实验四 BP神经网络模拟sin函数Word下载.docx

1、 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+.NetFramework3.52、 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：class NeuralNetwork #region Instance Fields /private fields private int

2、num_in; private int num_hid; private int num_out; private double, i_to_h_wts; private double, h_to_o_wts; private double inputs; private double hidden; private double outputs; private double learningRate = 0.3; private Random gen = new Random（）; #endregion #region Constructor / / Creates a new Neura

3、lNetwork, using the parameters / provided/summaryparam name=num_inNumber of inputs nodesnum_hidNumber of hidden nodesnum_outNumber of output nodes public NeuralNetwork（int num_in, int num_hid, int num_out） this.num_in = num_in; this.num_hid = num_hid; this.num_out = num_out; i_to_h_wts = new doublen

4、um_in + 1, num_hid; h_to_o_wts = new doublenum_hid + 1, num_out; inputs = new doublenum_in + 1; hidden = new doublenum_hid + 1; outputs = new doublenum_out; #region Initialization of random weights / Randomly initialise all the network weights. / Need to start with some weights. / This method sets u

5、p the input to hidden nodes and / hidden nodes to output nodes with random values public void initialiseNetwork（） / Set the input value for bias node inputsnum_in = 1.0; hiddennum_hid = 1.0; / Set weights between input & hidden nodes. for （int i = 0; i num_in + 1; i+） for （int j = 0; j num_hid; j+）

6、/ Set random weights between -2 & 2 i_to_h_wtsi, j = （gen.NextDouble（） * 4） - 2; / Set weights between hidden & output nodes. num_hid + 1; num_out; h_to_o_wtsi, j = （gen.NextDouble（） * 4） - 2; #region Pass forward / Does a complete pass through within the network, using the / applied_inputs paramete

7、rs. The pass thorugh is done to the / input to hidden, and hidden to ouput layersapplied_inputsAn double array which holds input values, which / are then preseted to the networks input layer public void pass_forward（double applied_inputs） / Load a set of inputs into our current inputs num_in; inputs

8、i = applied_inputsi; / Forward to hidden nodes, and calculate activations in hidden layer double sum = 0.0; sum += inputsj * i_to_h_wtsj, i; hiddeni = ActivationFunction.Sigmoid（sum）; / Forward to output nodes, and calculate activations in output layer sum += hiddenj * h_to_o_wtsj, i; /pass the sum,

9、 through the activation function, Sigmoid in this case /which allows for backward differentation outputsi = ActivationFunction.Sigmoid（sum）; #region Public Properties / gets / sets the number of input nodes for the Neural Network public int NumberOfInputs get return num_in; set num_in = value; / get

10、s / sets the number of hidden nodes for the Neural Network public int NumberOfHidden get return num_hid; set num_hid = value; / gets / sets the number of output nodes for the Neural Network public int NumberOfOutputs get return num_out; set num_out = value; / gets / sets the input to hidden weights

11、for the Neural Network public double, InputToHiddenWeights get return i_to_h_wts; set i_to_h_wts = value; / gets / sets the hidden to output weights for the Neural Network public double, HiddenToOutputWeights get return h_to_o_wts; set h_to_o_wts = value; / gets / sets the input values for the Neura

12、l Network public double Inputs get return inputs; set inputs = value; / gets / sets the hidden values for the Neural Network public double Hidden get return hidden; set hidden = value; / gets / sets the outputs values for the Neural Network public double Outputs get return outputs; set outputs = val

13、ue; / gets / sets the LearningRate （eta） value for the Neural Network public double LearningRate get return learningRate; set learningRate = value;训练过程：public void Train（） _nn.initialiseNetwork（）; training_times; foreach （TrainSet trainSet in _trainSets） double inputs = new double trainSet.Input ; d

14、ouble outputs = new double trainSet.Output ; _nn.pass_forward（inputs）; train_network（outputs）;权值变更函数：private void train_network（double outputs） /get momentum values （delta values from last pass） double delta_hidden = new double_nn.NumberOfHidden + 1; double delta_outputs = new double_nn.NumberOfOutp

15、uts; / Get the delta value for the output layer _nn.NumberOfOutputs; delta_outputsi = _nn.Outputsi * （1.0 - _nn.Outputsi） * （outputsi - _nn.Outputsi）; / Get the delta value for the hidden layer _nn.NumberOfHidden + 1; double error = 0.0; error += _nn.HiddenToOutputWeightsi, j * delta_outputsj; delta

16、_hiddeni = _nn.Hiddeni * （1.0 - _nn.Hiddeni） * error; / Now update the weights between hidden & output layer /use momentum （delta values from last pass）, /to ensure moved in correct direction _nn.HiddenToOutputWeightsj, i += _nn.LearningRate * delta_outputsi * _nn.Hiddenj; / Now update the weights b

17、etween input & hidden layer _nn.NumberOfHidden; _nn.NumberOfInputs + 1; _nn.InputToHiddenWeightsj, i += _nn.LearningRate * delta_hiddeni * _nn.Inputsj;激活函数（sigmoid函数）：public static double Sigmoid（double x） return 1.0 / （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 = new T

18、rainSetsetSize; setSize; double n = Math.PI * 2 / setSize; seti = new TrainSet（n * （i + 1）, Math.Sin（n * （i + 1） / 2 + 0.5）; NeuralNetwork network = new NeuralNetwork（1, 4, 1）;绘制拟合后的图形： Graphics g; g = panel1.CreateGraphics（）; g.Clear（panel1.BackColor）; double pi=Math.PI*2/setSize; g.FillRectangle（b

19、rush,（float）（pi*（i+1）*40,100-（float）（_nntrainer.GetOutPut（new doublepi*（i+1）0）*100,1,1）;输出任意角度的拟合值和正弦值： double _result = _nntrainer.GetOutPut（new double 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