介紹神經網絡算法在機械結構優化中的應用的例子

(大家要學習的時候只需要把輸入輸出變量更改為你自己的數據既可以了，如果看完了還有問題的話可以加我微博“極南師兄”給我留言，與大家共同進步)。

把一個結構的8個尺寸參數設計為變量，如上圖所示，

對應的質量，溫差，面積作為輸出。用神經網絡擬合變量與輸出的數學模型，首相必須要有數據來源，這里我用復合中心設計法則構造設計點，根據規則，八個變量將構造出81個設計點。然后在ansys

workbench中進行81次仿真(先在proe建模并設置變量，將模型導入wokbench中進行相應的設置，那么就會自動的完成81次仿真，將結果導出來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

]';%注意因為本人做了81組仿真試驗，這里的矩陣后面有轉置符號，在神經網絡模型中，輸入P的是8X81的矩陣(把程序復制過來之后格式沒對齊，大家自己調整一下啦)，對應的下面的輸出T的是3x81的矩陣。

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 為目標矢量

[PP,ps]=mapminmax(P,-1,1); %把P歸一化處理變為pp，在范圍(-1,1)內

%把T歸一化處理變TT，在范圍(-1,1)內，歸一化主要是為了消除不通量崗對結果的影響

[TT,ps]=mapminmax(T,-1,1);

% 創建三層前向神經網絡,隱層神經元為15輸出層神經元為3

net=newff(minmax(PP),[15,3],{'tansig','purelin'},'traingdm')

%

---------------------------------------------------------------

% 訓練函數：traingdm，功能：以動量BP算法修正神經網絡的權值和閾值。

% 它的相關特性包括：

% epochs：訓練的次數，默認：100

% goal：誤差性能目標值，默認：0

% lr：學習率，默認：0.01

% max_fail：確認樣本進行仿真時，最大的失敗次數，默認：5

% mc：動量因子，默認：0.9

% min_grad：最小梯度值，默認：1e-10

% show：顯示的間隔次數，默認：25

% time：訓練的最長時間，默認：inf

%

---------------------------------------------------------------

inputWeights=net.IW{1,1}?%當前輸入層權值和閾值

inputbias=net.b{1}

% 當前網絡層權值和閾值

layerWeights=net.LW{2,1}

layerbias=net.b{2}

% 設置網絡的訓練參數

net.trainParam.show = 2;

net.trainParam.lr = 0.05;

net.trainParam.mc = 0.9;

net.trainParam.epochs =10000;

net.trainParam.goal =

1e-3;

% 調用 TRAINGDM 算法訓練 BP 網絡(在構建net中有說明)

[net,tr]=train(net,PP,TT);

A = sim(net,PP) ; % 對 BP 網絡進行仿真，

A=mapminmax('reverse',A,ps) ; %

對A矩陣進行反歸一化處理()

% 計算仿真誤差

E = T - A

MSE=mse(E)

echo off

按上面的運行之后結果如圖所示。

如果輸出值與目標值完全相等則R=1，這里已經非常接近了，說明效果擬合效果還是可以的，右圖是訓練過程的平方和誤差變化，達到我們指定的誤差0.001時候，訓練停止。

總結

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