BP神经网络预测误差

Question

为什么优化的BP神经网络预测误差会比传统的BP神经网络预测误差要大?有什么解决办法吗？
采用了AOA-BP，PSO-BP，精度都比传统BP要差一点

Answer 1

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• 这篇博客: PSO粒子群优化算法中的 PSO与BP神经网络 部分也许能够解决你的问题, 你可以仔细阅读以下内容或跳转源博客中阅读:
  

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  function main
  clc;clear all;close all;
  MaxRunningTime=1; %该参数是为了使网络集成，重复训练MaxRunningTime次
  HiddenUnitNum=12;
  rand('state',sum(100*clock));
  TrainSamIn=-4:0.07:2.5;
  TrainSamOut=1.1*(1-TrainSamIn+2*TrainSamIn.^2).*exp(-TrainSamIn.^2/2);
  TestSamIn=2:0.04:3;
  TestSamOut=1.1*(1-TestSamIn+2*TestSamIn.^2).*exp(-TestSamIn.^2/2);
  [xxx,TrainSamNum]=size(TrainSamIn);
  [xxx,TestSamNum]=size(TestSamIn);
  % for HiddenUnitNum=3:MaxHiddenLayerNode %隐含层神经元的个数可以取逐渐增大的合理整数
      fprintf('\n the hidden layer node');HiddenUnitNum
      TrainNNOut=[];
      TestNNOut=[];
      for t=1:MaxRunningTime
          fprintf('the current running times is');t
          [NewW1,NewB1,NewW2,NewB2]=PSOTrain(TrainSamIn,TrainSamOut,HiddenUnitNum);
          disp('PSO算法训练神经网络结束，BP算法接着训练网络……');
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  %BP算法参数初始化，注意与上面PSO参数一致
  SamInNum=length(TrainSamIn);
  TestSamNum=length(TestSamIn);
  InDim=1;
  OutDim=1;
  %学习样本添加噪声
  rand('state',sum(100*clock))
  NoiseVar=0.01;
  Noise=NoiseVar*randn(1,SamInNum);
  SamIn=TrainSamIn;
  SamOutNoNoise=TrainSamOut;
  SamOut=SamOutNoNoise + Noise;
  MaxEpochs=300;
  lr=0.003;
  E0=0.0001;
  W1=NewW1;
  B1=NewB1;
  W2=NewW2';
  B2=NewB2;
  W1Ex=[W1 B1];
  W2Ex=[W2 B2];
  SamInEx=[SamIn' ones(SamInNum,1)]';
  ErrHistory=[];
  %网络参数初始化完毕
  %给动画初始画图和构建动画框架和背景
  HiddenOut=logsig(W1Ex*SamInEx);
  HiddenOutEx=[HiddenOut' ones(SamInNum,1)]';
  NetworkOut=W2Ex*HiddenOutEx;
  Error=SamOut-NetworkOut;
  %给误差的动画显示提供空矩阵和其维数
  SSEINIT=zeros(1,MaxEpochs);
  %这仅限于输出是一维的情况
  SSE=sumsqr(Error);
  %绘画动画显示的图形框架
  figure(1);
  rangecolour=linspace(0,1,MaxEpochs);
  %采用分区画图，把两幅动画在一个figure中显示
  %先画第一幅图形
  subplot(2,1,1);
  hold on
  axis([1 SamInNum min(SamOut) max(SamOut)]);
  hflash1=line(1:SamInNum,SamOut,'color',[rangecolour(1) 0 1-rangecolour(1)],...
      'linestyle','-','linewidth',2,'marker','d',...
      'markersize',2,'erasemode','none');
  hflash2=line(1:SamInNum,NetworkOut,'color',[rangecolour(1) 0 1-rangecolour(1)],...
      'linestyle','-','linewidth',2.5,'marker','h',...
      'markersize',2.3,'erasemode','xor');
  xlabel('训练样本的数目');
  ylabel('样本的输出值或网络的输出值');
  title('样本的输出值与网络的输出值动画显示','fontsize',13);
  legend('样本的输出值','网络的输出值');
  hold off
  %再画第二幅图形
  subplot(2,1,2);
  hold on
  axis([1 MaxEpochs -0.2*SSE SSE]);
  hflash3=line(1:MaxEpochs,E0*ones(1,MaxEpochs),'color',...
      [rangecolour(1) 0 1-rangecolour(1)],...
      'linestyle','--','linewidth',2,'marker','h',...
      'markersize',2,'erasemode','none');
  hflash4=line(1,SSE,'color',...
      [rangecolour(1) 0 1-rangecolour(1)],...
      'linestyle','-','linewidth',2,'marker','*',...
      'markersize',2,'erasemode','xor');
  xlabel('网络训练次数');
  ylabel('目标误差或网络输出误差');
  title('目标误差与网络输出误差动画显示','fontsize',13);
  legend('目标误差','网络输出误差');
  hold off
  
