实验四 BP神经网络模拟sin函数Word下载.docx
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单元数量：
d
单元i的输出：
单元i的激活函数：
线性函数
隐层：
单元j的输入：
单元j的输出：
单元j的激活函数：
非线性函数
输出层：
单元k的输入：
c
单元k的输出：
单元k的激活函数：
3、程序设计
1、编译环境
使用C#语言编写，编译器为VS2008，运行环境为Windows+.NetFramework3.5
2、程序运行流程
运行程序后，单击“训练”按钮，开始训练，训练完成后可以看到函数图像与各权值，输入x的值可以查看预测值与准确值。
3、类设计
神经网络类的定义：
classNeuralNetwork
{
#regionInstanceFields
//privatefields
privateintnum_in;
privateintnum_hid;
privateintnum_out;
privatedouble[,]i_to_h_wts;
privatedouble[,]h_to_o_wts;
privatedouble[]inputs;
privatedouble[]hidden;
privatedouble[]outputs;
privatedoublelearningRate=0.3;
privateRandomgen=newRandom（）;
#endregion
#regionConstructor
///<
summary>
///CreatesanewNeuralNetwork,usingtheparameters
///provided
/summary>
paramname="
num_in"
>
Numberofinputsnodes<
/param>
num_hid"
Numberofhiddennodes<
num_out"
Numberofoutputnodes<
publicNeuralNetwork（intnum_in,intnum_hid,intnum_out）
this.num_in=num_in;
this.num_hid=num_hid;
this.num_out=num_out;
i_to_h_wts=newdouble[num_in+1,num_hid];
h_to_o_wts=newdouble[num_hid+1,num_out];
inputs=newdouble[num_in+1];
hidden=newdouble[num_hid+1];
outputs=newdouble[num_out];
}
#regionInitializationofrandomweights
///Randomlyinitialiseallthenetworkweights.
///Needtostartwithsomeweights.
///Thismethodsetsuptheinputtohiddennodesand
///hiddennodestooutputnodeswithrandomvalues
publicvoidinitialiseNetwork（）
//Settheinputvalueforbiasnode
inputs[num_in]=1.0;
hidden[num_hid]=1.0;
//Setweightsbetweeninput&
hiddennodes.
for（inti=0;
i<
num_in+1;
i++）
for（intj=0;
j<
num_hid;
j++）
//Setrandomweightsbetween-2&
2
i_to_h_wts[i,j]=（gen.NextDouble（）*4）-2;
//Setweightsbetweenhidden&
outputnodes.
num_hid+1;
num_out;
h_to_o_wts[i,j]=（gen.NextDouble（）*4）-2;
#regionPassforward
///Doesacompletepassthroughwithinthenetwork,usingthe
///applied_inputsparameters.Thepassthorughisdonetothe
///inputtohidden,andhiddentoouputlayers
applied_inputs"
Andouble[]arraywhichholdsinputvalues,which
///arethenpresetedtothenetworksinputlayer<
publicvoidpass_forward（double[]applied_inputs）
//Loadasetofinputsintoourcurrentinputs
num_in;
inputs[i]=applied_inputs[i];
//Forwardtohiddennodes,andcalculateactivationsinhiddenlayer
doublesum=0.0;
sum+=inputs[j]*i_to_h_wts[j,i];
hidden[i]=ActivationFunction.Sigmoid（sum）;
//Forwardtooutputnodes,andcalculateactivationsinoutputlayer
sum+=hidden[j]*h_to_o_wts[j,i];
//passthesum,throughtheactivationfunction,Sigmoidinthiscase
//whichallowsforbackwarddifferentation
outputs[i]=ActivationFunction.Sigmoid（sum）;
#regionPublicProperties
///gets/setsthenumberofinputnodesfortheNeuralNetwork
publicintNumberOfInputs
get{returnnum_in;
set{num_in=value;
///gets/setsthenumberofhiddennodesfortheNeuralNetwork
publicintNumberOfHidden
get{returnnum_hid;
set{num_hid=value;
