基于时空RBF-NN进行非线性系统识别（Matlab代码实现）

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目录

​​💥1 概述​​

​​📚2 运行结果​​

​​🎉3 参考文献​​

​​🌈4 Matlab代码实现​​

💥1 概述

在本文中：实现了 RBF、分数 RBF 和时空 RBF 神经网络，用于非线性系统识别，可以找到用于非线性系统识别任务的径向基函数神经网络（RBF-NN）的三种变体。特别是，实现了具有常规和分数梯度下降的RBF，并将性能与时空RBF-NN进行了比较。

详细文章见参考文献。

📚2 运行结果

部分代码：

%%
 % tic
 for k=1:runs
     Ic(k)=0;
     If(k)=0;
     Ist(k)=0;
     U = zeros(3,1);
     U(2:end)=[-1 -1];
     for i1=1:len
         U(1:end-1)=U(2:end);
         U(end)=x(i1);
         for i2=1:n1
             ED_cf(:,i2)=exp((-(norm(U-c(i2))^2))/beeta^2);
         end
         
         for i2=1:n1
             ED_st(:,i2)=exp((-(abs(U-c(i2))))/beeta^2);
         end
         
         %% RBF
         y(i1)=sum(diag(W_c*ED_cf'))+bc;
         d(i1)= h(1)*U(end) +h(2)*U(end-1)+h(3)*U(end-2)+h(4)*(cos(h(5)*U(end)) +exp(-abs(U(end))))+0.1*randn();
         e_c=d(i1)-y(i1);
         Ic(k)=Ic(k)+e_c*e_c'./len;   %%% Objective Function        W_c=W_c+meu_c*e_c*ED_cf;
         
         bc=bc+meu_c*e_c;
         
         %% Fractional RBF
         yf(i1)=sum(diag(W_f*ED_cf'))+bf;
 %         d(i1)= h(1)*U(end) +h(2)*U(end-1)+h(3)*U(end-2)+h(4)*(cos(h(5)*U(end)) +exp(-abs(U(end))))+0.1*randn();
         e_f=d(i1)-yf(i1);
         If(k)=If(k)+e_f*e_f'./len;   %%% Objective Function        W_f=W_f+meu_f*e_f*ED_cf.*((1-alpha_f)+alpha_f*abs(W_f.^fp));
         bf=bf+meu_f*e_f.*((1-alpha_f)+alpha_f*abs(bf.^fp));
     
         
     end
 %     q_track(k) = q;
 end
 % time=toc
 save comparison_train.mat% plot(q_track)
 figure
 semilogy(Ic,'r')
 hold on
 semilogy(If,'k')
 semilogy(Ist,'b') Ist=0;
 x=[-1 -1 ones(1,round(len/4)) -ones(1,round(len/4)) ones(1,round(len/4)) -ones(1,round(len/4))];
 x=awgn(x,20);    U(2:end)=[-1 -1];
n1=length(c);
     Ic=0;
     for i1=1:len-1
         U(1:end-1)=U(2:end);
         U(end)=x(i1);
         for i2=1:n1
             ED_st(:,i2)=exp((-(abs(U-c(i2))))/beeta^2);
         end
         y(i1)=sum(diag(W_c*ED_cf'))+bc;
         d(i1)= h(1)*U(end) +h(2)*U(end-1)+h(3)*U(end-2)+h(4)*(cos(h(5)*U(end)) +exp(-abs(U(end))));
         e_c=d(i1)-y(i1);
         SE(i1)=e_c*e_c';   %%% Objective Function
         Ic(i1)=mean(SE);
         
         yf(i1)=sum(diag(W_f*ED_cf'))+bf;
 %         d(i1)= h(1)*U(end) +h(2)*U(end-1)+h(3)*U(end-2)+h(4)*(cos(h(5)*U(end)) +exp(-abs(U(end))));
         e_f=d(i1)-yf(i1);
         SEf(i1)=e_f*e_f';   %%% Objective Function
         If(i1)=mean(SEf);
         
         yq(i1)=sum(diag(W_st*ED_st'))+bst;
 %         d(i1)= h(1)*U(end) +h(2)*U(end-1)+h(3)*U(end-2)+h(4)*(cos(h(5)*U(end)) +exp(-abs(U(end))));
         e_st=d(i1)-yq(i1);
         SEq(i1)=e_st*e_st';   %%% Objective Function
         Ist(i1)=mean(SEq);
  plot(d,'cy')
 hold on
 plot(y,'r')
 plot(yf,'r')
 plot(yq,'b')
 legend('RBF','FRBF','desired','qRBF')
 %saveas(gcf,strcat('RBF.png'),'png')

🎉3 参考文献

[1]Khan, Shujaat, et al. “Spatio-Temporal RBF Neural Networks.” 2018 3rd {IEEE} International Conference on Emerging Trends in Engineering, Sciences and Technology ({ICEEST}), {IEEE}, 2018

​​🌈​​4 Matlab代码实现