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单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,数学建模与数学实验,神经网络,目的,内容,学习神经网络的基本原理与方法。,1,、人工神经元数学模型,4,、,BP,神经网络应用,3,、,BP,神经网络,Matlab,工具箱函数,2,、,BP,神经网络,一、人工神经元数学模型,BP,神经网络的拓扑结构如图所示。,1.BP,神经网络结构：,2,BP,神经网络学习算法及流程,以三层,BP,神经网络为例，它的训练过程包括以下几个步骤：,BP,神经网络的流程图：,三、,BP,神经网络,Matlab,工具箱函数,net=newff(PR, S1,S2,SN, TF1,TF2,TFN, BTF, BLF, PF),网络经过,177,次训练后，虽然网络的性能还没有达到,0,，但是输出的均方误差已经很小了，,MSE,2.95307e-006,，误差曲线如图,1,所示。为更直观地理解网络输出与目标向量之间的关系，见图,2,所示。, plot(P,T,-,P,Y,o),图,1 BP,神经网络训练误差曲线图 图,2,训练后,BP,神经网络仿真图,To Matlab exp12_4_1.m,BP,神经网络测试结果图,To Matlab exp12_4_2.m,To Matlab exp12_4_3.m,练习,1,、蠓虫分类问题,生物学家试图对两种蠓虫（,Af,与,Apf,）进行鉴别，依据的资料是触角和翅膀的长度，已经测得了,9,只,Af,和,6,只,Apf,的数据如下：,Af: (1.24,1.27),，,(1.36,1.74),，,(1.38,1.64),，,(1.38,1.82),，,(1.38,1.90),，,(1.40,1.70),，,(1.48,1.82),，,(1.54,1.82),，,(1.56,2.08),；,Apf: (1.14,1.82),，,(1.18,1.96),，,(1.20,1.86),，,(1.26,2.00),，,(1.28,2.00),，,(1.30,1.96).,（,i,）根据如上资料，如何制定一种方法，正确地区分两类蠓虫；,（,ii,）对触角和翼长分别为,(1.24,1.80),，,(1.28,1.84),与,(1.40,2.04),的三个标本，用所得到的方法加以识别；,（,iii,）设,Af,是宝贵的传粉益虫，,Apf,是某疾病的载体，是否应该修改分类方法,.,2,、人口预测下表是从,北京统计年鉴,中给出的,1980-2010,年的北京城近郊区户籍人口统计结果作为样本数据，,(1),建立人工神经网络模型,;(2),预测,2011,年的北京城近郊区户籍人口,.,数据处理后的样本数据：,样本用途,样本组数,输入一,输入二,输入三,输入四,输出,学,习,样,本,1,0.4984,0.5102,0.5213,0.534,0.5407,2,0.5102,0.5213,0.534,0.5407,0.5428,3,0.5213,0.534,0.5407,0.5428,0.553,4,0.534,0.5407,0.5428,0.553,0.5632,5,0.5407,0.5428,0.553,0.5632,0.5739,6,0.5428,0.553,0.5632,0.5739,0.5821,7,0.553,0.5632,0.5739,0.5821,0.592,8,0.5632,0.5739,0.5821,0.592,0.5987,9,0.5739,0.5821,0.592,0.5987,0.6043,10,0.5821,0.592,0.5987,0.6043,0.6095,11,0.592,0.5987,0.6043,0.6095,0.6161,12,0.5987,0.6043,0.6095,0.6161,0.6251,13,0.6043,0.6095,0.6161,0.6251,0.6318,14,0.6095,0.6161,0.6251,0.6318,0.6387,15,0.6161,0.6251,0.6318,0.6387,0.6462,16,0.6251,0.6318,0.6387,0.6462,0.6518,17,0.6318,0.6387,0.6462,0.6518,0.6589,18,0.6387,0.6462,0.6518,0.6589,0.6674,19,0.6462,0.6518,0.6589,0.6674,0.6786,20,0.6518,0.6589,0.6674,0.6786,0.6892,21,0.6589,0.6674,0.6786,0.6892,0.6988,22,0.6674,0.6786,0.6892,0.6988,0.7072,检,验,样,本,23,0.6786,0.6892,0.6988,0.7072,0.7132,24,0.6892,0.6988,0.7072,0.7132,0.7185,25,0.6988,0.7072,0.7132,0.7185,0.7309,26,0.7072,0.7132,0.7185,0.7309,0.7438,27,0.7132,0.7185,0.7309,0.7438,0.7496,
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