bp.m

对用BP算法所进行的神经网络进行仿真、训练。模拟综合出我们所需要的结果。

clear
%数据输入
huanghe_p=[370 503 434 575 490 420 560 640 558 343 326 405 446 423 422 697 598 377 435 472 451 667 601 689 541 485 425 389 382 707 422];
huanghe_t=[515 713 586 753 720 567 717 987 810 489 453 589 639 568 595 982 849 519 615 652 599 941 893 999 758 701 630 561 520 1040 535];

%归一化处理
p=(huanghe_p-min(huanghe_p))/(max(huanghe_p)-min(huanghe_p));
t=(huanghe_t-min(huanghe_t))/(max(huanghe_t)-min(huanghe_t));

%数据输入2：网络有关参数
EPOCHS=10000;
GOAL=0.000005;

%建立bp神经网络，并训练，仿真。其中输入为p，输出为t

%-------------------------隐层神经元确定-----------------------------

s=3:15;%s 为常向量，表示神经元的个数
res=zeros(size(s));%res将要存储误差向量，这里先置零

pn=[p(1:5);p(6:10);p(11:15);p(16:20)];
tn=[t(1:5);t(6:10);t(11:15);t(16:20)];
for i=1:length(s)             
      net=newff(minmax(pn),[s(i),4],{'tansig','purelin'},'trainlm');
      net.iw{1,1}=zeros(size(net.iw{1,1}))+0.5;
      net.lw{2,1}=zeros(size(net.lw{2,1}))+0.75;
      net.b{1,1}=zeros(size(net.b{1,1}))+0.5;
      net.b{2,1}=zeros(size(net.b{2,1}));
      net.trainParam.epochs=EPOCHS;
      net.trainParam.goal =GOAL;
      net=train(net,pn,tn);
      y=sim(net,pn);
e=tn-y;
error=mse(e,net);
res(i)=norm(error);
      
end
%选取最优神经元数，number为使得误差最小的隐层神经元个数
number=find(res==min(res));
if(length(number)>1) no=number(1)
else no=number
end

clear error，res
%选定隐层神经元数目后，建立网络，训练仿真。
net=newff(minmax(pn),[no,4],{'tansig','purelin'},'trainlm');
      net.iw{1,1}=zeros(size(net.iw{1,1}))+0.5;
      net.lw{2,1}=zeros(size(net.lw{2,1}))+0.75;
      net.b{1,1}=zeros(size(net.b{1,1}))+0.5;
      net.b{2,1}=zeros(size(net.b{2,1}));
      net.trainParam.epochs=EPOCHS;
      net.trainParam.goal =GOAL;
net=train(net,pn,tn);
y=sim(net,pn);
e=tn-y;
error=mse(e,net)%error为网络的误差向量
r=norm(error);%r为网络的整体误差
save net                        %保存最好的网络

%预测
input=[p(11:15);p(16:20);p(21:25);p(26:30)];
yuce=sim(net,input);

%结果反归一化
y1=[y(1,:) y(2,:) y(3,:) y(4,:)];
yuce1=[yuce(1,:) yuce(2,:) yuce(3,:) yuce(4,:)];
t1=y1*(max(huanghe_t(1:20))-min(huanghe_t(1:20)))+min(huanghe_t(1:20));
yuce2=yuce1*(max(huanghe_t(1:20))-min(huanghe_t(1:20)))+min(huanghe_t(1:20));

%计算误差
wucha=abs(t1-huanghe_t(1:20))./huanghe_t(1:20)
b=minmax(wucha);
average_wucha=mean(wucha);
%作图
figure(1)
plot(1:20,huanghe_t(1:20),'*-',1:20,t1,'o:')

figure(2)
plot(1:20,huanghe_t(11:30),'*-',1:20,yuce2,'o:')