bp.asv

用基于matlab语言实现的bp神经网络算法

%f(x)=1.1(1-x+2x^2)exp(-x^2/2)
%单输入，多输出。训练样本，样本数P=100，其中输入样本x服从【-4，4】内的均匀分布，样本输出喂
%fx+e,e为添加噪声，服从均值为0，标准差为0.1的正太分布。隐层采用sigmoid激活函数，输出层采用线性激活函数，f（u）=u。

function main()
SamNum=100;

TestSamNum=101;
HiddenUnitNum=10;
InDim=1;
OutDim=1;

%根据目标函数获得样本输入，输出
rand('state',sum(100*clock))
NoiseVar=0.1;
Noise=NoiseVar*randn(1,SamNum);
SamIn=8*rand(1,SamNum)-4;
SamOutNoNoise=1.1*(1-SamIn+2*SamIn.^2).*exp(-SamIn.^2/2);
%SamOutNoNoise=sin(SamIn);
SamOut=SamOutNoNoise+Noise;

TestSamIn=-4:0.08:4;
TestOut=1.1*(1-TestSamIn+2*TestSamIn.^2).*exp(-TestSamIn.^2/2);
%TestOut=sin(TestSamIn);

figure
hold on
grid 
plot(SamIn,SamOut,'r.');
xlabel('Inputx');
ylabel('OUtputy');

MaxEpochs=20000;
lr=0.003;
E0=0.5;

W1=0.2*rand(HiddenUnitNum,InDim)-0.1;
B1=0.2*rand(HiddenUnitNum,1)-0.1;
W2=0.2*rand(OutDim,HiddenUnitNum)-0.1;
B2=0.2*rand(OutDim,1)-0.1;

W1Ex=[W1 B1];
W2Ex=[W2 B2];

SamInEx=[SamIn' ones(SamNum,1)]';
ErrHistory=[];
for i=1:MaxEpochs
    
    HiddenOut=logsig(W1Ex*SamInEx);
    HiddenOutEx=[HiddenOut' ones(SamNum,1)]';
    NetworkOut=W2Ex*HiddenOutEx;
    
    Error=SamOut-NetworkOut;
    SSE=sumsqr(Error);
    
    ErrHistory=[ErrHistory SSE];
    
    if SSE<E0,break,end
    
    Delta2=Error;
    Delta1=W2'*Delta2.*HiddenOut.*(1-HiddenOut);
    
    %计算全职调整量
    dW2Ex=Delta2*HiddenOutEx';
    dW1Ex=Delta1*SamInEx';
    
    %权值调整
    W1Ex=W1Ex+lr*dW1Ex;
    W2Ex=W2Ex+lr*dW2Ex;
    
    %分离因曾到输出层的权值
    W2=W2Ex(:,1:HiddenUnitNum);
end

%显示计算结果
i
W1=W1Ex(:,1:InDim);
B1=W1Ex(:,InDim+1);
W2
B2=W2Ex(:,1+HiddenUnitNum);

%测试
TestHiddenOut=logsig(W1*TestSamIn+repmat(B1,1,TestSamNum));
TestNNOut=W2*TestHiddenOut+repmat(B2,1,TestSamNum);
plot(TestSamIn,TestNNOut,'b');

%绘制学习误差曲线
figure
hold on
grid
[xx,Num]=size(ErrHistory);
plot(1:Num,ErrHistory,'g--');