最小RBF网设计的进化优选算法及其在动力配煤过程状态预测建模中的应用

21120011ProceedingsoftheCSEEVol.21No.1Jan.20012001Chin.Soc.forElec.Eng.:02588013(2001)01006305RBF魏海坤,徐嗣鑫,宋文忠,吴福保(东南大学自动化研究所,江苏南京210096)EVOLUTIONARYSELECTINGALGORITHMFORDESIGNINGMINIMALRBFNETSANDITSAPPLICATIONINCOALBLENDINGWEIHaikun,XUSixin,SONGWenzhong,WUFubao(InstituteofAutomation,SoutheastUniversity,Nanjing210096,China)ABSTRACT:Thispaperproposesanevolutionaryselectingalgorithm(ESA)todesignRBFnets.Givenanaccuracylimit,ESAcandesignaRBFnetwitheasthiddenunits,sothenetworkwillgeneralizewell.Proposedalgorithmcanbeusedtoestablishmodelsofstateestimationprocessforsteamcoalblending.Oneofsuchmodelingproblems,softeningtemperaturepredictionofcoalash,isillustratedusingESAmethod.MinimalRBFnetdesignediscomparedwithRBFnetsobtainedwithOLSandclusteringmethod,resultshowsthatRBFnetdesignedwithESAmethodhasbettergeneralizationability.KEYWORDS:RBFnets;generalizationability;steamcoalblending;modeling:RBF,RBF,RBF,ESA2RBF,OLS,,RBF:RBF;;;:TQ520.62:A1,2,,,,,,,,BP,[1,2],BP:,,,BP,(RBF)[3]RBF,Moody,,,[4],RBF,,RBFRBF[5][6](OLS)OLS,,RBF[7];,,()CrossValidation,,RBF,RBF(ESA)ESA,RBF,ESARBF,ESA2OLSRBF(1),X=(x1,x2,,xn)TRn,W=(w1,w2,,wm)TRm,w0,f(X),(*)(RBF),,(t)=e-t2/2,RBF!*!,Cii,RBF,RBF,,OLS,[7]2.1OLSN,S=(X1,X2,,XN),()t=(y1,y2,,yN)RBF,,,RBF,N,Xi,i=1,2,,N,jhij=(!Xi-Cj!)(1)Cj=XjRBFRBFH=[hij],HRN∀NRBFf(Xi)=Nj=1hijwj=Nj=1wj(!Xi-Cj!)(2)yi=f(Xi),y=tT=(y1,y2,,yN)T,W=(w1,w2,,wN)Ty=HW(3)HRN∀N,W=H-1Y(4)RBF(N),HNM#NH^RN∀M,(3)y^=H^W0(5)=!y-y^!,yH^,W0=!H^W0-y!=minWCM!H^W-y!(6)W0W0=H^+y^(7)H^+H^H^+=(H^TH^)-1H^T(8),H^,RBFH^∃%,:1[7]H&RN∀NH,H&HH&H,H&=HP(9)PINHN!2[7]SRN∀M,M(9)PMH,H,(6)=!HSW0-y!=minWCM!HSW-y!(10),Sy:=g(S,y)RBF,0,6421:30,C={S|minWCM!HSW-y!0},S0C,:SC,col(S0)#col(S),col(S)S,S0H0H^MRBF,,RBF,:,RBF,:4O=[o1,o2,,oN]H,oi{1,2,,N},i=1,2,,N,i∋j,oi∋ojoiHHH,HN!OdOd=[o1,o2,,od],d#N,S0,O,d,dOOH,OOd2.2OLSOLSHHGramSchmidt:,HNP11,P21,,PN1,NEHN,yP11,P21,,PN1,Pk1(y),Pk1,Pk1E1;,N-1GramSchmidt,E1,P12,P22,,PN-12,yPj2,Pj1;M,OLS,[7]OLS,H,y,OLS,,O=[o1,o2,,oN]okPjk,3(ESA)(ESA),,3.1[8],,,(!+∀):!,;∀-1(!*∀);!,,,,3.2:ESA,RBFHN,N!,:d,,d(1,Fitness(O)=1d+K(11)O=[o1,o2,,oN];K,0#K1,d:Oi=[o1,o2,,oi]Si,i1N,i=k0,d=k,,,RBF:O=[o1,o2,,oN],651:RBFi,j#N,oioj,,,1,ESA(!