate.thepractical ;applicationofthetwomethodsisaffectedintheprocessof ;diagnosisofdefects.Inthel960s.thealgorithmofsupportvector ;machinerSVM)tJbasedonclassificationandregressionwas ;proposedbyVApNICetcwhichopenedanewwayforpaRern

    ;recognition.Thisalgorithmwithcharacteristicofeffectively ;solvingtheproblemofnonlineardataandover.1earningismore

    ;fitsforanalyzingsmallcombinationsandmodelsofSVMhave ;beentriedtoseekbycomparingthedetectioneffectsOf ;diflferentSVMmodelwithinputsofdif_ferentcombinationsof ;signaleigenvalue.Whenitcomestotheanalysisofthe ;non-linearproblem.Artificialneuralnetworks(ANNs)are ;superiortotheothermethods,therefore,ANNsbasedon ;fractaldimensionofsignalsisconstructed.Afterthedetection ;effeetsamongdifferentSVMsandANNsarecompared,an ;optimalmodelofnondestructivedetectionofspotweldingis ;foundinthispaper.

    ;1SIGNALEXTRACTIoNEXPERIMENT

    ;ANDMETHoD

    ;Theinstrumentemployedinthisexperimentwasstationary ;directcurrentspotweldingmachineDN8O.andlmmthick5052

    ;aluminumsheetswereusedastestsamplematerials,whose ;surfaceprocessingtechniquesareshowninTable1.

    ;ThisprojectissupposedbyNationa1NattilalScienceFoundationofChina ;(No.50575159).ScienceFoundationofMinistryofEducationofChina(No. ;106049).Doctora1FoundationofMinistryofEducationofChina(No. ;20060056058),andTianjinMunicipalNaturalScienceFoundationofChina

;(No.06YFJMJC03400).ReceivedMay9,2007;receivedinrevisedfo1”111

    ;Pctober27.2008;acceptedPctober30.2008

    ;Table1Procedureofsurfacetreatmenttoaluminum-alloys5052 ;Theadoptedparametersinthisstudyduringaluminum ;alloyweldingare:currentis18kA.weldperiodis60ms.and ;electrodepressureis2.2kN.Thesignalsofweldingcurrent. ;weldingvoltage,soundandelectrodedisplacementareobtained ;withsensorswhichareattachedtoheadofsDotweldingmachine ;Thesesignaloutputsareallshownwithmagnitudeofvoltage ;rangingfroml0VtO+l0VAllthedataarecollectedwitha

    ;DAO2010collectingcardwith4channelsalongwithwhicha ;2MHzsamplefrequencyisadopted.Datescollectedaredisplaced ;oncomputer.Atthesametimethesampledataarcstored. ;Becausethenuggetsizegreatlyinfluencesthespotwelding ;quality,thenuggetsizeisthoughtasthecriterionforevaluation ;ofthespotweldingquality.Plentyofexperimentsindicatethat ;thespotweldingqualitywillsatisfythedesignrequirement.if ;theratioofnuggetareaandelecodeareaismorethan80%.

    ;Basedonthisfact.allsamplesaredividedinto2categories ;usingpictureelementcomparingmethod:acceptablenuggetand ;off-gradenugget.

    ;2FEATUREEXTRACTIoNSoFSlGNALS

    ;Manyaditiona1methodsofpicking.upeigenvaluearenot ;soaccurateduetotheDseudostochasticcharacteristicsof ;weldingsignals.However,thechangesofweldingspotquality ;caninfluencecomplexityofsignaldatacurveanditscomplexity ;canbereflectedbyfractaldimensionglobally,inthisregard.this ;paperadoptsoneoffractaldimensions-boxcountingdimension ;astheeigenvectorofsignals.Thecalculationprocedureofbox ;conntingdimensionisdescribedasfollow:firstly,some ;quadrates(boxes)whichlengthsofsideareareconstructed;

    ;secondly,thenumberofintersectionN,e)ofboxeswith ;CHINESEJOURNALOFMECHANICALENGINEERING?77?

