Engineering5(2024)721–729Contents lists available at ScienceDirectEngineeringResearch
AdditiveManufacturing—Review
ApplyingNeural-Network-BasedMachineLearningtoAdditiveManufacturing:CurrentApplications,Challenges,andFuturePerspectives
XinboQia,?,GuofengChenb,YongLia,XuanChengb,ChangpengLibabStateKeyLaboratoryofTribology,TsinghuaUniversity,Beijing100084,ChinaCorporateTechnology,SiemensLtd.,Beijing100102,Chinaarticleinfoabstract
Additivemanufacturing(AM),alsoknownasthree-dimensionalprinting,isgainingincreasingattentionfromacademiaandindustryduetotheuniqueadvantagesithasincomparisonwithtraditionalsubtrac-tivemanufacturing.However,AMprocessingparametersaredif?culttotune,sincetheycanexertahugeimpactontheprintedmicrostructureandontheperformanceofthesubsequentproducts.Itisadif?culttasktobuildaprocess–structure–property–performance(PSPP)relationshipforAMusingtraditionalnumericalandanalyticalmodels.Today,themachinelearning(ML)methodhasbeendemonstratedtobeavalidwaytoperformcomplexpatternrecognitionandregressionanalysiswithoutanexplicitneedtoconstructandsolvetheunderlyingphysicalmodels.AmongMLalgorithms,theneuralnetwork(NN)isthemostwidelyusedmodelduetothelargedatasetthatiscurrentlyavailable,strongcomputationalpower,andsophisticatedalgorithmarchitecture.ThispaperoverviewstheprogressofapplyingtheNNalgorithmtoseveralaspectsoftheAMwholechain,includingmodeldesign,insitumonitoring,andqualityevaluation.CurrentchallengesinapplyingNNstoAMandpotentialsolutionsfortheseproblemsarethenoutlined.Finally,futuretrendsareproposedinordertoprovideanoveralldiscussionofthisinterdisciplinaryarea.ó2024THEAUTHORS.PublishedbyElsevierLTDonbehalfofChineseAcademyofEngineeringandHigherEducationPressLimitedCompany.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).Articlehistory:Received29July2024Revised6April2024Accepted9April2024Availableonline3July2024Keywords:Additivemanufacturing3DprintingNeuralnetworkMachinelearningAlgorithm1.IntroductionAdditivemanufacturing(AM),asopposedtotraditionalsubtractivemanufacturingtechnologies,isapromisingdigitalapproachforthemodernindustrialparadigmthathasgainedwidespreadinterestallovertheworld[1–4].Byfabricatingobjectslayerbylayerfromthree-dimensional(3D)computer-aideddesign(CAD)models,AMprovidesseveralbene?ts:①Itcreatesproductswithcomplexshapes,suchastopologicallyoptimizedstructures,whicharedif?culttomanufacturewithtraditionalcastingorforg-ingprocesses;②itcanbeusedtogeneratenovelcharacteristicsofmaterials,suchasdislocationnetworks[5],whichareveryattrac-tivetoacademicresearchers;and③itreducesmaterialwasteandthussavesoncostforindustry.However,AMpartsalsopresentdozensofuniquedefectsthatdifferfromthosethatappearintheircastandwroughtcounterparts;theseincludeporosityduetoalack?Correspondingauthor.E-mailaddress:qixinbo@gmail.com(X.Qi).offusionandgasentrapment,heavilyanisotropicmicrostructureinboththeperpendicularandparalleldirectionsrelativetotheprintingdirection,anddistortionduetolargeresidualstressintro-ducedbyahighcoolingrateandsteeptemperaturegradient[6].Itisthusessentialtobetterunderstandthecomplexrelationshipbetweenapowder’smetallurgicalparameters,theprintingprocess,andthemicrostructureandmechanicalpropertiesofAMparts.TheAMprocessalwaysinvolvesmanyessentialparametersthatcandeterminethe?nalproducts’performance.Forexample,inselectivelasermelting(SLM),theprocessingparameters—whichincludelaserpower,scanspeed,hatchspacing,andlayerthick-ness—allsigni?cantlyaffectthequalityoftheproducedparts.Unfortunately,therelationshipbetweentheseparametersandtheoutputqualityistoocomplicatedtofullyunderstand,asSLMisamulti-physicsandmultiscaleprocessthatincludespowder-laserinteractionatthemicroscale,meltpooldynamicsandcolumnargraingrowthatthemesoscale,andthermal–mechanicalcouplingatthemacroscale.Researchershavetriedtodevelopvariousphysicalmodelsinordertoclassifythisrelationshipina722X.Qietal./Engineering5(2024)721–729clearerandmoreaccurateway.Acharyaetal.[7]developedacom-putational?uiddynamics(CFD)andphase-?eldframeworktosimulategrainstructureevolutionintheas-depositedstateforthelaserpowder-bedfusion(PBF)process;Ferganietal.[8]proposedananalyticalmodeltoassessresidualstressintheAMprocessofmetallicmaterials;andChenetal.[9]adopteda?nite-elementmodeltoinvestigatemeltpoolpro?lesandbeadshape.Ascanbeseen,theabovesimulationsvaryfromthepowderscaletothepartscale,andconcentrateononlyoneortwoaspectsofthewholeprocessasaresultofthelackofanin-depthunderstand-ingofAM.ItiscurrentlyimpracticaltopredictthewholeAMprocessquicklyandaccuratelyviathesephysics-drivenmethodsinashorttime.Inadditiontotheabovementionedphysics-drivenmodels,data-drivenmodelshavebeenwidelyusedinthe?eldofAM;thesemodelshavetheuni?ednameofmachinelearning(ML)[10,11].Theoverwhelmingadvantageofthiskindofmodelisthattheydonotneedtoconstructalonglistofphysics-basedequations;instead,theyautomaticallylearntherelationshipbetweentheinputfeaturesandoutputtargetsbasedonpreviousdata.AmongMLmethods,theneuralnetwork(NN)algorithmisthemostwidelyusedandiscurrentlyunderrapiddevelopment,asaresultofthemassivedataavailabletoday,thegreatavailabilityofcomputationalresources,anditsadvancedalgorithmstructure[12].Forexample,NNsarethemainstimulatingforceintheseareas:computervision[13],voicerecognition[14],naturallanguageprocessing[15],andautonomousdriving[16].TheNNshowsitsgreatpowerinrecognizingtheunderlyingcomplicatedpatternsintheabovementionedtasks,mostofwhichwereoncethoughttobeonlypossibleforhumanbeings.Further-more,thereisanobvioustrendinthatthesuccessfulexperienceswithutilizingNNintheseareasarebeingtransferredintotraditionalmanufacturing?elds(whichofcourseincludeAM).TheNNhasexertedadeepandwideimpactonallvaluechaininnovationinindustry—fromproductdesign,manufacturing,andquali?cationtodelivery—anditisbelievedthattheimpactofNNwillbeincreasinglyintensive.ThispaperprovidesanoverviewofthecurrentprogressachievedbyresearchersinapplyingtheNNalgorithmtoAM.Itisorganizedasfollows:Section2givesabriefintroductionofAMtechnologiesandtheNNalgorithm,whileSection3summarizesdetailedapplicationsofNNinAM.Section4outlineschallengesandpotentialsolutions,andSection5describesfuturetrendsinthisarea.2.Methods2.1.AMtechnologiesAsaterminology,AMiscomparablewithtraditionalsubtractivemanufacturing(