www.elsevier.com/locate/commatsci
Artificialneuralnetwork(ANN)predictionofcompressivestrengthofVARTMprocessedpolymer
composites
ˇrulSeyhana,GoˇluA.Tug¨kmenTayfurb,MuratKarakurta,MetinTanog
aa,*DepartmentofMechanicalEngineering,IzmirInstituteofTechnology,Gu¸eKampu¨lbahc¨s35437,Urla/I_zmir,TurkeybDepartmentofCivilEngineering,IzmirInstituteofTechnology,Gu¸eKampu¨lbahc¨s35437,Urla/I_zmir,Turkey
Received26May2004;receivedinrevisedform21September2004;accepted14November2004
Abstract
Athreelayerfeedforwardartificialneuralnetwork(ANN)modelhavingthreeinputneurons,oneoutputneuron
andtwohiddenneuronswasdevelopedtopredicttheply-layupcompressivestrengthofVARTMprocessedE-glass/polyestercomposites.Thecompositesweremanufacturedusingfabricpreformsconsolidatedwith0,3and6wt.%ofthermoplasticbinder.ThelearningofANNwasaccomplishedbyabackpropagationalgorithm.Agoodagreementbetweenthemeasuredandthepredictedvalueswasobtained.Testingofthemodelwasdonewithinlowaverageerrorlevelsof3.28%.Furthermore,thepredictionsofANNmodelwerecomparedwiththoseobtainedfromamulti-linearregression(MLR)model.ItwasfoundthatANNmodelhasbetterpredictionsthanMLRmodelfortheexperimentaldata.Also,theANNmodelwassubjectedtoasensitivityanalysistoobtainitsresponse.Asaresult,theANNmodelwasfoundtohaveanabilitytoyieldadesiredlevelofply-layupcompressivestrengthvaluesforthecompositespro-cessedwiththeadditionofthethermoplasticbinder.Ó2004ElsevierB.V.Allrightsreserved.
PACS:81-20;81.70.B
Keywords:Compressivestrength;Artificialneuralnetwork(ANN);Polymercomposites;Preformingbinder;Multi-linearregression(MLR)
1.Introduction
Vacuum-assistedresintransfermolding(VARTM),aderivativeoftheliquidmolding(LM)process,hasbeenwidelyemployedtomanu-factureadvancedcompositestructuresespecially
Correspondingauthor.Tel.:+902327506597;fax:+902327506505/4986500.
ˇlu).E-mailaddress:metintanoglu@iyte.edu.tr(M.Tanog
*0927-0256/$-seefrontmatterÓ2004ElsevierB.V.Allrightsreserved.
doi:10.1016/j.commatsci.2004.11.001
100A.T.Seyhanetal./ComputationalMaterialsScience34(2005)99–105
fordefenseandcivilengineeringapplications[1,2].VARTMistypicallyathree-stepprocessincludinglay-upofafiberperformsonatool,infusionofthepreformwithaliquidresin,andthecureofinfusedresinwithinthepreform.Fibervolumefraction(Vf)isoneofthecriticalpropertyforthepolymercompositesanditmayhavesomesignificanteffectsonthecompositemechanicalproperties.Thedegreeofthecompactionofthefiberpreformisknowntohavesomesignificanteffectsonthefibervolumefraction,porosityformationandresinflowcharacteristicwithinthereinforcement[3].There-fore,understandingtheeffectsofpreformcompac-tionandmutuallyfibervolumefractiononthecompositemechanicalbehaviorisessential.Therecenttechniquetoconsolidatethefiberperformsistousepowderedthermoplasticbindersbetweentheadjacentpliestocompactthembriefly[1,4].Binder-coatedplieswithvariousbinderconcentra-tioncanbestackedtogetherunderapplicationofheatandpressure.Asthethicknessofthefabricpreformreduces,ingeneral,thefibervolumefrac-tionincreases.Inthepreviouswork[5],itwascon-cludedthatcompressivestress–strainbehavioroftheE-glass/polyestercompositesloadedalongtheply-layupandin-planedirectionwereconsid-erablyaffectedbythepreformingbinder.Preformcompactionexperimentsrevealedthatthehighestcompactioncanbeobtainedwith3wt.%ofthebinderandthefurtherincreaseofbinderconcen-trationresultedinincreasingofthepreformthick-ness.Itwasalsorevealedthatthecompositescomposedoffabricpreformswith3wt.%ofbinderexhibitedthehighestply-layupandin-planecom-pressivestrengthandmodulusthanthosewith0and6wt.%ofbinder.
Inaddition,fiberpreformcompactionduringVARTMprocessmaynotbeuniformacrossthelengthofthepart,astheresinfillsthepreformfromonesidebythemeansofvacuumpressure[5,4].Thus,thefibervolumefractionandresinper-meabilitymaynotbeconstantandvariesthroughthepart.Thismayresultinconsiderablethicknessvariationsandnon-uniformmechanicalpropertiesthroughthecompositepart[5,2].Theunderstand-ingoftheinfluenceofseveralfactorsinVARTMthataffecttheoverallmechanicalpropertiessuchasstrengthofthecompositesmaybeimportant.Thesefactorsmayincludethethermoplasticbin-dercontent(%wt.),fiberpreformthicknesspriortoVARTMprocessingandthecompositefibervolumefraction.Eachofthemmayhavevaryingdegreesofeffectontheoverallstrengthofthecom-positeparts[1].However,ananalyticalmodeltodescribetheeffectsofsuchfactorstogetheronthestrengthcanbeverycomplex[4,6].Therefore,anartificialneuralnetwork(ANN)approachcanbeusedasapowerfultoolinmodelingtheeffectsofavariousparametersonply-layupcompressivestrengthofthecomposites.Acertainamountofexperimentaldataisnecessarytodevelopawell-performingneuralnetwork,includingitsarchitec-ture,trainingfunctionsandtrainingalgorithms[7,8].ThegreatestadvantageofANNisitsabilitytomodelcomplexnon-linear,multi-dimensionalfunctionrelationshipswithoutanypriorassump-tionsaboutthenatureoftherelationships[9,6].Asanexample,Zhangetal.[8]developedanANNmodeltopredictthedynamicmechanicalpropertiesofPTFE-basedcompositeswithvariousshortcarbonfibercontents.TheyfoundthatthenumberoftrainingdatasetisanimportantparameterinANNpredictivequality.Therefore,anone-outputneuralnetworkissuggestedtobeuseinitiallyforhighpredictivequalitybeforeasufficientdatabaseisavailable.Wearperformanceofpolyethylene(PE),polyurethane(PUR),andanepoxymodifiedbyhygrothermallydecomposedpolyurethane(EP-PUR)wasalsopredictedbythesameauthorsusinganANNmodel[6].Theyconcludedthatawell-trainedANNmodelisthekeytodesignandanalysisstructure–propertyrela-tionsofthepolymercomposites.
Inthepresentstudy,anANNapproachwasemployedtopredicttheeffectsofthethermoplasticbinderconcentration(Cb),fabricpreformthick-nesspriortoprocess(t)andcompositefibervol-umefraction(Vf)ontheply-layupcompressivestrengthofVARTMprocessedE-glassfiberrein-forcedpolyestercomposites.TheANNssoftwarewastrainedandtestedwithsetsofexperimentaldataconsistingofCb,t,andVfasinputandcom-positeply-layupcompressivestrengthasoutput.Furthermore,thepredictionsoftheANNmodelwerecomparedtothosewithamulti-linearregres-sion(MLR)model.