    ;difierent1engthsofsideandnonblankboundedsubsetAof ;signalsaggregationiscalculated;thirdly,thesenumbersare ;firedinthecoordinatesystemwithahorizontalaxisof-Ins ;versusalongitudinalaxisoflnN,s1,theratesofslopeof ;thesefiredstraightlinesarethoughtastheboxcounting ;dimension.Theboxcountingdimensionsofweldingcurrent, ;weldingvoltage,soundandelectrodedisplacementwhichwere ;collectedduringspotweldingarecalculatedusingthisprogram ;whichisprogrammedaccordingtotheabovemethod.Thebox ;countingdimensionsofeachsignaIareshowninTable2. ;Table2Boxcountingdimensionofsignals

;3DETECTIoNoFSPoTWELDINGBASEDON

    ;SUPPoRTVECToRMACHINE

    ;3.1Principleofsupportvectormachine

    ;SVM【一.basedonstatisticlearningtheoryisanovel ;learningmachine,whichbalanceslearningabilityandstructural ;complexityofthemodelbasedonsmallsamples.sothismodel ;canavoideffectivelylocaloptimization.Andithasasmall ;parameterssetbypeopleinadvancewh…

    ;ich

    ;

    ;makeithavebetter

    ;generalizationandpopularizationability….Thebasicstrategy

    ;ofSVMistoseekdecisionruleswithpopularizationability.The ;analysisprocessofSVMisdescribedasfollows. ;Firstly,supposethereisasampleaggregatenamed ;{,Y,}1,?R,Yi?{-+1},andthenanSVMcanbedefined

    ;bypossiblemappingsR--4R.whereRarelower

    ;dimensionalspacesaggregateandwhereRarehigher ;dimensionalspacesaggregate.Thelargestintervalclassification ;hyperplanecanbeshownas

    ;A=?()+b

    ;where=?a,O(x)isobtainedinthehigherdimensionali=1

    ;spaces,andwhereaiandbareLagrangianmultipliersand ;constant,respectively.

    ;AccordingtothetheoryofReproduceKernelHilbertSpace ;(RKHS),thekernelfunctionKCx.,x,)=[(t)?(,)]which ;satisfiestheconditionofMercercanbeobtainedinlower ;dimensionalspaces.Thentheproblemofseekingtheoptimal ;classificationhyperplaneusingLagrangianoptimizationmethodis ;conversedtothesolutionofitsdualproblem,whichcanbe ;describedas

    ;?1

    ;maxQ(a)=?口一{?q,Y,(?xj)(1),f,,f

    ;whereshouldsubjecttotheconstraintandwhere(,xj)is ;kernelfunction

    ;N

    ;ZYO’i=0?0i=1,…,Nf

    ;Kemelfunctionsusuallyadoptthefollowthreeones: ;polynomialfunction.Gaussianbasisfunctionandtheradialbase ;function.

    ;Onlyasmallnumberofnonzerosolutionsareobtained ;fromEq.(1),thesevectorscorrespondingtononzerosolution ;are1ookedonassuppoRvectors.Thentheoptimizationdecision ;functioncanbewrittenas

;()=sgn{[?()+6}=sgfl{(t,_)+6)(2)

    ;Ifthesedatacannotbeclassifiedwitherrorfreeinhigher

    ;dimensionalspaces,arelaxquantum(?o)whichisusedto

    ;balancethemaximumclassificationintervalandtheminimum ;misclassificationsamplesisintroducedtosuppo~vectormachine. ;Thentheoptimumequationcanbedescribedas

    ;min)=at,lf+c()(3)

    ;i=1,?,N

    ;whereCispenaltycoefficient.

    ;Theoptimumclassificationplanefunctioncanbewrittenas ;max.(a)=?—1??YYNNJ

    ;(,1

    ;,l1,=l

    ;C?q?0?yq=0

    ;(4)

    ;Thenthedecisionfunctionf(x)canbeobtainedusingthe ;Karush.Ku恤一T1errules.

    ;LIUPenfei,etal:Detectionmethodofspotweldingbasedonmulti-informationfusionandf

    ractal

    ;3.2Detectionofweldingspotbasedonsupportvector ;machine

    ;Theradialbasefunction(RSF)(K(xi,x,)=tan[k(x,, ;x,)0];i,,=1,…,?)isusedasthekemelfunctionofSVMin

    ;thispaper.AndtheoptimalparametersofSVM(penalty ;coefficientC=300,widthparametero=5)arefoundthroughtests. ;AprogramofSVMisprogrammedaccordingtoEqs.(1)(4).