i.e.,casting,forging,andcomputernumericalcon-trol(CNC));itcanbedividedintoseveralcategoriesbasedondif-ferentprintingtechnologies[17].Amongthem,PBF[18],binderjetting(BJ)[19],andmaterialextrusion(ME)[20]arethreewidelyusedtechnologies.PBFusesathermalsourcetobuildpartslayeruponlayerbysinteringormelting?nemetal/plasticpowders.Basedondifferentapplicationcases,PBFcanfurtherbedividedintoselectivelasersintering(SLS),SLM,electronbeammelting(EBM),andsoon.SLSandSLMbothutilizealaserasthethermalsource;however,inSLM,thematerialisfullymeltedratherthansinteredasinSLS[21,22].Incontrast,thethermalsourceofEBMisanelectronbeam,whichresultsincertainadvantagessuchassmallerresidualstressandlessoxidation,incomparisonwithlaser-basedtechnologies[23].TheBJprocessusestwomaterials:apowder-basedmaterialandabinder.Thebinderisselectivelydepositedontoareasofthepowderbed,andbondstheseareastogethertoformasolidpartonelayeratatime[24].Fuseddepo-sitionmodeling(FDM)isakindofMEtechnology.Duringprinting,moltenmaterialsareextrudedfromthenozzleofanFDMprintertoformlayers,asthematerialhardensimmediatelyafterextrusion[25].ItcanbeseenthattherearevariouskindsofAMtechnologies,andthattheseproducedifferentkindsofdatasheets.Howtoorga-nizethesedatawithauni?edformatandintegratethedata-?owintothesubsequentMLalgorithmsisachallengingtask.2.2.NNalgorithmNNsareakindofsupervisedML,whileotherformsofMLareunsupervisedlearning.Theeasiestmethodtodistinguishbetweenthesetwopatternsistocheckwhetherthedatasetthattheyoper-ateonhaslabelsornot.Thatistosay,inanNNalgorithm,thedataislabeled—thatis,themodelhasbeentoldthe‘‘answer”totheinputs.ThisissuitableforanAMcase,sincetherearealwayscleartargetsandquali?cationmethodsforthismanufacturingtech-nique.AnNNhasstrongevaluatingskillsforrepresentingcomplex,highlynonlinearrelationshipsbetweeninputandoutputfeatures,andithasbeenshownthatanetworkwithonlyonehiddenlayerbutsuf?cientneuronscanexpressanarbitraryfunction.Thearchi-tectureorsettingsofanNNconsistofthreekindsoflayers:theinputlayer,hiddenlayer,andoutputlayer[26].Eachlayerconsistsofnodesorneurons,whichborrowtheideafromneurologicalsciences.Theparametersorcoef?cientsinNNarecalledweights,andrepresenttheconnectionmagnitudesbetweenneuronsinadjacentlayers.ThevaluesofweightsaredeterminedbytrainingtheNNiteratively,inordertominimizethelossfunctionbetweenpredictionsandactualoutputs.Withinthistypeofprocess,themostfamousandwidelyusedmethodforupdatingweightsiscalledbackpropagation,whichusesthemathematicalchainruletoiterativelycomputegradientsforeachlayer[27].Oncetrainingisachieved,theNNwillhavethecapacitytoinfertheoutputsbasedonpreviouslyunseeninputs.Manytypesofspeci?cNNshavebeenproposedbyresearchersoverthedecadesofitsdevelop-ment.ThefollowingthreeclassesofNNshaveprovedtheirvalueandgainedwidepopularity.①Themultilayerperceptron(MLP)[28]isthemosttypicalNN;itscommonmathematicaloperationsarelinearsummationandnonlinearactivation(suchasthesigmoidfunction).Itiswidelyusedindealingwithtabulardata.②Theconvolutionalneuralnetwork(CNN)[13]dominatesimageprocessing,sinceitconsidersthespatialrelationshipbetweenimagepixels.Itisnamedafterthemathematical‘‘convolution”operation.