identification.m

用神经网络对具有随机噪声的二阶系统模型进行辨识.

w10ij=[.01 .01 .02; .1 .11 .02; .01 0 .1; .11 .01 .02;.1 .1 .02; .11 .1 .1;.1 .1 .1;0 .1 .1;.1 0 .1];     
w11ij=[.1 .2 .11; .02 .13 .04; .09 .08 .08; .09 .1 .06; .1 .11 .02; .06 0 .1;.1 .1 .1;0 .1 0;.1 .1 .1];     
w20j=[.01;.02;.1;.2;.1;.1;.1;.1;.1];    
w21j=[0; 0.1; .1; .02;0;.1;.1;.1;.1];
q0j=[.9 .8 .7 .6 .1 .2 .1 .1 .1];     
q120j=q0j;
q11j=[.5 .2 .3 .4 .1 .2 .1 .1 .1];
q12j=q11j;
w121ij=w20j*q0j;
w120ij=w20j*q11j;    
 f1=5;
q2j=0;                      % 阀值
p0=.2;
k1=1;
p1=.3;
w=0;
xj=[1 1 1];            % 输入 

error=0.0001;
a1=[1 1 1 1];
n=1;
e1=0;
e0=0;
e2=0;
e3=0;
e4=0;
yo=0;
ya=0;
yb=0;
y0=0;
y1=0;
y2=0;
y3=0;
u=0;
u1=0;
u2=0.68;
u3=.780;
u4=u3-u2;
k1=1;
kn=28;
e3=.055; z1=0;
z12=0; q123j=0; t2j=0; o12j=0;r=0;r1=0; s=0.1;d2j=0;
%+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
% 计算隐层输出
  v1=randn(40,1);
for m=1:40
     s1=0.1*v1(m)
 yn=.3366*y2+.6634*u1+s*s1;

y1=y2;
y2=yn;
 yp=yn;
u0=u1;
u1=u2;
 ya(m)=yn;
    for  k=1:100
% 计算隐层1输出
 for  i=1:9
   x1=[w11ij(i,1)*xj(:,1)]+[w11ij(i,2)*xj(:,2)]+[w11ij(i,3)*xj(:,3)];
   x=x1+q11j(:,i);
   o=1/[1+exp(-x)];
   o11j(i)=o;
  end
% 计算隐层2输出   
 for  i=1:9
 for  j=1:9
   z1=z1+w121ij(i,j)*o11j(:,j);
   end
   z=z1+q12j(:,i);
   o=1/[1+exp(-x)];
   o12j(i)=o;
  end
 % 计算输出层的输出
   for  i=1:9
   yb=yb+w21j(i,:)*o12j(:,i);
   end
   yi=yb+p1;
   y=1/[1+exp(-yi)];

 %   计算目标值与实际输出的误差
   e0=e1;
   e1=e2;
   e2=[(yp-y).^2]/2;
   e(k)=e2;
   xj1=e2;
  xj2=e1;         
   xj3=e0;          
   xj=[xj1 xj2 xj3]; 
 
% revising right value (1)
  for   i=1:9
      d1=o11j(:,i)*[1-o11j(:,i)]*d2j*w21j(i,:);%计算第1隐层误差反传信号
      do=o11j(:,i)*d1;
       qw=q11j(:,i)-q0j(:,i);
      q2j=q11j(:,i)+.8*do+.4*qw;
       q3j(:,i)=q2j;
   for j=1:3
      dw=w11ij(i,j)-w10ij(i,j);
      w12ij=w11ij(i,j)+.8*do*xj(j)+.6*dw;
      w13ij(i,j)=w12ij;
   end
  end      
      w10ij=w11ij;

      w11ij=w13ij;
       q0j=q11j;
      q11j=q3j;
% revising right value (2)
  for   i=1:9
      d1=o12j(:,i)*[1-o12j(:,i)]*d2j*w21j(i,:);%计算第2隐层误差反传信号
      do=o12j(:,i)*d1;
       qw=q12j(:,i)-q120j(:,i);
      t2j=q12j(:,i)+.8*do+.4*qw;
       q123j(:,i)=t2j;
   for j=1:9
      dw=w121ij(i,j)-w120ij(i,j);
      w122ij=w121ij(i,j)+.8*do*o11j(j)+.6*dw;
       w123ij(i,j)=w122ij;
   end
  end      
      w120ij=w121ij;

      w121ij=w123ij;
       q120j=q12j;
      q12j=q123j;
% revising right value (3)
 if  m<4,   r=0.2;  r1=0.0001  ;
else
r=0.14;   r1=0.005;
end
 for  i=1:9
      d2j=y*(1-y)*(yp-y);  %计算输出误差反传信号
      dw=w21j(i,:)-w20j(i,:);
      w22j=w21j(i,:)+r*d2j*o12j(i)+.4*dw+r1*e2;
      w23j(i,:)=w22j;    
  end
      w20j=w21j;
      w21j=w23j;
      ph=p1-p0;
      p2=p1+.96*(yp-y)+.58*ph+r1*e2;
      p0=p1;
      p1=p2;
     
 u=y;
 % k=k+1;
if  e2<=.005  break;
else
     end
     end
 ya(m)=yp*f1;
 e3(m)=e2;
 ym(m)=y*f1;
 v(m)=s1;
%  m=m+1
m6=m
end
     w11ij=w13ij
     w121ij=w123ij
     w21j=w23j
m1=m;
 % grapher
 subplot(3,1,1) 
 m=1:m6;
 plot(m,ya,m,ym,'rx'), title('Identified model by MBP algorithm'),xlabel('k'),ylabel('ya  and  ym')
 legend('ya is system','ym is identified model'); %图标炷 

 subplot(3,1,2)

 m=1:m6;
 plot(m,e3),xlabel('k'),ylabel('error')

 subplot(3,1,3)
 m=1:m6;
plot(m,v),xlabel('k'),ylabel('random noise')