隋新武

黑龙江财经学院华业论文（设计）基于BP神经网络的非线性函数拟合系统设计摘要随着工业的快速进步与发展，数据拟合在工业应用中的作用越来越大。在实际的工程问题中，存在着许多复杂的工业模型，这些模型无法用数学公式表达。为了更精确地控制被控对象，数学模型的准确性是首要因素，因此非线性拟合模型在控制系统辨识中起着举足轻重的地位。针对上述问题，设计一种基于B神经网络的非线性函数拟合系统。首先，以MATLAB为仿真平台，设计非线性公式，用MATLAB计算生成非线性数据：然后，采用BP神经网络为拟合模型，通过实验分析确定隐藏层个数、激活函数类型和学习率数值等相关模型参数：最后，通过选择均方误差MSE、平均绝对误差MAE和均方根误差RMSE为评价指标，对数据拟合模型进行训练和测试。实验结果表明，设计模型的平均绝对误差MAE为0.0090368，均方误差MSE为0.0063983，均方根误差RMSE为0.07999，满足设计要求，验证了算法的有效性。关键词：非线性拟合：激活函数；BP神经网络；MATLAB仿真黑龙江财经学院华业论文（设计）Design of nonlinear function fitting system based on BPneural networkAbstractWith the rapid progress and development of industry,data fitting plays an increasinglyimportant role in industrial application.In practical engineering problems,there exist manyindustrial models which cannot be expressed by mathematical models.In order to control thecontrolled object more accurately,the accuracy of mathematical model is the first factor,sothe nonlinear fitting model plays an important role in the identification of control system.Tosolve these problems,this paper designs a nonlinear function fitting system based on BPneural network.Firstly,using MATLAB as the simulation platform,the nonlinear formula isdesigned,and the nonlinear data is calculated and generated by MATLAB.Then,BP neuralnetwork was used as the fitting model,and the model parameters such as the number ofhidden layers,the type of activation function and the value of learning rate were determinedthrough experimental analysis.Finally,MSE,MAE and RMSE were selected as evaluationindexes to train and test the data fitting model.The experimental results show that the MAE,MSE and RMSE of the designed model are 0.0090638,0.0063983 and 0.07999,which meetthe design requirements and verify the effectiveness of the algorithm.Key words:nonlinear fitting;activation function;BP neural network;MATLABsimulation0黑龙江财经学院华业论文（设计）目录绪论…1非线性函数拟合研究相关概述1.1课题研究的背景及意义1.2国内外研究现状....……21.3论文章节安排.....42非线性函数的设计......….52.1非线性函数概述.·2.2数据集的生成.....2.2.1 MATLAB数值计算.....52.3数据可视化....52.4数据集的划分与保存.....3基于BP神经网络的非线性拟合模型设计….73.1人工神经网络概述.....·73.2BP神经网络基本原理...73.3激活函数......….93.3.1 sigmoid激活函数.·3.3.2Tanh激活函数..93.3.3Relu激活函数...103.4损失函数.……103.4.1MSE均方误差...113.4.2RMSE均方根误差..113.4.3MAE平均绝对误差113.5梯度下降算法....··….124实验分析与结果..134.1实验平台的搭建........134.2数据归一化.......144.2.1最大-最小归一化..…….144.2.2Z-Score归一化.............144.3BP神经网络模型的结构设计原则......144.3.1网络层数的确定......144.3.2输入数据和输出数据的确定..................144.3.3各层节点的设计原则.......黑龙江财经学院华业论文（设计）4.4神经网络结构设计和训练..154.4.1神经网络模型隐含层节点数的确定...............164.4.2神经网络模型学习率的确定..........164.4.3神经网络模型训练及仿真结果.17结论……...20参考文献.…21致谢.……….23附录.0