③Therecurrentneuralnetwork(RNN)[29]playsakeyroleindealingwithtemporaldynamics,sinceitbuildsconnec-tionsbetweenthenodesinonelayer.ThemostfamousRNNislongshort-termmemory(LSTM),whichaccuratelyreproducesthe?nite-elementsimulationinthefollowingcase.3.ApplicationsAMisavaluechainincorporatingmanyaspects:modeldesign,materialselection,manufacturing,andqualityevaluation.Thissec-tionstressestheapplicationofNNstothefollowingpartsofAM:design,insitumonitoring,andtheprocess–property–performancelinkage.3.1.DesignforAMDesignforAM(DfAM)involvesbuildingaCADmodelofAMparts;thus,itisthe?rstandcrucialstepforthewholeprocessingchain.However,therearealwaysdeviationsbetweenCADmodelsandtheprintedparts,becauseofresidualstressintroducedbydis-tortionintheprocessingresults.Thus,compensationisusuallyperformedinordertoobtainanAMpartwithhighaccuracy.ChowdhuryandAnand[30]presentedanNNalgorithmtodirectlyX.Qietal./Engineering5(2024)721–729723compensatethepartgeometricdesign,whichhelpstocounter-balancethermalshrinkageanddeformationinthemanufacturedpart.Thewholeprocessisasfollows:①ACADmodeloftherequiredpartisprepared,anditssurface3DcoordinatesareextractedastheinputoftheNNmodel;②athermo–mechanical?nite-elementanalysissoftware(suchasANSYSorABAQUS)isusedtosimulatetheAMprocesswithade?nedsetofprocessparameters.ThedeformedsurfacecoordinatesareextractedastheoutputoftheNNmodel;③anNNmodelwith14neuronsandmeansquareerror(MSE)asthelossfunctionistrainedtolearnthedifferencebetweentheinputandoutput;and④thetrainednetworkisimplementedtoSTL?letomaketherequiredgeometriccorrectionssothatmanufacturingthepartusingthemodi?edgeometryresultsinadimensional-accurate?nishedproduct.Koeppeetal.[31]proposedaframeworkthatcombinedexperiments,?nite-elementmethod(FEM)simulation,andNNs,asillustratedinFig.1.First,theyconductedactualexperimentstovalidateFEMsimulation.Next,FEMwasusedtorun85simulationsamplesbasedonadifferentparametriccombinationofgloballoads,displacementandstrutradius,andcellscale.ThesearetheNNinputfeatures,andtheoutputsarethemaximumVonMisesandequivalentprincipalstresses.TheNNarchitecturecontainsafullyconnectedlayerwith1024recti?edlinearunits,twoLSTMcellswith1024units,respectively,andafullyconnectedlinearoutputlayer.ItshouldbenotedherethatLSTMisselectedandrecommendedbecauseofitsexcellentcapacityindealingwithtimeseriesevents.Aftertraining,anNNcanreproducetheloadinghistoryingoodagreementwithanFEMsimulation.Fromthispointon,theNNcanactasasubstitutefortraditionalnumericalsimulationmethodswithalowoperatingvelocity.Unliketheabovetwocases,whichappliedanNNtoDfAM,McCombetal.[32]attemptedtoestablishanautoencoder(akindofNNthatlearnsfromtheinputandthentriestoreconstructtheinputwithhighaccuracy)tolearnalow-dimensionalrepresenta-tionofthepartdesign.Inadditiontothisautoencoder,theotherthreenetworksweretrainedtodeterminetherelationshipbetweenthedesigngeometriesandthreeDfAMattributes(i.e.,partmass,massofsupportmaterial,andbuildtime).Inthisway,acombinationofthesefourNNscanbeutilizedtoevaluatetheattributesofpartsdesignedforAM.AnotherinterestinginstanceofapplyingMLtoDfAMconcernsthesecuritylevelofthe3Dprint-ingprocess.Lietal.