MNIST神经网络matlab 神经网络matlab案例

介绍神经网络算法在机械结构优化中的应用的例子

(大家要学习的时候只需要把输入输出变量更改为你自己的数据既可以了，如果看完了还有问题的话可以加我微博“极南师兄”给我留言，与大家共同进步)。

把一个结构的8个尺寸参数设计为变量，如上图所示，

对应的质量，温差，面积作为输出。用神经网络拟合变量与输出的数学模型，首相必须要有数据来源，这里我用复合中心设计法则构造设计点，根据规则，八个变量将构造出81个设计点。然后在ansys

workbench中进行81次仿真(先在proe建模并设置变量，将模型导入wokbench中进行相应的设置，那么就会自动的完成81次仿真，将结果导出来exceel文件)

Matlab程序如下

P=
[20 2.5 6 14.9
16.5 6 14.9 16.5
15 2.5 6 14.9
16.5 6 14.9 16.5
25 2.5 6 14.9
16.5 6 14.9 16.5
20 1 6 14.9
16.5 6 14.9 16.5
20 4 6 14.9
16.5 6 14.9 16.5
20 2.5 2 14.9 16.5 6 14.9 16.5
20 2.5 10 14.9
16.5 6 14.9 16.5
20 2.5 6 10 16.5
6 14.9 16.5
20 2.5 6 19.8 16.5
6 14.9 16.5
20 2.5 6 14.9
10 6 14.9 16.5
20 2.5 6 14.9
23 6 14.9 16.5
20 2.5 6 14.9 16.5
2 14.9 16.5
20 2.5 6 14.9 16.5
10 14.9 16.5
20 2.5 6 14.9 16.5
6 10 16.5
20 2.5 6 14.9 16.5
6 19.8 16.5
20 2.5 6 14.9 16.5
6 14.9 10
20 2.5 6 14.9 16.5
6 14.9 23
17.51238947 1.75371684 4.009911573 12.46214168 13.26610631 4.009911573 12.46214168 19.73389369
22.48761053 1.75371684 4.009911573 12.46214168 13.26610631 4.009911573 12.46214168 13.26610631
17.51238947 3.24628316 4.009911573 12.46214168 13.26610631 4.009911573 17.33785832 19.73389369
22.48761053 3.24628316 4.009911573 12.46214168 13.26610631 4.009911573 17.33785832 13.26610631
17.51238947 1.75371684 7.990088427 12.46214168 13.26610631 4.009911573 17.33785832 19.73389369
22.48761053 1.75371684 7.990088427 12.46214168 13.26610631 4.009911573 17.33785832 13.26610631
17.51238947 3.24628316 7.990088427 12.46214168 13.26610631 4.009911573 12.46214168 19.73389369
22.48761053 3.24628316 7.990088427 12.46214168 13.26610631 4.009911573 12.46214168 13.26610631
17.51238947 1.75371684 4.009911573 17.33785832 13.26610631 4.009911573 17.33785832 13.26610631
22.48761053 1.75371684 4.009911573 17.33785832 13.26610631 4.009911573 17.33785832 19.73389369
17.51238947 3.24628316 4.009911573 17.33785832 13.26610631 4.009911573 12.46214168 13.26610631
22.48761053 3.24628316 4.009911573 17.33785832 13.26610631 4.009911573 12.46214168 19.73389369
17.51238947 1.75371684 7.990088427 17.33785832 13.26610631 4.009911573 12.46214168 13.26610631
22.48761053 1.75371684 7.990088427 17.33785832 13.26610631 4.009911573 12.46214168 19.73389369
17.51238947 3.24628316 7.990088427 17.33785832 13.26610631 4.009911573 17.33785832 13.26610631
22.48761053 3.24628316 7.990088427 17.33785832 13.26610631 4.009911573 17.33785832 19.73389369
17.51238947 1.75371684 4.009911573 12.46214168 19.73389369 4.009911573 17.33785832 13.26610631
22.48761053 1.75371684 4.009911573 12.46214168 19.73389369 4.009911573 17.33785832 19.73389369
17.51238947 3.24628316 4.009911573 12.46214168 19.73389369 4.009911573 12.46214168 13.26610631
22.48761053 3.24628316 4.009911573 12.46214168 19.73389369 4.009911573 12.46214168 19.73389369
17.51238947 1.75371684 7.990088427 12.46214168 19.73389369 4.009911573 12.46214168 13.26610631
22.48761053 1.75371684 7.990088427 12.46214168 19.73389369 4.009911573 12.46214168 19.73389369
17.51238947 3.24628316 7.990088427 12.46214168 19.73389369 4.009911573 17.33785832 13.26610631
22.48761053 3.24628316 7.990088427 12.46214168 19.73389369 4.009911573 17.33785832 19.73389369
17.51238947 1.75371684 4.009911573 17.33785832 19.73389369 4.009911573 12.46214168 19.73389369
22.48761053 1.75371684 4.009911573 17.33785832 19.73389369 4.009911573 12.46214168 13.26610631