    ;Accordingtoevaluationcriterionofnuggetquality,thenuggets ;aredividedintotwogroups:Whenthenuggetareaislargerthan ;80%electrodetiparea,thenuggetisacceptable,otherwiseitis ;offgrade.36groupsofdataarepickedupassampledata.The ;former18groupsareusedastrainingsamples.Theformer9 ;groupsofthemaresignalsofacceptablenuggetsizes,thelatter9 ;groupsarethesignalsofsmallnuggetsizes.Andthelatter18 ;groupsaretestingsampleswhichareusedtotestthedetection ;1.O

    ;0

    ;l

    ;l

    ;l

    ;tJ

    ;1f

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    ;Predictednugget

;oActualnugget

    ;

    ;n

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    ;fl

    ;1

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    ;NumberofsamplesN

    ;(a)DetectionofSVMwithinputofcu~entsignals

    ;NumberofsamplesN

    ;(c)DetectionofSVMwithinputofvoicesignals

    ;effectsoftrainedSVM.Similarly,theformer9groupsofthemare ;signalsamplesofacceptablenuggetsizes,andthelatter9groups ;aresignalsamplesofsmallnuggetsizes.Thedetectionprocedure ;ofSVMisshowninFig.1.ThedetectioneffectsofSVMmodels ;basedonvariouscombinationsof4signalsareshowninFig.2. ;TrainingdataIlTestdata

    ;FeatureI

    ;TrainingSVMl7JL\/

    ;TrainedSVM

    ;JrL

    ;TmellFalse

    ;Fig.1DetectionprocessofSVM

    ;NumberofsamplesN

    ;(b)DetectionofSVMwithinputofvoltagesignals ;NumberofsamplesN

    ;(d)DetectionofSVMwithinputofcurrentandsoundsignals ;Fig.2DetectionresultsofdifferentSVMs

    ;AsCallbeseenfromTable3,Fig.2andFig.3,theminimum ;detectablerateis61%whenSVMissinglesigna1input.Andit ;reaches67%.ifSVMhas2inputnumbers.Ifinputnumbersof ;SVMreach3and4.thedetectableratesare72%and78% ;respectively.Theabovechangingtrendindicatesthatthe ;detectableratesofSVMincreasealongwiththeincreaseofits ;inputsignalnumbers.Butthecomparativestudyonthedetection ;effectofdifferentSVMsshowsthattheSVMwhoseinputs ;includesoundsignalhasabetterdetectioneffect,andeventhe ;detectableratereaches78%.IfSVMhassinglesigna1ofsound.

    ;Onecontrary,thedetectableratesappearareductivetrend ;whentheelectrodedisplacementsignalisaddedtotheinputsof ;SVM.

    ;Irable3DetectablerateofSVM

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    ;NumberofmodelsN

    ;Fig3DetectablerateofSVMmodels

    ;ItjsalsoseenfromFig.2.Fig.3andTable3thatthe ;detectionmodelOfSVMwithsoundsigna1inDuthasahigh ;detectablerate.Thereasonmaybethatsoundsigna1issensitiveto ;spatter.Throughcomparingshapesofnuggets,wefindthatthe ;shapesofacceptablenuggetsareroundandtheshapesofsmall ;nuggetsareirregularorisland.Thisphenomenonindicatesthat ;spatter1OSSof1iquidmetalresultsintl1esmallsizenuggetsofspot ;welding.Andbecausesoundsignalissensitivetosparer.itsbox ;countingdimensionshaveremarkabledifferencebetweenthe ;signalscontaminatedbysparernoiseandtheoneswhichhaveno ;spatternoisein.thedecisionfunctionofainedSVMhasahigh

    ;discriminationtotestsamplesofsignals.Asflresult,theSVM ;basedonsoundsigna1hasahighdetectablerate.

    ;ThereasonoflowdetectablerateofSVMwithelecode

    ;displacementsignalsmaybethattheelectrodedisplacementis ;influencedbyformationandgrowthofnugget.sometimesitis ;alsoaffectedbyposition,quantityandmodeofthespatter ;generatedduringspotwelding,whichmakenondeterministic ;vibrationofelectrodeobvious.Asaresultthecharacteristicof ;boxcountingdimensionofelectrodedisplacementsignalswhen ;nuggetsareacceptablehasnoobviousdifferencefromtheones ;whennuggetsareoffgrade.whichleadsthedecisionfunctionof

    ;trainedSVMtohavea1owdiscriminationtotestsamplesof ;signals,andmakesSVMbasedonelectrodedisplacementsignals ;havealowdetectablerate.