[33]trainedaCNNtodetectandrecognizeille-galcomponents(e.g.,guns)madethroughAM.AftertheCNNiswellconstructed,itisintegratedintotheprintersinordertodetectgunprintingatanearlystageandthenterminatethemanufactur-ingprocessintime.Theauthorscollectedadatasetof61340two-dimensional(2D)imagesoftenclasses,includinggunsandothernon-gunobjects,correspondingtotheprojectionresultsoftheoriginal3Dmodels.TheCNNmodeliscomposedoftwoconvolu-tionallayers,twopoolinglayers,andonefullyconnectedlayer.Accordingtotheexperimentalresults,theerrorrateofclassi?ca-tioncanbereducedto1.84%.3.2.InsitumonitoringInsitumonitoringfordataacquisitionfrommultiplesensorsprovides?rst-handinformationregardingproductqualityduringtheAMprocess.Ifthesereal-timedatacanbeanalyzedsyn-chronouslyandaccurately,completeclosed-loopcontrolformanufacturingisrealized.Thedatasourceisdividedintothreetypes,includingone-dimensional(1D)data(e.g.,spectra),2Ddata(e.g.,images),and3Ddata(e.g.,tomography)[34].Eachdatatypehasitsprosandcons.Forexample,1Ddatacanbeprocessedfasteranditshardwareisrelativelycheaper;however,itmayprovidelessusefulinformationthantheothers.Twoexampleswillbeproposedtodemonstratetheusageofthesedifferenttypesofsignaldata.Shevchiketal.[35,36]presentedastudyoninsituqualitymonitoringforSLMusingacousticemission(AE)andNNs,whichisdepictedinFig.2.TheAEsignalsarerecordedusinga?berBragggratingsensor,whiletheselectedNNalgorithmisaspectralconvolutionalneuralnetwork(SCNN),whichisanextensionofatraditionalCNN.Theinputfeaturesofthemodelaretherelativeenergiesofthenarrowfrequencybandsofthewaveletpackettransform.Theoutputfeatureisaclassi?cationofwhetherthequalityoftheprintedlayerishigh,medium,orpoor.Itwasreportedthattheclassi?cationaccuraciesusingSCNNareashighas83%,85%,and89%forhigh,medium,andpoorworkpiecequalities,respectively.Recently,Zhangetal.[37]builtavisionsystemwithahigh-speedcameraforprocessimageacquisition.Thesystemcandetecttheinformationofthreeobjects:themeltpool,plume,andspatter,asillustratedinFig.3.Thefeaturesoftheseobjectsarecarefullyextractedbasedontheauthors’understandingofthephysicalmechanismsoftheprocessinordertofeedthemintothetraditionalMLalgorithm.However,theauthorsstressthattheCNNmodeldoesnotrequirethisfeature-extractionstep,asitstillhasahighaccuracyof92.7%inquality-levelidenti?ca-tion.ItisbelievedthatCNNhasgreatpotentialtoachievereal-timemonitoringinindustrialapplications.Thecasesmen-tionedabovemainlyfocusonpurelyinsitumonitoringoftheAMprocess;however,thequali?cationresultoftheNNmodelcannotaffecttherealmanufacturinginreverse.Onthecontrary,thefollowingcaserealizesclosed-loopcontrolbyseamlesslyintegratingavision-basedtechniqueandanNNtoolforliquidmetaljetprinting(LMJP)[38].First,Wangetal.developedavisionsystemwithacharge-coupleddevice(CCD)cameratoFig.1.ApplicationofanNNmodeltopredictthedeformationofanAMstructure.(a)Specimens,whicharemanufacturedandtestedundercontrolledloadingconditions;(b)theFEM,whosesimulationresultsarevalidatedbyspecimens;(c)theNN,whichistrainedbythedatageneratedbytheFEM,andthenusedtopredictthedeformationhistoryinafasterwaythantheFEM.FC:fully-connectedlayers.ReproducedfromRef.