17.51238947 3.24628316 4.009911573 17.33785832 19.73389369 4.009911573 17.33785832 19.73389369
22.48761053 3.24628316 4.009911573 17.33785832 19.73389369 4.009911573 17.33785832 13.26610631
17.51238947 1.75371684 7.990088427 17.33785832 19.73389369 4.009911573 17.33785832 19.73389369
22.48761053 1.75371684 7.990088427 17.33785832 19.73389369 4.009911573 17.33785832 13.26610631
17.51238947 3.24628316 7.990088427 17.33785832 19.73389369 4.009911573 12.46214168 19.73389369
22.48761053 3.24628316 7.990088427 17.33785832 19.73389369 4.009911573 12.46214168 13.26610631
17.51238947 1.75371684 4.009911573 12.46214168 13.26610631 7.990088427 17.33785832 13.26610631
22.48761053 1.75371684 4.009911573 12.46214168 13.26610631 7.990088427 17.33785832 19.73389369
17.51238947 3.24628316 4.009911573 12.46214168 13.26610631 7.990088427 12.46214168 13.26610631
22.48761053 3.24628316 4.009911573 12.46214168 13.26610631 7.990088427 12.46214168 19.73389369
17.51238947 1.75371684 7.990088427 12.46214168 13.26610631 7.990088427 12.46214168 13.26610631
22.48761053 1.75371684 7.990088427 12.46214168 13.26610631 7.990088427 12.46214168 19.73389369
17.51238947 3.24628316 7.990088427 12.46214168 13.26610631 7.990088427 17.33785832 13.26610631
22.48761053 3.24628316 7.990088427 12.46214168 13.26610631 7.990088427 17.33785832 19.73389369
17.51238947 1.75371684 4.009911573 17.33785832 13.26610631 7.990088427 12.46214168 19.73389369
22.48761053 1.75371684 4.009911573 17.33785832 13.26610631 7.990088427 12.46214168 13.26610631
17.51238947 3.24628316 4.009911573 17.33785832 13.26610631 7.990088427 17.33785832 19.73389369
22.48761053 3.24628316 4.009911573 17.33785832 13.26610631 7.990088427 17.33785832 13.26610631
17.51238947 1.75371684 7.990088427 17.33785832 13.26610631 7.990088427 17.33785832 19.73389369
22.48761053 1.75371684 7.990088427 17.33785832 13.26610631 7.990088427 17.33785832 13.26610631
17.51238947 3.24628316 7.990088427 17.33785832 13.26610631 7.990088427 12.46214168 19.73389369
22.48761053 3.24628316 7.990088427 17.33785832 13.26610631 7.990088427 12.46214168 13.26610631
17.51238947 1.75371684 4.009911573 12.46214168 19.73389369 7.990088427 12.46214168 19.73389369
22.48761053 1.75371684 4.009911573 12.46214168 19.73389369 7.990088427 12.46214168 13.26610631
17.51238947 3.24628316 4.009911573 12.46214168 19.73389369 7.990088427 17.33785832 19.73389369
22.48761053 3.24628316 4.009911573 12.46214168 19.73389369 7.990088427 17.33785832 13.26610631
17.51238947 1.75371684 7.990088427 12.46214168 19.73389369 7.990088427 17.33785832 19.73389369
22.48761053 1.75371684 7.990088427 12.46214168 19.73389369 7.990088427 17.33785832 13.26610631
17.51238947 3.24628316 7.990088427 12.46214168 19.73389369 7.990088427 12.46214168 19.73389369
22.48761053 3.24628316 7.990088427 12.46214168 19.73389369 7.990088427 12.46214168 13.26610631
17.51238947 1.75371684 4.009911573 17.33785832 19.73389369 7.990088427 17.33785832 13.26610631
22.48761053 1.75371684 4.009911573 17.33785832 19.73389369 7.990088427 17.33785832 19.73389369
17.51238947 3.24628316 4.009911573 17.33785832 19.73389369 7.990088427 12.46214168 13.26610631
22.48761053 3.24628316 4.009911573 17.33785832 19.73389369 7.990088427 12.46214168 19.73389369
17.51238947 1.75371684 7.990088427 17.33785832 19.73389369 7.990088427 12.46214168 13.26610631
22.48761053 1.75371684 7.990088427 17.33785832 19.73389369 7.990088427 12.46214168 19.73389369