    ;ItisshownfromthecomparisonofdetectioneriectsofSVM ;modelsinFig2thatfalloutratioismostlyinfluencedbyerror ;detectionofoff-gradenuggets.Itshowsthatboxcounting ;dimensionofsignalshasnostrikingcharacteristicswhennuggets ;isoffgrade.Anditisalsoseenthatalmostal1thedetectioneffects ;ofSVMwhoseinputsincludesoundsignalsarebeRer,onthe ;contrary.almostalldetectionaccuracyofSVMwhoseinputs ;includeelectrodedisplacementsigna1islower.Thesemaybethat ;thecombinationofelectrodedisplacementsignalsandother ;signalsmakethesignalcharacteristicsofthetwostatesofnugget ;sizeslessobvious.andsoitaffectstheclassificationeffectof ;decisionfunctionOfSVM.ItisshownfromthecomparisoninFig ;3thatthedetectionmodelOfSVMbasedonboxcounting ;dimensionofsoundandvoltagesignalshasahighdetectablerate, ;whichreaches83%.Sothismode1ofSVM(modelcanbe

    ;1pokedonastheoptimumonebasedonboxcountingdimension ;ofsignals.

    ;4DETECTIONOFWELDINGSPoTBASEDoN

    ;ARTIFlCIALNEURALNETWORKS

    ;BecauseoftheadvantagesofANNsinpanemrecognition,a ;BPneuralnetworkisusedinqualitydetectionofspotweldingin ;thisstudyANNsmaybedefinedasstructurescomprisedof ;denselyinterconnectedadaptivesimpleprocessingelements ;(neurons)thatarecapableofperformingmassivelycomputations ;fordataprocessing.Anditcanbetrainedtorecognizepatterns ;andthemodelsandthenbeappliedtopatternsofnewdata.The ;structuresandtheprocessoftrainingandpredictionOfANNsare ;shownasfollows.

    ;rl1CreatingANNs:ItisshowninFig.4thattheANNsused ;inthisstudyconsistsof3layers:aninputlayer,ahiddenlayerand ;anoutputlayer.Thenumbersofneuronofinputlayerarevector ;numbersofpendingevents.Andtheneuronsofoutputlayer ;representthedependentvailables.thenumberofwhichisdefined ;asconstant1.Betweenthetwo1ayersthereisahiddenlayerwith ;9neurons.Differenttransforfunctionsbetweenlayerscanbe ;selected.InthisPaDer.thesametransfersigmoidfunctionis ;adoptedinal1theANNs’models.

    ;Hiddenlayer

    ;er

    ;Outputs

    ;Fig.4Topologyofartificialneuralnetworks

    ;f2)TrainingANNs:theANNsaretrainedusingthetraining ;samples.Intraining,therepresentativetrainingsamplesare ;presentediterativelytotheANNs.Anerrorterm.basedonthe ;differencebetweenthepredictedoutputanddesiredoutput.isen

    ;propagatedbackthroughtheANNstocalculatechangesofthe ;interconnectionweights.Andtl1eadjustmentofinterconnection ;weightsisendedwhentheerrorisbelowthedesiredvalues.Then ;thetrainingoftheANNsjsoveL

    entestsamplesare ;r3TestingperformancesofANNs:?

    ;providedtotheANNs,theyapplytheirpastexperiencetoproduce ;predictedoutputsanderroriterns.Thepredictedaccuracyof ;mode1isobtainedthroughcomparingtheactualvaluesoftest ;samplesandpredictedoutputsOfANNs.becauseANNswith ;differentinputshavedifferentdetectioneffectstoo.theANNs ;withdifferentcombinationsof4groupsofsignalscollected ;duringspotweldingisconstructedandained.Thegoalerroris

    ;0.003duringtraining.ItisindicatedthattheANNswithsingle ;soundsignalsistheoptimumoneinmodelswithsignalinput.the ;onewithinputsofcurrentandvoltagesignalsistheoptimumone ;inmodelswim2inputs.andtheonewithvoltage.soundand ;electrodedisplacementsignalsaretheoptimummodelinmodels ;with3inputs.throughcomparingdetectioneffectofallmodels0f ;ANNs.

    ;ThedetectionresultsareshowninFig.5toFig.8,inthese ;figures,allsymbolshavethesamemeaningwiththisdefinition, ;thesymbolofcircledenotestheactualqualityofweldingspot, ;andthesymbolofasteriskdenotesthepr

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