A.T.Seyhanetal./ComputationalMaterialsScience34(2005)99–105101
2.Experimental
Experimentalprocedurewasdescribedindetailinthepreviouswork[7].Inbrief,compositepartswerefabricatedusingE-glassfabricsandCamelyaf266thermosettingpolyesterresinsbothpurchasedfromCamElyafofCorpofTurkey.Cobaltnaph-thenate(CoNAP)in0.3wt.%andmethylethylketoneperoxide(MEKP)in1.5wt.%wereusedtoaccelerateandtopolymerizethethermosettingpolyestermatrixresin,respectively.Abisphenol-A-basedthermoplasticpolyester(ATLAC363E)withfumerategroupsinthebackbonewithamelt-ingtemperatureof60°Cwasemployedaspre-formingbinder.Fabricpreformscontainingof25layersofstackswith3and6wt.%ofthermoplasticpolyesterbinderwereobtainedbyapplicationofheatandpressureasdescribedindetailelsewhere[1,5].Thepreformthicknesswithandwithoutbin-derwasmeasuredusingamicrometer.Thethick-nessvaluesofthepreformswithandwithoutbinderweretheaverageofthemeasurementsfromatleast10differentpointsandassumedascon-stantforallsamplespriortoVARTMprocessing.Thepreformsweremeasuredtohaveaveragethicknessof21.80,13.15,and16.60mmfor0,3and6wt.%ofbinder,respectively.ThecompositepanelsweremanufacturedbyVARTMmethodusingthefabricpreformswithandwithoutbinderunderavacuumpressureof10Pa.Aftercuringoftheresinatroomtemperature,thecuredpanelswerepost-curedat110°Cfor2h.Thefibervol-umefractionvaluesofeachcompositespecimenssubjectedtocompressiontestweremeasuredbasedonthematrixburn-outtechnique.CompressiontestmethodaccordingtoASTMD695-Mwasusedtomeasuretheply-layupcompressivestrengthofthecompositespecimenswithandwithoutbinder.
3.Artificialneuralnetworks
ANNsarebasicallyadata-drivenblack-box
modelcapableofsolvinghighlynon-linearcom-plexproblems.Theyhavetheabilitytocapturetherelationshipbetweeninputandoutputvari-ablesfromgivenpatterns(historicaldataor
measureddataoninputandoutputvariablesofthesystemoftheconcern)andthisenablesthemtosolvelarge-scalecomplexproblems.Thenet-worklearnsbasicallybyfindingtheoptimalnet-work-connection-weightsthatwouldgenerateanoutputvectorascloseaspossibletothetargetval-uesoftheoutputvector,withtheselectedaccu-racy.Theoptimalnetwork-connection-weightsarefoundbyminimisingtheerrorfunction.Theoptimalnetwork-connection-weightsstoretherelationshipbetweentheinputandoutputvari-ablesofthesystemfromthegivenpatterns.
Inthisstudy,three-layerfeedforwardartificialneuralnetwork(ANN)modelhavingthreeinputneurons,oneoutputneuronandtwohiddenneu-ronswasused.Thecorrespondingmodelillustra-tionisgiveninFig.1.Inafeedforwardnetwork,theinputquantitiesarefirstnormalizedtoarangeof0.1–0.9withthefollowingequation.Xi¼0:1þ0:8ÃðXiÀXminiÞ=ðXmaxiÀXminiÞ
ð1Þ
whereXmaxiandXminiarethemaximumandmin-imumvaluesoftheithnodeintheinputlayerforallthefeeddatavectors,respectively.TheweightswereassignedarandomvaluebetweenÀ1and1.Beforeitsapplicationtoanyproblem,thenetworkisfirsttrained,wherebythedifferencebetweenthetargetoutputandthecalculatedmodeloutputateachoutputneuronisminimizedbyadjustingtheweightsandbiasesthroughsometrainingalgo-rithm.Duringtraining,aneuronreceivesinputsfromapreviouslayer,weightseachinputwithaprearrangedvalue,andcombinestheseweightedinputs.Thecombinationofweightedinputsisrep-resentednetj¼Xas
xivijð2Þ
Fig.1.IllustrationofthreelayerfeedforwardANNmodel.
