附录A修改版本.doc

附录A MATLAB程序A.1 第三章程序1.D-FNN程序Function w1, w2, width, rule, e, RMSN = DFNN (p, t, parameters)%This is D-FNN training program.%Input:% p is the input data, which is r by q matrix% r is the No. of input% t is the output data, which is s2 by q matrix% q is the No. of sample data.% parameters is a vector which defines the predefined parameters% parameters(1)= kdmax (max of accommodation criterion)% parameters(2)= kdmin (min of accommodation criterion)% parameters(3)= gama (decay constant)% parameters(4)= emax (max of output error)% parameters(5)= emin (min of output error)% parameters(6)= beta (convergence constant)% parameters(7)=width0 (the width of the first rule)% parameters(8)= k (overlap factor of RBF units)% parameters(9)= kw (width updating factor)% parameters(10)=kerr (significance of a rule)%Output:% w1 is the centers of the RBF units , which is a u by r matrix% w2 is the weights, which is s2 by u(1+r) matrix% width is the widths of RBF units, which is a 1 by u matrix%Revised 11-3-2006%Copyright Wu shiqian.If narginkd If e(i)ke CRBF=CRBF IN; % Add a new rule Wb=k*d; Width=width wb; W1=CRBF; u,v=size(w1); % caculating outputs of RBF after growing for all data A=RBF(dist(w1,ALLIN),/width); A0=sum(A); A1=A./(ones(u,l)*A0); A2=transf(A1,ALLIN); If u*(r+1)=N % caculating error reduction rate tT=ALLOUT PAT=A2; W,AW=orthogonolize(PAT); SSW=sum(W.*W);SStT=sum(tT.*tT); Err=(W*tT).2)./(SStT*SSW0;errT=err; Errl=zeros(u,s2*(r+1); Errl(:)=errT; err21=err1; Err22=sum(err21.*err21)/(s2*(r+1); err23=sqrt(err21.*err21)/(s2*(r+1); err23=sqrt(err22); No=find(err23ke width(ind)=kw*width(ind); aa=RBF(dist(wl,ALLIN),l./width)； aa0=sum(aa);aal=aa./(ones(s,l)*aa0); aa2=transf(aal,ALLIN); w2=ALLOUT/aa2; outaa2=w2*aa2; sse2=sumspr(ALLOUT_outaa2)/(i*s2); RMSE(i)=sqrt(sse2); rule(i)=selse aal=RBF(dist(wl,ALLIN),l./width); aa01=sum(aal);aall=aal./(ones(s,l)*aa0l); aa21=tranf(aall,ALLIN); w2=ALLOUT/aa21: outaa21=w2*aa21; sse3=sumsqr(ALLOUT_outaa21)/(s2*i); RMSE(i)=sqrt(sse3); rule(i)=s end endend 2 几个用于D_FNN的子程序orthogonalize程序functionw,a= orthogonalize(p)% This program is used transform pinto orthogonalized w% Revised 11-3-2006% Copyright Wu Shiqian.u,v=size(p);w(:,l)=p(:,k);a=eye(v);for k=2:v b=zeros(u,l); for i=l:k-1a(i,k)=w(:,i)*p(:,k)/(w(:,i)*w(;,i);b=b+a(i,k)*w(:,i); end w(:,k)=p(:,k)-bend2) RBF程序Function a = RBF(d,w)% This program is used to calculate the RBF units% Input:% d is the distance matrix% w is the width matrix% Output:% a is the output of RBF units % Revised 11-3-2006% Copyright Wu Shiqianif nargin=0 ekfmax=ckf(i);endd,ind=min(dist(CRBF,IN);kd=max(kdmax*gama(i-1),kdmin); if dkdke=max(emax*beta(i-1),emin);if ekf(i)ke%generate new neuron CRBF=CRBF;IN; width=width k*d; u,v=size(CRBF); if u*(r+1)=N RBFOUT2=RBF(dist(CRBF,ALLIN),1./width); pa2=RBFOUT2./(ones(u,1)*sum(RBFOUT2); pTSK2=transf(pa2,ALLIN); W,A=orthogonalize(pTSK2); SSW=sum(W.