  for i=2:MaxEpochs
      HiddenOut=logsig(W1Ex*SamInEx);
      HiddenOutEx=[HiddenOut' ones(SamInNum,1)]';
      NetworkOut=W2Ex*HiddenOutEx;
      
      Error=SamOut-NetworkOut;
      SSE=sumsqr(Error)
   %让第二幅动画逐点显示
            SSEINIT(:,i)=SSE;
  %对于神经网络训练过程中发生震荡的瞬间图像将其显示出来
    ErrHistory=[ErrHistory SSE];
    SSEINIT(:,1);
    SSEINIT(:,2);
    SSEINIT2=SSEINIT(:,i);
    SSEINIT1=SSEINIT(:,i-1);
  if SSE<E0,break, end   
      Delta2=Error;
      Delta1=W2'*Delta2.*HiddenOut.*(1-HiddenOut);
  
      dW2Ex=Delta2*HiddenOutEx';
      dW1Ex=Delta1*SamInEx';
  
      W1Ex=W1Ex+lr*dW1Ex;
      W2Ex=W2Ex+lr*dW2Ex;
      W2=W2Ex(:,1:HiddenUnitNum);
      if SSEINIT2>SSEINIT1
  %如果网络学习时发生震荡，每10步显示一次
      if mod(i,10)==0
          Counter(i)=SSEINIT(:,i);
          Len=size(Counter);
          figure(Len(1,2));
         subplot(2,1,1);
        hold on
  axis([1 SamInNum min(SamOut) max(SamOut)]);
  hflash5=line(1:SamInNum,SamOut,'color',[rangecolour(1) 0 1-rangecolour(1)],...
      'linestyle','-','linewidth',2,'marker','d',...
      'markersize',2,'erasemode','none');
  hflash6=line(1:SamInNum,NetworkOut,'color',[rangecolour(MaxEpochs) 0 1-rangecolour(MaxEpochs)],...
      'linestyle','-','linewidth',2.5,'marker','h',...
      'markersize',2.3,'erasemode','xor');
  xlabel('训练样本的数目');
  ylabel('样本的输出值或网络的输出值');
  title('神经网络学习震荡时拟合曲线','fontsize',13);
  legend('样本的输出值','网络的输出值');
  hold off
  %再画第二幅图形
  subplot(2,1,2);
  hold on
  axis([1 MaxEpochs -2*SSEINIT(:,2) 2*SSEINIT(:,2)]);
  hflash7=line(1:MaxEpochs,E0*ones(1,MaxEpochs),'color',...
      [rangecolour(1) 0 1-rangecolour(1)],...
      'linestyle','--','linewidth',2,'marker','h',...
      'markersize',2,'erasemode','none');
  hflash8=line(1:i,SSEINIT(:,1:i),'color',...
      [rangecolour(1) 0 1-rangecolour(1)],...
      'linestyle','-','linewidth',2,'marker','*',...
      'markersize',2,'erasemode','xor');
  xlabel('网络训练次数');
  ylabel('目标误差或网络输出误差');
  title('神经网络学习震荡时误差','fontsize',13);
  legend('目标误差','网络输出误差');
  hold off
      end
      end
  %动画开始放映    
  set(hflash2,'XData',1:SamInNum,'YData',NetworkOut,'color',...
      [rangecolour(MaxEpochs) 0 1-rangecolour(MaxEpochs)]);
  set(hflash4,'XData',1:i,'YData',SSEINIT(:,1:i),...
      'color',[rangecolour(MaxEpochs) 0 1-rangecolour(MaxEpochs)]);
  drawnow;                       
  end
  