+∀),RBF3.3ESA0RBF,00,ESA;0,ESARBFRBF,,0,,;0,RBF,RBF,RBFESA,,RBFRBF,,,ESA0:,RBF,#,ESAN,N1,ETrain,#=ETrain/N1,0=N#=E*TrainN/N1,25%,[9]RBF,Cohonen[10]SOFM4RBF,ESARBF,ESAOLS4.1,SiO2Al2O3Fe2O3CaOMgOTiO2K2ONa2O,RBF81,8,205,ESA,,155,502RBF23(14),,=9.25,()ETrain=3.4639∀105#=ETrain/155=2.2348∀103,0=205#=4.5812∀105,=9.250,ESA205,RBF11,1,w0=1388.6ESA10,9,0.7,100,304.2ESAOLSESA,OLSESAESA,50STest2,105STrain,50STest1ESA66211RBFTab.1RBFnetModelparameters1(0.05,1.76,15.12,7.40,17.37,22.64,11.13,0.60)-43.92(0.54,0.10,18.79,10.10,10.75,29.90,2.20,0.70)-87.43(1.80,0.26,37.13,21.80,11.07,10.68,6.01,2.00)-299.64(2.57,0.55,55.95,18.02,15.06,2.66,2.13,1.21)-1028.65(1.22,3.00,47.74,12.40,7.40,17.58,2.55,0.78)-186.96(1.07,0.42,53.64,32.60,6.71,2.08,0.86,1.05)115.67(2.40,0.33,39.93,25.14,6.42,1.19,1.13,0.00)229.88(2.50,0.30,62.00,23.00,6.70,2.13,1.20,1.00)-511.89(1.10,0.36,58.32,19.10,12.60,2.63,1.04,1.20)1134.610(1.40,0.84,63.48,19.48,4.62,5.48,0.88,0.85)-618.811(1.98,0.81,65.55,23.39,3.46,2.13,0.50,0.90)779.9RBF,STrain,STest1,25,=8.25,RBFETrain=1.0473∀105OLSESARBFSTrain,OLSESA=8.25,0=ETrain=1.0473∀10522,STest1,RBF,;ESARBF,ESA,RBF,,RBF,;OLS,,OLSESA,155(STrain+STest1)STest1STrain,=8.25,OLSESA0=(1.4073∀105)/105∀155=2.0774∀105333,,;OLS;ESA,,,,RBFESA32usingSTrainTab.2LearningresultwhenusingSTrainOLSESA8.258.258.25252820ETrain1.4073∀1051.0836∀1051.1095∀105ETest11.5689∀1053.9832∀1051.7285∀105ETest22.2445∀1052.9311∀1052.4041∀1053STrain+STest1Tab.3LearningresultwhenusingSTrain+STest1OLSESA8.258.258.25253125ETrain1.4073∀1052.0231∀1052.0483∀105ETest22.2445∀1056.9241∀1051.8922∀1055RBFESARBF,,,RBF,ESARBF,OLS,,ESARBFESA,,:[1],,,.[J].,1998,19(5):637641.[2],,,.[J].,1997,22(4):343348.[3],.RBF[J].,1997,26(4),272283.[4]MoodyJ.Theeffectivenumberofparameters:ananalysisofgeneralizationandregularizationinnonlinearlearningsystem[C].NIPS4,SanMateo,CA,1992,847854.[5]MoodyJ.AndDarkenC.Fastlearninginnetworksoflocallytunedprocessingunits[J].NeuralComputation.1989,1(2):281294.(72continuedonpage72)671:RBFVj,m/s;nj;Li,m;Lj,m;∃S,m;∃H,m13,,,,,,,,,,,,,,,13Fig.13Thedistributionofthemomentofthemomentumfluxalongwithfurnaceheight,2:,;,,5(1),,(2),,(3),:[1].[J].,1992,23(3):110.[2].[M].:,1987.[3].[M].:,1988.[4].[D].:,1999.:19991019;:19991126:(1972),,,(贾瑞君)(67continuedfrompage67)[6]ChenS,CowanCFN,GrantPM.Orthogonalleastsquareslearningalgorithmsforradialbasisfunctionnetworks[J].IEEETransNeuralNetworks,1991,2(2),302309.[7]SherstinskyA,PicardRW.Ontheefficiencyoftheorthogonalleastsquarestrainingmethodforradialbasisfunctionnetworks[J].IEEETransNeuralNetworks,1996,7(1):95200.[8]SchwefelHP.Ontheevolutionofevolutionarycomputation.in:zuradaJM,MarkIIRJ,RobinsonCJeds.ComputationalIntelligence:ImitatingLife[C].NewYork:IEEEPress,1994:116124.[9]KearnsM.Aboundontheerrorofcrossvalidationusingtheapproximationandestimationrates,withconsequencesforthetrainingtestsplit[J].NeuralComputation,1997,9(5):11431161