[31]withpermissionofElsevier,ó2024.724X.Qietal./Engineering5(2024)721–729Fig.2.SchemeoftheAMqualitymonitoringandanalyzingsystem.Thework?owisasfollows:AnacousticsignalisemittedduringtheAMprocess,andthencapturedbysensors;anSCNNmodelis?nallyappliedtotherecordeddatainordertodistinguishwhetherthequalityoftheprintedlayerisadequateornot.ReproducedfromRef.[35]withpermissionofElsevier,ó2024.Fig.3.SchemeoftheSLMprocessmonitoringcon?guration.Ahigh-speedcameraisusedtocapturesequentialimagesofthebuiltprocess;aCNNmodelisappliedtoidentifyqualityanomalies.CMOS:complementarymetal-oxidesemiconductor;ROI:regionofinterest.ReproducedfromRef.[37]withpermissionofElsevier,ó2024.capturethejettingimages,whichcontainvariousdropletpatterns.Second,theyformulatedanNNmodeltoestablishacomplexrelationshipbetweenthevoltagelevelandthedropletfeatures.Thus,thereal-timejettingbehaviorandtheidealbehavior(inwhicheachpulseoftheinputsignalgeneratesonlyasingledropletwithsuf?cientvolumeandwithoutsatellitesbehindit)canbeconvertedintoexactvoltagevaluesaccordingtotheNNmodel.Finally,proportionalintegralderivative(PID)controltechnologywasusedtocomparethesevaluesinordertoadjustthedrivevoltageandstabilizetheprintingprocessaccordingly.3.3.Process–property–performancelinkageFromatechnologicalandeconomicpointofview,processparameterselectionfortheoptimizationoftheperformanceofAMpartsishighlydesirable.Constructingadirectlinkagebetweenprocess,property,andperformanceisofgreatinteresttoscientistsandengineers.Thislinkageisoftenhighlynonlinear,sincetheamountoftheinputvariablesisusuallygreaterthanthree.Asaresult,itisverydif?culttoidentifytheunderlyingmathematicalformulaforsuchalinkage.Becauseofitsintrinsicnonlinearcharacteristics,NNmodelshavebeenappliedtoformulatetheseX.Qietal./Engineering5(2024)721–729Table1
NNapplicationtobuildprocess–property–performancelinkage.AMtechniqueFDMFDMFDMFDMFDMBJBJBJSLSSLSSLSSLSSLSSLSSLSSLLMDEBMWAAMProcessingparametersLayerthickness,orientation,rasterangle,rasterwidth,airgapLayerthickness,orientation,rasterangle,rasterwidth,airgapOrientation,slicethicknessLayerthickness,orientation,rasterangle,rasterwidth,airgapLayerthickness,orientation,rasterangle,rasterwidth,airgapLayerthickness,printingsaturation,heaterpowerration,dryingtimeLayerthickness,printingsaturation,heaterpowerration,dryingtimeLayerthickness,printingsaturation,heaterpowerration,dryingtimeLaserpower,scanspeed,scanspacing,layerthicknessLaserpower,scanspeed,scanspacing,layerthicknessZheight,volume,boundingboxLaserpower,scanspeed,hatchspacing,layerthickness,scanmode,temperature,intervaltimeLayerthickness,laserpower,scanspeedLaserpower,scanspeed,hatchspacing,layerthickness,powdertemperatureLaserpower,scanspeed,hatchspacing,layerthickness,scanmode,temperature,intervaltimeLayerthickness,borderovercure,hatchovercure,?llcuredepth,?llspacingandhatchspacingLaserpower,scanningspeed,powderfeedingrateSpreadertranslationspeed,rotationspeedBeadwidth,height,centerdistanceofadjacentdepositionpathsProperty/performanceCompressivestrengthWearvolumeVolumetricerrorDimensionalaccuracyDimensionalaccuracySurfaceroughnessShrinkagerate(Y-axis)Shrinkagerate(Z-axis)DensityDimensionBuildtimeShrinkageratioOpenporosityTensilestrengthDensityDimensionalaccuracyGeometricalaccuracyVolume,roughnessOffsetdistance725Ref.