  W2=W2Ex(:,1:HiddenUnitNum);
  W1=W1Ex(:,1:InDim);
  B1=W1Ex(:,InDim+1);
  B2=W2Ex(:,1+HiddenUnitNum); 
  TrainHiddenOut=logsig(W1*SamIn+repmat(B1,1,SamInNum));
  TrainNNOut=W2*TrainHiddenOut+repmat(B2,1,SamInNum);
  TestHiddenOut=logsig(W1*TestSamIn+repmat(B1,1,TestSamNum));
  TestNNOut=W2*TestHiddenOut+repmat(B2,1,TestSamNum);
  
  figure(MaxEpochs+1);
  hold on;
  grid;
  h1=plot(SamIn,SamOut);
  set(h1,'color','r','linestyle','-',...
      'linewidth',2.5,'marker','p','markersize',5);
  hold on 
  h2=plot(TestSamIn,TestSamOut);
  set(h2,'color','g','linestyle','--',...
      'linewidth',2.5,'marker','^','markersize',7);
  h3=plot(SamIn,TrainNNOut);
  set(h3,'color','c','linestyle','-.',...
      'linewidth',2.5,'marker','o','markersize',5);
  h4=plot(TestSamIn,TestNNOut);
  set(h4,'color','m','linestyle',':',...
      'linewidth',2.5,'marker','s','markersize',5);
  xlabel('Input x','fontsize',13);ylabel('Output y','fontsize',13);
  box on;axis tight;
  %title('PSO-BP神经网络误差测试图');
  legend('网络学习实际样本值','网络测试实际样本值',...
      '网络学习网络输出值','网络测试网络输出值');
  hold off;
      end
  % end
  fidW1=fopen('d:\W1.txt','a+');fidB1=fopen('d:\B1.txt','a+');
  fidW2=fopen('d:\W2.txt','a+');fidB2=fopen('d:\B2.txt','a+');
  for i=1:length(W1)
      fprintf(fidW1,'\n %6.5f',W1(i));
  end
  for i=1:length(B1)
      fprintf(fidB1,'\n %6.5f',B1(i));
  end
  for i=1:length(W2)
      fprintf(fidW2,'\n %6.5f',W2(i));
  end
  for i=1:length(B2)
      fprintf(fidB2,'\n %6.5f',B2(i));
  end
  fclose(fidW1);fclose(fidB1);fclose(fidW2);fclose(fidB2);
  
  

  function [NewW1,NewB1,NewW2,NewB2]=PSOTrain(SamIn,SamOut,HiddenUnitNum);
  Maxgeneration=700;
  E0=0.0001;
  Xmin=-10;
  Xmax=10;
  Vmin=-5;
  Vmax=5;
  M=100;
  c1=2.7;
  c2=1.3;
  w=0.9;
  [R,SamNum]=size(SamIn);
  [S2,SamNum]=size(SamOut);
  generation=1;
  Done=0;
  
  Pb1=zeros(HiddenUnitNum,R+S2+1,M);
  Pb2=zeros(S2,M);
  Pg1=zeros(HiddenUnitNum,R+S2+1);
  Pg2=zeros(S2,1);
  E=zeros(size(SamOut));
  rand('state',sum(100*clock));
  startP1=rand(HiddenUnitNum,R+S2+1,M)-0.5;
  startP2=rand(S2,M)-0.5;
  startV1=rand(HiddenUnitNum,R+S2+1,M)-0.5;
  startV2=rand(S2,M)-0.5;
  endP1=zeros(HiddenUnitNum,R+S2+1,M);
  endP2=zeros(S2,M);
  endV1=zeros(HiddenUnitNum,R+S2+1,M);
  endV2=zeros(S2,M);
  startE=zeros(1,M);
  endE=zeros(1,M);
  for i=1:M
      W1=startP1(1:HiddenUnitNum,1:R,i);
      W2=startP1(1:HiddenUnitNum,R+1:R+S2,i);
      B1=startP1(1:HiddenUnitNum,R+S2+1,i);
      B2=startP2(1:S2,i);
      for q=1:SamNum
          TempOut=logsig(W1*SamIn(:,q)+B1);
          NetworkOut(1,q)=W2'*TempOut+B2;
      end
      E=NetworkOut-SamOut;
      startE(1,i)=sumsqr(E)/(SamNum*S2);
      Pb1(:,:,i)=startP1(:,:,i);
      Pb2(:,i)=startP2(:,i);
  end
  [val,position]=min(startE(1,:));
  Pg1=startP1(:,:,position);
  Pg2=startP2(:,position);
  Pgvalue=val;
  Pgvalue_last=Pgvalue;
  
