实验四 BP神经网络模拟sin函数.doc

实验四 BP神经网络模拟sin函数一、 问题描述BP神经网络模拟sin函数根据人工神经网络学习算法，实现正弦曲线的拟合。要求能随机自动生成数量为n的正弦值作为训练集，并根据训练集拟合曲线，最后能通过输入x值测试理论与拟合sinx的拟合度。二、 设计思想思维学普遍认为，人类大脑的思维分为抽象（逻辑）思维、形象（直观）思维和灵感（顿悟）思维三种基本方式。逻辑性的思维是指根据逻辑规则进行推理的过程；它先将信息化成概念，并用符号表示，然后，根据符号运算按串行模式进行逻辑推理；这一过程可以写成串行的指令，让计算机执行。然而，直观性的思维是将分布式存储的信息综合起来，结果是忽然间产生想法或解决问题的办法。这种思维方式的根本之点在于以下两点:1.信息是通过神经元上的兴奋模式分布储在网络上;2.信息处理是通过神经元之间同时相互作用的动态过程来完成的。人工神经网络就是模拟人思维的第二种方式。这是一个非线性动力学系统，其特色在于信息的分布式存储和并行协同处理。虽然单个神经元的结构极其简单，功能有限，但大量神经元构成的网络系统所能实现的行为却是极其丰富多彩的。人工神经网络由大量的神经元构成。这些神经元一般分为三种：输入层神经元，隐层神经元和输出层神经元。输入层：单元i的输入：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：单元数量： 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：单元数量：c 单元k的输出：单元k的激活函数：非线性函数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：class NeuralNetwork #region Instance Fields /private fields private int 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 NeuralNetwork, using the parameters / provided / / Number of inputs nodes / Number of hidden nodes / Number 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 doublenum_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; #endregion #region Initialization of random weights / / Randomly initialise all the network weights. / Need to start with some weights. / This method sets up 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+) / Set random weights between -2 & 2 i_to_h_wtsi, j = (gen.NextDouble() * 4) - 2; / Set weights between hidden & output nodes. for (int i = 0; i num_hid + 1; i+) for (int j = 0; j num_out; j+) / Set random weights between -2 & 2 h_to_o_wtsi, j = (gen.NextDouble() * 4) - 2; #endregion #region Pass forward / / Does a complete pass through within the network, using the / applied_inputs parameters. The pass thorugh is done to the / input to hidden, and hidden to ouput layers / / An 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 for (int i = 0; i num_in; i+) inputsi = applied_inputsi; / Forward to hidden nodes, and calculate activations in hidden layer for (int i = 0; i num_hid; i+) double sum = 0.0; for (int j = 0; j num_in + 1; j+) sum += inputsj * i_to_h_wtsj, i; hiddeni = ActivationFunction.Sigmoid(sum); / Forward to output nodes, and calculate activations in output layer for (int i = 0; i num_out; i+) double sum = 0.0; for (int j = 0; j num_hid + 1; j+) sum += hiddenj * h_to_o_wtsj, i; /pass the sum, through the activation function, Sigmoid in this case /which allows for backward differentation outputsi = ActivationFunction.Sigmoid(sum); #endregion #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; / / gets / 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 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 Neural 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 = value; / / gets / sets the LearningRate (eta) value for the Neural Network / public double LearningRate get return learningRate; set learningRate = value; #endregion 训练过程：public void Train() _nn.initialiseNetwork(); for (int i = 0; i training_times; i+) foreach (TrainSet trainSet in _trainSets) double inputs = new double trainSet.Input ; double 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.NumberOfOutputs; / Get the delta value for the output layer for (int i = 0; i _nn.NumberOfOutputs; i+) delta_outputsi = _nn.Outputsi * (1.0 - _nn.Outputsi) * (outputsi - _nn.Outputsi); / Get the delta value for the hidden layer for (int i = 0; i _nn.NumberOfHidden + 1; i+) double error = 0.0; for (int j = 0; j _nn.NumberOfOutputs; j+) error += _nn.HiddenToOutputWeightsi, j * delta_outputsj; delta_hiddeni = _nn.Hiddeni * (1.0 - _nn.Hiddeni) * error; / Now update the weights between hidden & output layer for (int i = 0; i _nn.NumberOfOutputs; i+) for (int j = 0; j _nn.NumberOfHidden + 1; j+) /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 between input & hidden layer for (int i = 0; i _nn.NumberOfHidden; i+) for (int j = 0; j _nn.NumberOfInputs + 1; j+) /use momentum (delta values from last pass), /to ensure moved in correct direction _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： Tra