[39][40][41][42][43][44][44][44][45][46][47][48][49][50][51][52][53][54][55]SL:stereolithography;LMD:lasermetaldeposition;WAAM:wireandarcadditivemanufacturing.mathematicalrelationshipsforvariousAMprocesses.Table1[39–55]summarizestheapplicationofNNsintoAM(infact,NNisreferredtohereasMLP,sinceallthedatasetsarethetabulartype),andliststheinputvaluesoftheprocessingparametersandtheoutputvaluesoftheproperty/performance.AscanbeseeninTable1,differentAMtechniquesshouldselectdifferentinputfea-tures,sincethekeyfactorsindeterminingtheAMpartarediffer-ent.Furthermore,becausealargenumberofparameterscanexertin?uenceonthe?nalproducts,determiningwhichparame-terstoselectrequiresadeepknowledgeoftheAMprocess.ThistopicwillbediscussedindetailinSection4.3.ThedetailedsettingoftheNNalgorithmissummarizedinTable2.ThetypicalhyperparameterstodetermineanNNstructureusuallyconsistoffourparts:thenumberofhiddenlayers,numberofneuronsinonelayer,activationfunction,andlossfunction.(1)Numberofhiddenlayers.Inthe‘‘Layer/neuron”columnofTable2,‘‘5-8-1”meansthatthisNNcontainsthreelayers:theinputlayerhas?veneurons,theonlyhiddenlayerhaseightneu-rons,andtheoutputlayerhasoneneuron.Ascanbeseenfromthetable,onehiddenlayerissuf?cientforalargemajorityofAMproblems.(2)Numberofneuronsinonelayer.TheneuronnumbersoftheinputlayerandoutputlayeraredeterminedbytheproblemTable2
DetailedinformationontheNNalgorithm.AMtechniqueFDMFDMFDMFDMFDMBJBJBJSLSSLSSLSSLSSLSSLSSLSSLLMDEBMWAAMLayer/neuron5-8-15-8-14-15-12-15-6-45-7-34-6-14-20-14-11-14-9-14-6-13-7-17-7-13-9-15-27-17-8-16-20-53-9-32-200-23-12-1ActivationfunctionTanhTanhSigmoid——SigmoidSigmoidSigmoidSigmoid———TanhSigmoid—Sigmoid—SigmoidSigmoiditself.However,thenumberofneuronsfortheonlyhiddenlayerneedstobeselectedcarefully,sinceitisdirectlyrelatedtotheunder?ttingandover?ttingproblemsinML[56].AccordingtoTable2,wesuggest5–10neuronstobethestartingpointfordeterminingtheoptimalnumberofhiddenunitsforAMapplications.(3)Activationfunction.Theactivationfunctionisthenonlin-eartransformationovertheinputsignal(x);itdecideswhetheraneuronshouldbeactivatedornot.ThisisofvitalimportancetotheNN,becauseanetworkwithoutanactivationfunctionisjustalinearregressionmodel,andcannothandlecomplicatedtasks.Somepopulartypesofactivationfunctionsareasfollows:SigmoidexT?11teàxe1Te2Te3TTanhexT?2à11teà2xReLUexT?maxe0;xTInarealimplementation,thegradienttowardeitherendofthesigmoidandtanhfunctionsandatthenegativeaxisoftheReLUfunctionisgoingtobesmallandevenzero;asaresult,theweightsErrorfunctionMAE—MAE——MSEMSEMSESSE—MSEMSERMSEMSEMAEMSERMSEMAEMSEDataset323237527271616161534130333666321401204535Error(%)1.210–7.94.070–0.120.2–8.54.0–19.68.0–29.171.05–1.360154.35–27.600–9.10.9–9.2—62.0–5.81.74–2.27—Ref.[39][40][41][42][43][44][44][44][45][46][47][48][49][50][51][52][53][54][55]MAE:meanabsoluteerror;RMSE:rootmeansquareerror;SSE:sumsquareerror.
将基于神经网络的机器学习方法应用于增材制造 - 应用现状、当前挑战和未来前景 - 图文