  while(~Done)
      for num=1:M
          endV1(:,:,num)=w*startV1(:,:,num)+c1*rand*(Pb1(:,:,num)-startP1(:,:,num))+c2*rand*(Pg1-startP1(:,:,num));
          endV2(:,num)=w*startV2(:,num)+c1*rand*(Pb2(:,num)-startP2(:,num))+c2*rand*(Pg2-startP2(:,num));
          for i=1:HiddenUnitNum
              for j=1:(R+S2+1)
                  endV1(i,j,num)=endV1(i,j,num);
                  if endV1(i,j,num)>Vmax
                      endV1(i,j,num)=Vmax;
                  elseif endV1(i,j,num)<Vmin
                          endV1(i,j,num)=Vmin;
                  end
              end
          end
          for s2=1:S2
              endV2(s2,num)=endV2(s2,num);
              if endV2(s2,num)>Vmax
                 endV2(s2,num)=Vmax;
              elseif endV2(s2,num)<Vmin
                     endV2(s2,num)=Vmin;
              end
          end
          endP1(:,:,num)=startP1(:,:,num)+endV1(:,:,num);
          endP2(:,num)=startP2(:,num)+endV2(:,num);
          for i=1:HiddenUnitNum
              for j=1:(R+S2+1)
                  if endP1(i,j,num)>Xmax
                     endP1(i,j,num)=Xmax;
                  elseif endP1(i,j,num)<Xmin
                         endP1(i,j,num)=Xmin;
                  end
              end
          end
          for s2=1:S2
              if endP2(s2,num)>Xmax
                 endP2(s2,num)=Xmax;
              elseif endP2(s2,num)<Xmin
                 endP2(s2,num)=Xmin;
              end
          end  
          W1=endP1(1:HiddenUnitNum,1:R,num);
          W2=endP1(1:HiddenUnitNum,R+1:R+S2,num);
          B1=endP1(1:HiddenUnitNum,R+S2+1,num);
          B2=endP2(1:S2,num);
          for q=1:SamNum
              TempOut=logsig(W1*SamIn(:,q)+B1);
              NetworkOut(1,q)=W2'*TempOut+B2;
          end
          E=NetworkOut-SamOut;
          SSE=sumsqr(E)   %便于在命令窗口观察网络误差的变化情况
          endE(1,num)=sumsqr(E)/(SamNum*S2);
          if endE(1,num)<startE(1,num)
              Pb1(:,:,num)=endP1(:,:,num);
              Pb2(:,num)=endP2(:,num);
              startE(1,num)=endE(1,num);
          end
      end
      w=0.9-(0.5/Maxgeneration)*generation;
      [value,position]=min(startE(1,:));
      if value<Pgvalue
          Pg1=Pb1(:,:,position);
          Pg2=Pb2(:,position);
          Pgvalue=value;
      end
      if (generation>=Maxgeneration)
          Done=1;
      end
      if Pgvalue<E0
          Done=1;
      end
      
      startP1=endP1;
      startP2=endP2;
      startV1=endV1;
      startV2=endV2;
      startE=endE;
      generation=generation+1;
  end
  W1=Pg1(1:HiddenUnitNum,1:R);
  W2=Pg1(1:HiddenUnitNum,R+1:R+S2);
  B1=Pg1(1:HiddenUnitNum,R+S2+1);
  B2=Pg2(:,1);
  NewW1=W1;
  NewW2=W2;
  NewB1=B1;
  NewB2=B2;
  
  

  BP与PSO

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