计算方法和在有限元神经网络分析硬件电路的实现(IJISA-V3-N5-6)

I.J.IntelligentSystemsandApplications,2011,5,41-47PublishedOnlineAugust2011inMECS()Copyright©2011MECSI.J.IntelligentSystemsandApplications,2011,5,41-47ComputingMethodandHardwareCircuitImplementationofNeuralNetworkonFiniteElementAnalysisLikunCuiCollegeofscienceofInnerMongoliauniversityofTechnology,Hohhot,China；Email:[e-mail]nauticsNorthwesternPolytechnicalUniversity,Xi'an,ChinaEmail:[e-mail]ofInnerMongoliauniversityofTechnology,Hohhot,ChinaEmail:[e-mail]-Thefiniteelementanalysisintheoryofelasticityiscorrespondedtothequadraticprogrammingwithequalityconstraint,whichcanbefurthertransformedintotheunconstrainedoptimization.Inthepaper,theneuralnetworkoffiniteelementsolvingwasobtainedonthebasisofHopfieldneuralnetworkthatwasreformed.Andtheno-errorsolvingoffiniteelementneuralnetcomputationwasrealizedintheory.Andadesignmethodtoconstructanartificialneuronbyusingelectronicdevicessuchasoperationalamplifier,digitalcontrolledpotentiometerandsoonwaspresented.Aprogrammablehardwareneuralnetworkoffiniteelementcanbebuildupbyusinganalogswitchestointerconnectinputs/outputsofhardwareneurons.Theweights,biasesandconnectioninthehardwareneuralnetworkoffiniteelementcanbeadjustedautomaticallybymicroprocessoraccordingtotheresultsoftraintocontrollingsystem,Thisprogrammablehardwareneuralnetworkoffiniteelementhassomemoreadaptabilityfordifferentsystems.Inaddition,theauthorspresentthecomputersimulationandanaloguecircuitexperimenttoverifythismethod.Theresultsarerevealedthat:1)TheresultsofimprovedHopfieldneuralnetworkarereliableandaccuracy;2)TheimprovedHopfieldneuralnetworkmodelhasanadvantageoncircuitrealizationandthecomputingtime,whichisunrelatedwithcomplexityofthestructure,isconstant.Itispracticalsignificancefortheresearchandcalculation.IndexTerms-Finiteelementmethod;Hopfieldneuralnetwork;analoguecircuit;simulation;operationalamplifier;digitalcontrolledpotentiometerI.INTRODUCTIONWiththerapiddevelopmentofcomputersoftwareandhardwaretechnology,finiteelementmethodhasbeenwidelyappliedtothestructureanalysisanddesign.Itisveryslowtodealwithlarge-scaleandcomplexengineeringstructureandtheefficiencyislowbecausethetraditionalcalculationprogramforstructureoptimizationisbasedonallserialalgorithmsinasinglecomputer[1].Andthecontradictionbetweenthelargecomputesscaleandlowcomputationalabilitybecomesmoreandmoreurgent,sotheparallelcomputingmethodhasimportantmeaningforfiniteelementmethod.However,commonmethodscannotcreateenoughcomputationalefficiencyneededinpractice[2].Theneuralnetworkisalarge-scalenonlineardynamics'system,andithasowncharacters,suchashighparallelprocessingability,strongrobustness,fault-tolerance,learningabilityandadaptability,andshowstosuperiorityinsettingupmodelforcomplicatedsystem,soitissuitedformanyaspectsinindustryandprofession.Inaddition,theneuralnetworkisconsideredasadynamiccircuit,anditcanbeusedforhigh-speedparallelcomputationandiseasytoattainthesolutionswithinthetimeconstant[3].So,thefiniteelementanalysisintheoryofelasticityissolvedbymodifiedHopfieldneuralnetworkandverifiedbythecomputersimulationandanaloguecircuitexperimentinthepaper.Thearticlealsoprovidesadesignmethodtoconstructanartificialneuronintheorybyusingelectronicdevicessuchasoperationalamplifier,digitalcontrolledpotentiometer,analogyswitchandsoon.Aprogrammablehardwareneuronnetworkscanbebuiltupbyusinganalogswitchestointerconnectinputs/outputsofhardwareneurons.Theweights,biases,activationfunctionsandconnectioninthehardwareneuronnetworkscanbeadjustedautomaticallybymicroprocessoraccordingtotheresultsoftraintocontrollingsystem.Thisprogrammablehardwareneuronnetworkshassomemoreadaptabilityfordifferentsystems.II.ELASTICITYFINITEELEMENTSMODELUSINGIMPROVEDHOPFIELDNEURALNETWORKThefiniteelementanalysisintheoryofelasticityiscorrespondedtothequadraticprogrammingwithequalityconstraint,whichcanbefurthertransformedintotheunconstrainedoptimizationandtheHopfield42ComputingMethodandHardwareCircuitImplementationofNeuralNetworkonFiniteElementAnalysisCopyright©2011MECSI.J.IntelligentSystemsandApplications,2011,5,41-47neuralnetworkisagoodmethodinthefieldofoptimizationcalculation,sothatproblemcanbesolvedbythismethod.Besidethis,thepreviousworkonneuralnetworkhasindicatedthatthepotentialenergyfunctionalequalstotheobjectivefunctionofthefiniteelementmethodandthemaximumorminimumpoint,whichisthestableequilibriumpointofthenetworksystem,isthesolution.„A.QuadraticOptimalMethodforElasticityTheoryProblemsItiswellknownthatsystemoptimizationisthenatureofcomputation.Inthissection,adetailexplanationisproposedforthispointinthecontextofelasticity[4].1)EquilibriumEquation,0ijjifσ+=()iVV∈=1,2,3,(1)Where,ijjσisstressandifisvolumeforce.2)GeometricalEquation,,1()2ijijjiuuε=+(,)ijVV∈=1,2,3,(2)Whereijεisstrainand,ijuisdisplacement.3)PhysicsEquationijijklklDσε=(,,,1,2,3,)ijklVV=∈(3)WhereijklDiselasticconstant4)BoundaryConditioniiTT=()iSSσ∈=1,2,3,(4)iiuu=()uiSS∈=1,2,3,(5)WhereiTisareaforce,SσisforceboundaryanduSisdisplacement