一种可求逆的模糊神经网络模型及其在热轧产品中应用

20031212:100026788(2003)12201282051,1,1,2(1.,,710049;2.,710049):L,,,L,L:;;;:TP18:AAReversibleFuzzyNeuralNetworkandItsApplicationtoHotRollingMillProductionXINGJin2sheng1,LIJin2ling1,WANGYing2luo1,WANBai2wu2(1.SchoolofManagement,Xi’anJiaotongUnversity,Xi’an710049,China;2.TheAcademyofEngineeringandSciences,Xi’anJiaotongUnversity,Xi’an710049,China)Abstract:AkindofFNNandlearningalgorithmispresentedinthispaper.UsingtheFNN,bynon2linefunction’soutputvalue,theregionofinputvectormaybegetexpediency,suchthatforanyvectorintheregion,theerrorbetweenthenon2linefunctionandtheFNNoutputvaluemaybesmallarbitrary.ThenewFNNisusedinthecontrolofhotrollingmillproductionandasatisfyingresultisobtained.Keywords:FNN;region;reversible;hotrollingmillproduction:2002209217:[2001]5:(1964-),,,L1,:(,el1),,L,KDD,,L,,L,L,,,,L2[1,2]©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.y=F(X)=6mi=1wiAi(X)6mi=1Ai(X)=WA(X)W=(w1,w2,,wm)m,A(X)=(K1(x1)áK2(x2)ááKn(xn))T,Kk(x)=(L1k(x),L2k(x),,Lmkk(x)),áKronecker[3],m=7ni=1mi,X=(x1,x2,,xn)ZL1k(x),L2k(x),,Lmkk(x))Xkxkmk,,,Z[0,1],y=f(X),,yi=f(X(i)),(X(i),yi),X(i)yiZ,L1k(x)=1x0,1mk0x[0,1]-0,1mk(1)Lik(x)=1xi-1mk,imk0x[0,1]-i-1mk,imk,n[0,1]nm7nk=1ik-1mk,ikmk,ik{1,2,,mk}(3)ik=1(3)ZX[0,1]n,i1,i2,,inX7nk=1ik-1mk,ikmkZA(X)1,m-10,1WZ,,WZWZ,[4-7],,:ZW,,(1),(2)Z,m,m,,,WZWZZ,,Z(X(i),yi),X(i)7nk=1ik-1mk,ikmk,M:X(i1,i2,,in,yi)(4)(i1,i2,,in,yi),(i1,i2,,in)X(i),yiWZ(i1,i2,,in,yi),v,,VZ(i1,i2,,in,yi),,,,,;Z92112©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.Z,7nk=1ik-1mk,ikmk,X7nk=1ik-1mk,ikmkûf(X)-F(X)ûFsupûf(Z1)-f(Z2)û,Z1,Z27nk=1ik-1mk,ikmkf(X),mk(k=1,2,,n),F(X)f(X)Z3(X(i),yi)(i=1,2,,N1)N1,X(i)(i=N1+1,N1+2,,N1+N2)N2ZN1N2Zy=F(X)=6mi=iwiAi(X)6mi=1Ai(X)=WA(X)(5):(X(i),yi)(i=1,2,,N1),2(5),VZVn+1,N1ZV,(5)Zm1,m2,,mn,N1,,,Z,,Z:1)m1,m2,,mnZ2)(X(1),y1),,v1,k=1,V=v1.3)k=k+1ZX(k)VZ,4);vk,V=Vvk;4)kN13),ZN1(X(i),yi)(i=1,2,,N1)ZXN1+1,:1)XN1+1Z2),XN1+1(),XN1+1yN1+1Z,Z,Z4l(n+1)V,el1v,,el1vZ:031200312©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.Vv,ûyk-vû=ûvk’,n+1-vû=miniûvi,n+1-vûyk=vk’,n+1Z(k1,k2,,kn)Z(4)7nk=1ik-1mk,ikmk,nZ5,?,?Zy=f(X)n,Vvyk,E0,m1,m2,,mn,X1[0,1]n,x17nk=1ik-1mk,ikmk,ûf(X1)-ykûEZy=f(X),[0,1]nZ,E0,D0,X1[0,1]n,ûX(k)-X1ûD,ûf(X(k))-f(X1)ûEZf(X(k))=yk.m1,m2,,mn,6ni=11mi2D2,X17nk=1ik-1mk,ikmk2ûX(k)-X1ûD,ûf(X(k))-f(X1)ûEZ,v,m1,m2,,mn,,el1Z6,el132Z4928,3,(el1)(0.05)87.5%Zel110,41032,100(),,el1(0.05),1.1%%186.54687.16283.77777.12378.94882.34484.76979.34578.431085.75,1,el1,(32),77.12%Z7,,Zel1,Z13112©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.:[1]KoskoB,IsadaS.Fuzzylogic[J].ScientificAmerican,1993,267(1):76-81.[2]KoskoB.Optimalfuzzyrulescoverextrema[J].InternationalJournalofIntelligentSystems,1995,10(2);249-255.[3].[M].:,1997.[4]KohonenT.Self2OrganizationandAssociativeMemory[M].BerlinHeidelberg:Springer2Verlag,1984.[5]RobbJ.Muirnead.Aspactsofmultivariatestatisticaltheory[M].NewYork,JohnWileyandSonsInc,1982.[6].(2)[M].:,1997.[7].[M].:,1995.(127),L,BPL2),L,L3),;;;L4),L,L:[1],,.[M].:,1988.[2],.[J].,1998,21(1):90-93.[3],.[J].(),2002,17(2)19-22.[4].[M].:,2001.[5],,,.MATLAB[M].:,2001.[6].[D].:,1998.[7],.[J].,1999,14(4):338-344.[8],,.[J].,1997,19(2):108-110.[9],.[J].,1997,17(2):67-71.231200312©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.