Matlab神经网络工具箱BP算法比较

:2005-01-21　　23　5　　　　20065　　:1006-9348(2006)05-0142-03MatlabBP蒲春,孙政顺,赵世敏(,100084):BP,,。MatlabBP,。,。,,BP,BP,BP。:;;:TP391.9　　:AComparisonofBPAlgorithmsinMatlabNNToolboxPUChun,SUNZheng-shun,ZHAOShi-min(Dep.tofAutomation,TsinghuaUniversity,Beijing100084,China)ABSTRACT:BPfeedforwardnetwork,themostwidelyusedneuralnetwork,hasmanyalgorithmsatpresen.tAdvan-tagesanddisadvantagesofvariousBPalgorithmsprovidedinMatlabneuralnetworktoolboxarestudiedsothatpeoplecanchoosemoresuitableandfasteralgorithmswhendifferentconditionsanddifferentproblemsarefaced.Afterintro-ducingthebasicprincipleofthesealgorithms,studyofsimulationiscarriedoutbyusingasingleinvertedpendulumasexample.Choosingsimpleandcomplexnetsrespectively,andchangingthelearningsteps,theiterationstepsandsimulationtimeofvariousBPalgorithmsindifferentconditionsarecompared.AdvantagesofnewBPalgorithmsarevalidated.AdviceonhowtoselectBPfunctionisgiven.KEYWORDS:Neuralnetworktoolbox;BPalgorithm;Invertedpendulum1　,,。,。、、,。。,,,。,,。。,。BP。BPWidrow-Hoff,,。BP:。BP。BP,。Matlab,BP,BP。,。2　MatlabBP1)traingd:BP。,。dX=lr*dperf/dX,d(),lr,X,perf,—142—mse。traingd,,,,,。2)traingdm:。,,,dX=mc*dXprev+lr*(1-mc)*dperf/dX,prev,mc。3)BP。,。,,。4)traingda,traingdx:。,BP。。,,。,。mse(k+1)mse(k),lr=lrinc*lr;mse(k+1)1.04*mse(k),lr=lrdec*lr;mse(k+1)mse(k)1.04*mse(k),。traingdatraingdx,traingdxtraing-da。5)trainrp:BP。,,。dX=deltaX.*sign(gX),gX,deltaX,gX。。6)traincgf,traincgp,traincgb,trainscg:。Fletcher-Reeves、Polak-Ribiers、Powell-Beale、。。,,,。Trainscg,,。,。7)trainbfg:。X=X+a*dX,dX,a。,dX=-H-1*gX,HHessian。Trainbfg,Hessian,,。8)trainoss:。。X=X+a*dX,dX,a。,dX=-gX+Ac*Xstep+Bc*dgX,Xstep,dgX,AcBc。Hessian,trainosstrainbfg,。9)trainlm:Levenberg-Marquardt,dX=-(jXT*jX+I*mu)-1jXT*E,jXJacobian,E,mu。,,,。,mem-reducJacobian。,。10)trainbr:。Levenberg-Marquardt,。3　BP。、、。:1)()();2)();3);4)。:r:　θ:　M:　m:J:　L:F:　F1:G0:,,,:·x1·x2·x3·x4=0I2*2M*-1N*M*-1F*x1x2x3x4+0M*-1G*u:—143—M*=M+mmlmLJ+mL2,F*=-F00-F1N*=000mgL,G*=Go0X=(x1x2x3x4)T=(rθ·rθ·)TBP,1。,12,1,0.00010.00001;4,30,50,20,1,0.0001。,。,1(X,,traingdtraingdm(goal=0.0001)0.05,)1　BP(goal=0.0001)(goal=0.00001)(goal=0.0001)(s)(s)(s)traingd429971.9558×103XXXXtraingdm23061949.6570XXXXtraingda13905559.6250XX228012.9487×103traingdx6203223.9530684372.5544×1032646273.1410trainrp81729.31206802150.947020642.4530traincgf21914.469044221.992016538.3600traincgp23615.359080434.569027461.0790traincgb16012.094043019.678014439.0940trainscg46829.328068025.576022655.1250trainbfg586.984025313.2790371.9175×103trainoss46531.29706219240.386019949.7030trainlm112.3120145.14808286.4370trainbr1213.65701295.8310335.0967×1034　1,BP,,。0.01,,。,Levenberg-Marquardt,。。,。,bp。,,trainlm。、bp、。。,Hessian,。。:[1]　,.MATLABBP[J].,2002,19(2):130-135.[2]　,.BPMatlab[J].,2003,19(1):6-9.[3]　.[D].:,2003.[4]　,,.[J].(),2003,29(2):122-126.[5]　,.[M].,1998.1-17.[]　(1981-),(),,,:;(1945-),(),,,:;(1967-),(),,,:。—144—