102A.T.Seyhanetal./ComputationalMaterialsScience34(2005)99–105
Table1
Input(X)andoutput(Y)parametersofANN[5]Codex1x2x3Y
Parameter
Thermoplasticbinderamount(wt.%)Fiberpreformthickness(mm)Compositefibervolumefraction(-)Ply-layupcompressivestrength(MPa)
Minimum013.150.34415
Maximum621.800.57574
wherenetjisthesummationoftheweightedinputforthejthneuron,xiistheinputfromtheithneu-rontothejthneuron,andvijistheweightfromtheithneuroninthepreviouslayertothejthneuroninthecurrentlayer.
Thenetjispassedthroughatransferfunctiontodeterminethelevelofactivation.Iftheactivationofaneuronstrongenough,itproducesanoutputthatissentasaninputtotheotherneuronsinthesuccessivelayer.Inthepresentstudy,asigmoidfunctiongiveninEq.(3)isemployedasanactiva-tionfunctioninthetrainingofthenetwork.fðnetjÞ¼
11þeÀnetj
ð3Þ
ThelearningofANNswasaccomplishedbyabackpropagationalgorithmwheretheinformationisprocessedintheforwarddirectionfromtheinputlayertothehiddenlayerandthentotheout-putlayer.
Theobjectiveofabackpropagationnetworkis,byminimizingapredeterminederrorfunction,to
findtheoptimalweightsthatwouldgenerateanoutputvectorY=(y1,y2,...yp)ascloseaspossi-bletargetvaluesofoutputvectorT=(t1,t2,t3...tp)withaselectedaccuracy.Apredeterminederrorfunctionhasthefollowingform:
XX2
E¼ðyiÀtiÞð4Þ
p
p
whereyiisthecomponentofanANNoutputvec-torY,ti,isthecomponentofatargetoutputvec-
Fig.2.Resultsoftraining:(a)ANNmodelprediction,(b)MLRpredictionand(c)themodeltrendwithdataorder.
A.T.Seyhanetal./ComputationalMaterialsScience34(2005)99–105103
torT,pisthenumberofoutputneuronsandPisthenumberoftrainingpatterns.
Theleastsquareerrormethod,alongwithageneralizeddeltarule,isusedtooptimizethenetworkweights.Thegradientdescentmethodwithmomentumterm,alongwiththechainruleofderivatives,isemployedtomodifynetworkweightsasVijðnÞ¼Àd
oE
þaVijðnÀ1ÞoVij
ð5Þ
wheredisthelearningratethatisusedtoincreasethechanceofavoidingthetrainingprocessbeingtrappedinalocalminimainsteadofaglobalmin-ima.TheANNiscodedusingC++.
4.Resultsanddiscussion
ANNshavingthreeinputandoneoutputneu-ronswereusedtomodeltheply-layupcompres-
sivestrengthofthecomposites.Thenumberofhiddenneuronswastakentwoasaresultoftryingdifferentnumberofneurons.Theinputvariablesusedinthemodelsweretheamountofthermo-plasticbinder,initialfiberpreformthicknesspriortoVARTMprocessandcompositefibervolumefraction.Ply-layupcompressivestrengthofthecompositeswasusedastheoutputfortheneuralnetworks.TheinputandoutputparametersaregiveninTable1withtheirminimumandmaxi-mumvalues.TheANNsalgorithmwritteninC++wastrainedandtestedwithsetsofexperi-mentaldataconsistingofinputandoutputvalues.Duringtheneuralnetworkschemeourinputparametersarepresentedtotheinputlayernodes,inputlayernodesareonlyusedforinputpresenta-tion.Theneachinputparametersaremultipliedbythecorrespondingweightparameter.Afterthemultiplication,resultsaresummedandinsertedtotheconnectedmiddlelayernode.Presentedresultsareevaluatedwiththesigmoidactivation
Fig.3.Resultsoftesting:(a)ANNmodelprediction,(b)MLRpredictionand(c)themodeltrendwithdataorder.