*W); SStT=sum(ALLOUT.*ALLOUT); err=(W*ALLOUT).2)./(SStT*SSW); err1=zeros(u,s2*(r+1);err1(:)=err;err2=sqrt(sum(err1.*err1)/(s2*(r+1);No=find(err2=0 eemax=e(i);endke=max(emax*beta.(i-1),emin);if dkdif e(i)ke CRBF=CRBF IN;wb=k*d;width=width wb;w1=CRBF;u,v=size(w1);A=RBF(dist(w1,ALLIN),1./width);A0=sum(A);A1=A./(ones(u,1)*A0);A2=transf(A1,ALLIN);if u*(r+1)=N tT=ALLOUT;PAT=A2;W,AW=orthogonalize(PAT);SSW=sum(W.*W);SStT=sum(tT.*tT);err=(W*Tt).2)./(SStT*SSW);errT=err; err1=zeros(u,s2*(r+1);err1(:)=errT;err21=err1;err22=sum(err21.*err21)/(s2*(r+1);err23=sqrt(err22);No=find(err23ke width(ind)=kw*width(ind); a=RBF(dist(w1,ALLIN),1./width); aa0=sum(aa);aal=aa./(ones(s,l)*aa0); aa2=transf(aal,ALLIN); w2=ALLOUT/aa2; outaa2=w2*aa2;sse2=sumsqr(ALLOUT-outaa2)/(i*s2);rmse2=sqrt(sse2);tr(i)=rmsel; neutr(i)=s; elseaa1=RBF(dist(w1,ALLIN),1./width);aa01=sun(aa1);aall=aal./(one(s,1)*aa01);aa21=transf(aall,ALLIN); W2=ALLOUT/aa21; outaa21=w2*aa21; Sse3=sumsqr(ALLOUT-outaa21)/(i*s2);198 rmse3=sqrt(sse3);tr(i)=rmse3; neutr(i)=s;endend end LSEtime=etime(clock,t0); % %LLS-Kalman Filter Algorithm % T0=clock;ALLIN=;ALLOUT=; %For the fist rule CRBF=p(:,1);alter=1;width=;width(1)=2; aa=200; bb=0.001; for i=1:q data=i ds(i)=i; IN=p(:,i); OUT=t(:,); ALLIN=ALLIN IN;ALLOUT=ALLOUT OUT; r,N=size(ALLIN); u,r=size(CRBF); RBFOUT=RBF(dist(CRBF,ALLIN),1./width); pa=RBFOU./(ones(u,1)*sum(RBFOUT); Ptsk=transf(pa,ALLIN); if alter=1 WEGHT=bb*ones(u*(r+1),1); Si=aa*eye(u*(r+1); for iter=1:i Si=Si-(Si*pTSK(:iter)*pTSK(:iter)*Si/(1+pTSK(:,iter)*Si*pTSK(:,iter);WEIGHT=WEIGHT+Si*pTSK(:,iter)*(ALLOUT(:,iter)-pTSK(:,iter)*WEIGHT; end alter=0;else Si=Si-(Si*pTSK(:i)*pTSK(:i)*Si/(1+pTSK(:,i)*Si*pTSK(:,i);WEIGHT=WEIGHT+Si*pTSK(:,i)*(ALLOUT(:,i)-pTSK(:,i)*WEIGHT;endALLESTOUT=WEIGHT*Ptsk;rmse(i)=sqrt(sumsqr(ALLOUT-ALLESTOUT)(i*s2);neuron(i)=u;%for computation of per set errortRBFOUT1=RBF(dist(CRBF,IN),1./width);Pa1=RBFOUT1/sum(RBFOUT1);pTSK=transf(pa1,IN); %convert to TSK modelACTOUT=WEIGHT*pTSK;ae(i)=sqrt(sumsqt(OUT-ACTOUT)/s2);z1=ae(i)-aemax;if z1=0 aemax=ae(i); endd,ind=min(dist(CRBF,IN);Kd=max(kdmax*gama(i-1),kdmin);if dkdke=max(emax*beta(i-1),emin);if ae(i)ke %generate new neuron CRBF=CRBF;IN;width=width*d;u,v=size(CRBT);if u*(r+1)=N RBFOUT2=RBF(dist(CRBF,ALLIN),1./width); pa2=RBFOUT2./(ones(u,1)*sum(RBFOUT2); pTSK2=transf(pa2,ALLIN); W,A=orthogonalize(pTSK2)； SSW=sum(w. * w); SStT=sum(ALLOUT.