Kohonen自组织网络在混沌时间序列预测中的应用(Ⅱ)

20001010:100026788(2000)1020079205Kohonen(Ê)1,2(1.,100871;2.,100871):Kohonen,.:;;Kohonen:O212.1aTheApplicationofKohonenSelf2orgnizationNetworktoPredictionofChaoticTimeSeries(Ê)WANGMing2jin1,CHENGQian2sheng2(1.GuanghuaSchoolofManagement,PekingUniversity,Beijing1000871;2.SchoolofMathematicalScience,PekingUniversity,Beijing1000871)Abstract:Inthispaper,wecontinueourdiscussionoftheapplicationofthenonlinearpredictionmodelwhichwasgiveninourpreviouswork.Thepredictionofnoisychaotictimeseriesusingthismodelanditsrelationshipwiththeembeddingdimensionsarestudiedthroughnomericalexperiences.Keywords:chaotictimeseries;radialbasisfunction;Kohonenself2orgnizationnetwork1{st},st=s(tSs),t=1,2,,ns.(1.1)s(t),Ss.,,,,,.,80,[2,3]L,(themethodofdelays),{st}Rmx(t),x(t)=(st,st+Sd,st+2Sd,,st+(m-1)Sd),(1.2)m,Sd=kSs(k),Sdk.Takens[3],mE2d+1(d),x(t)Rm.RmF:RmRm,x(t+1)=F(x(t)),(1.3)f:RmR,st+(m-1)Sd+1=f(st,st+Sd,,st+(m-1)Sd).(1.4)a:1998209230转载(F)fd(Fd){st},,,f,f[46],Taylor.[1],Kohonen,L[1],L:,,,,L2[1],fd:1)mk,Rm,{x(t)},t=1,2,,N,{x(t)}t=1NL,;{x(t)}t=NL+1NL+NT,,Rf2Rp2[1];2)Nc(NL)Kohonen,m,ijwij,[1]wij(t),wij,wj=(w1j,w2j,,wmj),j=1,2,,Nc;3)fd(x)=6Ncj=1Kj5(x-c}j)+Lx+L0.(2.1)(x(t),st+(m-1)Sd+1)t=1,2,,NL,K=(K1,K2,,KNc),L=(L1,L2,,Lm),L05(r):R+R(radialbasisfunction).,5(r)=exp(-r2öR2).[1],HenonLorenz,,,L3[7],.,,.,,{st},yt=st+Et,(3.1){Et,tE1},(IID).(observationalnoise);,{st}st=f(st-1-(m-1)Sd,,st-1-Sd,st-1),(3.2){yt}yt=f(yt-1-(m-1)Sd,,yt-1-Sd,yt-1)+Et.(3.3)(systemnoise),(3.3)..,,,,,,08200010中国科技论文在线(m,r)rLog2Log,.,,,R.L.Smith[8](3.1)..L,(over2fitting),,,,.,.[1],Henon,Gaussianwt,{wt}{st},(1.2).1.1HenonmSNLNcR2fR2p10à2110060.03120.063010à2120060.04510.057525à2110060.14940.278225à21100100.14070.279525à2120060.26490.234125à21200100.21280.216450à2110060.51120.675850à21100100.66480.825050à2120060.57420.538250à21200100.56590.6917,,,.,:,,,,,Casdagli[5],(),;Kohonen,.,,,,,(Henon).,,.125àGuassianHenon,,m=2,Sd=1,NL=100,Nc=6,100,,Henon.,LAlbanoetal.[8]BP.1810(Ê)中国科技论文在线[3],,.,,.,.Casdagli[5],,.,m,mm3,,m.m3..Mackey2Glass.Mackey2Glassxa=ax(t-S)1+x(t-S)c-bx,(4.1)(atime2delaydifferentialequation),([9]).a=0.2,b=0.1,c=10,S[9],S4.53;4.53S13.3;S=13.3;S16.8,,S,FarmerKaplan2Yorke[9]S=17,3.580.04,S=302.94,S=100,7.1.S=100,,.:x(t+$t)2-b$t2+b$tx(t)+$t2+b$t{f(x(t-S))+f(x(t-S+$t))}.(4.2)f(u)=aõu1+uc,$t=Sö1000=0.1.0.9,105,2000,Ss=50$t=5,{st},st=x(t0+t+50$),t=1,2,.(4.3),,15.,216,(2.1),228200010中国科技论文在线(NL,Nc)m=10,,m,.Sugharaetal.[10].,m=10.,,().,,,(7.0),[11].,.5[1]Kohonen.,,,L,.,,,,L:[1],.Kohonen[J].,1997,17(7):1217.[2]PackardNH,CrutchfieldJP,FarmerJD,ShawRS.Geometryfromatimeseries[J].Phys.Rew.Lett.1980,45:712715.[3]TankensF.Detectingstrangeattractorsinturbulence[A].DynamicalSystemsandTubulence[C].D.RandandL.2S.YoungSpringer,1981:366381.[4]FarmerJD,SidorowichJJ.Predictingchaotictimeseries[J].Phys.Rew.Lett,1987,24:845848.(92)3810(Ê)中国科技论文在线(2),,Z,,:Wj=1R6mi=1riõWijj=1,2,,n(4)R=6mi=1riWjj,6ni=1Wj=1Z6mj=1wj=1R6nj=16mi=1riõwij=1R6ni=16mj=1riõwij=1R6ni=1ri6mj=1wij=1R6mi=1ri=12(1),(4),W1=0.293,W2=0.473,W3=0.234Z5,CBRLCBRLL,,,DelphiAHP;,LL:[1]SaatyTL.TheAnalyticHierarchyProcess:Planning,PrioritySetting[M].ResourceAllocationMcGraw2Hill,NewYork,1980.[2]MeadeLM,LilesDH,SarkisJ.JustifyingStrategicAlliancesandPartnering:aPrerequisiteforVirtualEnterprising[J].Omega,IntJMgmtSci,1997,l25(1):2942.[3]LawrenceMSeifert,JoeZhu.IdentifyingExcessesandDeficitsinChineseIndustrialProductivity(1953-1990):aWeightedDataEnvelopmentAnalysisApproach[J].Omega,Int.J.Mgmt.Sci,1998,26(2):279296..(83)[5]CasdagliM.Nonlinearpredictionofchaotictimeseries[J].PhysicaD,1989,35:335356.[6]GencayR.Nonlinearpredictionofnoisytimeserieswithfeedforwardnetworks[J].Phys.LettA,1994,187:397403.[7]SmithLA.Identicationandpredictionoflowdimensionaldynamics[J].PhysicaD,1992,58:5076.[8]AlbanoAM,PassamanteA,HedigerT,FarrellME.Usingneuralnetstolookforchaos[J].PhysicaD,1992,58:19.[9]FarmerJD.Chaoticattractorofaninfinite2dimensionchaoticsystem[J].PhysicaD,1982,4:366393.[10]SugiharaG,MayRM.Nonlinearforecastingasawayofdistinguishingchaosfrommeasurementerrorintimeseries[J].Nature,1990,344:734741.[11]AbarbanelHDI,BrownR,SidorowichJJ,LSh.Tsimring.Theanalysisofobservedchaoticdatainphysicalsystems[J].RevModPhys,1993,65:13311392.29200010中国科技论文在线