///gets/setsthenumberofoutputnodesfortheNeuralNetwork
publicintNumberOfOutputs
get{returnnum_out;
set{num_out=value;
///gets/setstheinputtohiddenweightsfortheNeuralNetwork
publicdouble[,]InputToHiddenWeights
get{returni_to_h_wts;
set{i_to_h_wts=value;
///gets/setsthehiddentooutputweightsfortheNeuralNetwork
publicdouble[,]HiddenToOutputWeights
get{returnh_to_o_wts;
set{h_to_o_wts=value;
///gets/setstheinputvaluesfortheNeuralNetwork
publicdouble[]Inputs
get{returninputs;
set{inputs=value;
///gets/setsthehiddenvaluesfortheNeuralNetwork
publicdouble[]Hidden
get{returnhidden;
set{hidden=value;
///gets/setstheoutputsvaluesfortheNeuralNetwork
publicdouble[]Outputs
get{returnoutputs;
set{outputs=value;
///gets/setstheLearningRate（eta）valuefortheNeuralNetwork
publicdoubleLearningRate
get{returnlearningRate;
set{learningRate=value;
训练过程：
publicvoidTrain（）
_nn.initialiseNetwork（）;
training_times;
foreach（TrainSettrainSetin_trainSets）
double[]inputs=newdouble[]{trainSet.Input};
double[]outputs=newdouble[]{trainSet.Output};
_nn.pass_forward（inputs）;
train_network（outputs）;
权值变更函数：
privatevoidtrain_network（double[]outputs）
//getmomentumvalues（deltavaluesfromlastpass）
double[]delta_hidden=newdouble[_nn.NumberOfHidden+1];
double[]delta_outputs=newdouble[_nn.NumberOfOutputs];
//Getthedeltavaluefortheoutputlayer
_nn.NumberOfOutputs;
delta_outputs[i]=
_nn.Outputs[i]*（1.0-_nn.Outputs[i]）*（outputs[i]-_nn.Outputs[i]）;
//Getthedeltavalueforthehiddenlayer
_nn.NumberOfHidden+1;
doubleerror=0.0;
error+=_nn.HiddenToOutputWeights[i,j]*delta_outputs[j];
delta_hidden[i]=_nn.Hidden[i]*（1.0-_nn.Hidden[i]）*error;
//Nowupdatetheweightsbetweenhidden&
outputlayer
//usemomentum（deltavaluesfromlastpass）,
//toensuremovedincorrectdirection
_nn.HiddenToOutputWeights[j,i]+=_nn.LearningRate*delta_outputs[i]*_nn.Hidden[j];
//Nowupdatetheweightsbetweeninput&
hiddenlayer
_nn.NumberOfHidden;
_nn.NumberOfInputs+1;
_nn.InputToHiddenWeights[j,i]+=_nn.LearningRate*delta_hidden[i]*_nn.Inputs[j];
激活函数（sigmoid函数）：
publicstaticdoubleSigmoid（doublex）
return1.0/（1.0+Math.Pow（Math.E,-x））;
建立训练集和输入层，隐层，输出层分别为1，4，1的神经网络实例：
TrainSet[]set=newTrainSet[setSize];
setSize;
doublen=Math.PI*2/setSize;
set[i]=newTrainSet（n*（i+1）,Math.Sin（n*（i+1））/2+0.5）;
}NeuralNetworknetwork=newNeuralNetwork（1,4,1）;
绘制拟合后的图形：
Graphicsg;
g=panel1.CreateGraphics（）;
g.Clear（panel1.BackColor）;
doublepi=Math.PI*2/setSize;
g.FillRectangle（brush,（float）（pi*（i+1））*40,100-（float）（_nntrainer.GetOutPut（newdouble[]{pi*（i+1）}）[0]）*100,1,1）;
输出任意角度的拟合值和正弦值：
double_result=_nntrainer.GetOutPut（newdouble[]{Double.Parse（x_value.Text）}）[0];
result.Text=（（_result-0.5）*2）.ToString（）;
sinx.Text=Math.Sin（Double.Parse（x_value.Text））.ToString（）;
4、程序运行截图
1、程序界面
2、训练结果
3、对比预测值与准确值
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