*ALLOUT) err=(W * ALLOUT).2)./(SStT * SSW) err1=zeros(u,s2 8 (r+1);errl( : )=err; err2=sqrt(sum(err1. * err1)/9s2 * (r+1); No=find(err2ke width(ind)=kw*width(ind);alter=1;endendlsekmtime=etime(clock,t0);meanerr=mean(e);meanae=mean(ae);meanekf=mean(ekf);figure,plot(ds,neutr,r,ds,neuron,ro,ds,nekf,r+);title(Fuzzy rule generation);xlabel(Sample patterns);figure,plot(ds,e,r,ds,ae,ro,ds,ekf,r+);title(Actual Output Error);xlabel(Sample patterns);figure,plot(ds,tr,r,ds,rmse,ro,ds,rmsekf,r+);title(Root mean squared error);xlabel(Sample patterns); 3 第5章程序 1.Hermite 函数逼近 % Static function approximation by D-FNN % The underlying function is Hermite function shown in chapter 5 % Revised 11-3-2006 %Copyright Wu Shiqian clc clear, close all rand(seed,5); p=rand(1,200)*8-4; t=1.1*(1-p+2*p.2).*exp(-p.2./2); r,q=size(p);s2,q=size(t); % Setting initial values kdmax=2; kdmin=0.2; gama=0.977;beta=0.9;width0=2; emax=1.1;emin=0.02;k=1.1;kerr=0.0015; parameters(1)=kdmax;parameters(2)=kdmin;parameters(3)=gama; parameters(4)=emax;parameters(5)=emin;parameters(6)=beta; parameters(7)=width0;parameters(8)=k;parameters(9)=kw; parameters(10)=kerr; wl,w2,width,rule,e,RMSE=DFNN(p,t,parameters); TA=RBF(dist(wl,p),1./width); TA0=sum(TA);u,v=size(wl); TA1=TA./(ones(u,1)*TA0); TA2=transf(TA1,p); outTA2=w2*TA2; figure,plot(e,r); title(Actual output error); xlabel(Input sample patterns); figure,plot(RMSE,r); title(Root mean squared error (RMSE); xlabel(Input sample patterns); figure,plot(p,t,r+,p,outTA2,bo); title(Desired and actual outputs); xlabel(Input data); 2.非线性动态系统的辨识 % Nonlinear Dynamic System Identification in chapter 5 by D-FNN % Revised 11-3-2006 % Copyright Wu Shiqian. clc, clear,close all y=zeros(1,200);y(2)=1;a=sin(2*pi/25); p(:,1)=1;0;a;t(1)=sin(2*pi*2/25); for k=3:200 y(k+1)=(y(k)*y(k-1)*(y(k)+2.5)./(1+y(k).2+y(k-1).2)+sin(2*pi*k/25); x1(k-1)=y(k); x2(k-1)=y(k-1) x3(k-1)=sin(2*pi*k./25); p=x1;x2;x3; t(k-1)=y(k+1); end % Setting initial values kdmax=4;kdmin=0.2gama=0.97;beta=0.9;width0=2;emax=1; emin=0.02;k=1.1;kw=1.1;kerr=0.002; parameters(1)=kdmax;parameters(2)=kdmin;parameters(3)=gama; parameters(4)=emax;parameters(5)=emin;parameters(6)=beta; parameters(7)=width0;parameters(8)=k;parameters(9)=kw; parameters(10)=kerr; wl,w2,width,rule,e,RMSE=DFNN(p,t,parameters); TA=RBF(dist(wl,p),1./width); TA0=sum(TA);u,v=size(wl); TA1=TA./(ones(u,1)*TA0); TA2=transf(TA1,p); outTA2=w2*TA2; figure,plot(rule,r); title(Fuzzy rule eneration); xlabel(Input sample patterns); figure,plot(e,r); title(Actual output error); xlabel(Input sample patterns); figure,plot(RMSE,r); title(Root mean squared error (RMSE); xlabel(Input sample patterns); figure; k=1:199; plot(k,t,r-loutTA2,ro); title(Comparison between desired and actual outputs); xlabel(Time t); 3.Mackey-Glass 时间序列预测 % Mackey-Glass time-series prediction in chapter 5 by D-FNN % Revised 11-3-2006 % Copyright Wu Shiqian. clc, clear,clo