104A.T.Seyhanetal./ComputationalMaterialsScience34(2005)99–105
functionintheeachmiddlelayerneuron.Obtainedresultsaremultipliedagainwiththecorrespondingoutputweightfunctiontopresentthroughtheout-putlayer.Atthistime,outputlayerisconstructedwithonelinearoutputnode(whichrepresentsourcompressivestrengthestimationwithinthepresentstudy).OutputlayernodegivesusournetworkÕsoutput.Theobtainedresultiscomparedwiththeknowntargetvaluetocalculatetheerrorvalue.ObtainederrorvalueÕsgradientwithrespecttothecorrespondingweightvalueleadustotheopti-malsolutionbyfindingtheoptimalweights.
Biastermwasnotusedduringmodelingbutamomentumtermwasusedtohelptoobtainfasterconvergenceduringiterations.Thisprovidedtheiterationprocessnottogetstuckinlocalminima,butrapidlyreachedthedesiredglobalminima.Therewereatotalof45datasetsthatweredividedintotwogroupsfortrainingandtesting,eachcon-taining30and15sets,respectively.Theprogramwasinstructedtorunfor100,000iterationsandtheoptimalweightswerecalculatedwithanaver-agepercentagetrainingerrorof3.28%.Inaddi-tion,MLRmodelwiththesameinputdatawasalsoemployedtoevaluatetheresultswithANNmodel.Fig.2(a)and(b)showsthetrainingoftheANNmodelandtheMLRpredictions,respec-tively.ANNmodelpredictedtheexperimental
Fig.4.Predictionoftheply-layupcompressivestrengthofthecompositeswith3wt.%ofbinderforsensitivityanalysis.(a)ANNpredictionand(b)trendwithexperimentaldataorder.
A.T.Seyhanetal./ComputationalMaterialsScience34(2005)99–105105
strengthmeasurementswiththecorrelationcoeffi-cient(R2)of0.94,showingbetteragreementthanthoseofMLRwiththecorrelationcoefficient(R2)of0.83.Thus,asseeninFig.2(c),thevalueswiththeANNmodelpredictionwereabletofol-lowthetrendbetter,ascomparedthosewithMLRmodelprediction.Fig.3(a)and(b)showsthecorrelationcoefficients(R2)of0.97and0.81fortheANNtestingsetandMLRmodel,respec-tively.InFig.3(c),ANNmodelandMLRpredic-tionswithexperimentaldataorderisgiven.Furthermore,thesensitivityanalysiswasper-formedbyfeedingply-layupcompressivestrengthofthecompositeswith0and6wt.%ofbinderasinputintothedevelopedANNmodeltopredictthecompressivestrengthforthecompositeswith3wt.%ofbinderasoutput.Fig.4(a)and(b)showsthesensitivityanalysisresults.Thecorrelationcoefficient(R2)was0.88(Fig.4(a)).Theexactval-uesofthemeasuredstrengthscouldnotbeobtainedfromthemodelasseenin(Fig.4(b)).Thiswastobeexpectedbecausethemodelwasconservativeandneededmoretrainingdatatolearntheextremes.
5.Conclusion
AnANNapproachwassuccessfullyappliedtopredicttheply-layupcompressivestrengthofthecompositesbyconsideringtheeffectsofthether-moplasticbinderamount,fiberpreformthicknesspriortoVARTMprocessandthecompositefibervolumefraction.ThecomparisonoftheANNpre-dictionswiththeexperimentalmeasurementswassatisfactory.Moreover,thepredictedvaluesofANNmodelwerecomparedwiththoseofamul-ti-linearregression(MLR)model.ItwasfoundthatANNhadbetterpredictionsoftheexperimen-talcompressivestrengthvaluesthanthosewithMLR.Furthermore,thesensitivityanalysiswasdonetoevaluatetheperformanceoftheANNmodel.Theresultswerefoundtobeconsistent
withtheexperimentalobservations,buttohavealowercorrelationcoefficient(R2).ThisindicatesthatthenumberoftrainingdatasetiscriticalfortheANNmodelsensitivityandpredictivequality.Asaresult,itmaybeconcludedthattheANNisausefultoolincharacterizingtheeffectsofsomecriticalmaterialparametersonthepropertiesofthepolymercompositesifespeciallyasufficientamountofexperimentaldataisobtained.
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