17.51238947 3.24628316 7.990088427 17.33785832 19.73389369 7.990088427 17.33785832 13.26610631
22.48761053 3.24628316 7.990088427 17.33785832 19.73389369 7.990088427 17.33785832 19.73389369
]';%注意因为本人做了81组仿真试验，这里的矩阵后面有转置符号，在神经网络模型中，输入P的是8X81的矩阵(把程序复制过来之后格式没对齐，大家自己调整一下啦)，对应的下面的输出T的是3x81的矩阵。
T=[150.749 2.28499 13.466
165.148 2.64021 9.6525
138.061 1.92976 17.2795
149.446 2.25704 13.766
151.642 2.31293 13.166
147.146 2.22947 14.062
154.131 2.3405 12.87
144.164 2.2576 13.76
155.889 2.31237 13.172
150.646 2.28499 13.466
150.621 2.28499 13.466
147.091 2.22947 14.062
154.166 2.3405 12.87
144.289 2.2576 13.76
155.553 2.31237 13.172
150.653 2.28499 13.466
150.704 2.28499 13.466
148.424 2.37609 12.4879
134.952 2.01917 16.3197
154.264 2.41865 12.0311
141.207 2.06864 15.7885
156.492 2.44051 11.7964
142.671 2.08358 15.6282
152.473 2.44664 11.7306
138.329 2.09663 15.488
159.696 2.41252 12.0969
145.947 2.05559 15.9287
155.401 2.41865 12.0311
141.73 2.06864 15.7885
157.408 2.45858 11.6024
144.1 2.10166 15.4341
163.483 2.50114 11.1455
150.483 2.15114 14.9029
154.111 2.3943 12.2924
140.418 2.03738 16.1242
149.253 2.40044 12.2266
135.997 2.05043 15.984
151.518 2.4223 11.9919
137.257 2.06537 15.8237
158.05 2.46485 11.535
143.739 2.11485 15.2925
153.641 2.3943 12.2924
140.723 2.03738 16.1242
158.956 2.43686 11.8355
146.933 2.08685 15.593
160.731 2.4768 11.4068
149.315 2.11987 15.2386
156.842 2.48293 11.341
145.17 2.13292 15.0984
156.942 2.45858 11.6024
143.948 2.10166 15.4341
152.503 2.44664 11.7306
138.486 2.09663 15.488
154.84 2.4685 11.4959
139.795 2.11157 15.3276
161.574 2.52914 10.845
147.502 2.17913 14.6024
156.975 2.44051 11.7964
143.06 2.08358 15.6282
162.688 2.50114 11.1455
150.483 2.15114 14.9029
164.588 2.54108 10.7168
153.024 2.18415 14.5485
160.908 2.52914 10.845
147.794 2.17913 14.6024
151.437 2.4223 11.9919
137.386 2.06537 15.8237
156.979 2.48293 11.341
144.915 2.13292 15.0984
159.167 2.50479 11.1063
146.229 2.14786 14.9381
155.699 2.49285 11.2345
140.767 2.14284 14.992
161.782 2.4768 11.4068
149.124 2.11987 15.2386
157.819 2.46485 11.535
143.8 2.11485 15.2925
159.553 2.50479 11.1063
146.186 2.14786 14.9381
166.512 2.56542 10.4554
153.896 2.21542 14.2129
]'; % T 为目标矢量
[PP,ps]=mapminmax(P,-1,1); %把P归一化处理变为pp，在范围(-1,1)内
%把T归一化处理变TT，在范围(-1,1)内，归一化主要是为了消除不通量岗对结果的影响
[TT,ps]=mapminmax(T,-1,1);
% 创建三层前向神经网络,隐层神经元为15输出层神经元为3
net=newff(minmax(PP),[15,3],{'tansig','purelin'},'traingdm')
%
---------------------------------------------------------------
% 训练函数：traingdm，功能：以动量BP算法修正神经网络的权值和阈值。
% 它的相关特性包括：
% epochs：训练的次数，默认：100
% goal：误差性能目标值，默认：0
% lr：学习率，默认：0.01
% max_fail：确认样本进行仿真时，最大的失败次数，默认：5
% mc：动量因子，默认：0.9
% min_grad：最小梯度值，默认：1e-10
% show：显示的间隔次数，默认：25
% time：训练的最长时间，默认：inf
%
---------------------------------------------------------------
inputWeights=net.IW{1,1} %当前输入层权值和阈值
inputbias=net.b{1}
% 当前网络层权值和阈值
layerWeights=net.LW{2,1}
layerbias=net.b{2}
% 设置网络的训练参数
net.trainParam.show = 2;
net.trainParam.lr = 0.05;
net.trainParam.mc = 0.9;
net.trainParam.epochs =10000;
net.trainParam.goal =
1e-3;
% 调用 TRAINGDM 算法训练 BP 网络(在构建net中有说明)
[net,tr]=train(net,PP,TT);
A = sim(net,PP) ; % 对 BP 网络进行仿真，
A=mapminmax('reverse',A,ps) ; %
对A矩阵进行反归一化处理()
% 计算仿真误差
E = T - A
MSE=mse(E)
echo off

按上面的运行之后结果如图所示。

如果输出值与目标值完全相等则R=1，这里已经非常接近了，说明效果拟合效果还是可以的，右图是训练过程的平方和误差变化，达到我们指定的误差0.001时候，训练停止。