介紹神經(jīng)網(wǎng)絡(luò)算法在機(jī)械結(jié)構(gòu)優(yōu)化中的應(yīng)用的例子

(大家要學(xué)習(xí)的時(shí)候只需要把輸入輸出變量更改為你自己的數(shù)據(jù)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(jìn)步)。

把一個(gè)結(jié)構(gòu)的8個(gè)尺寸參數(shù)設(shè)計(jì)為變量，如上圖所示，

對(duì)應(yīng)的質(zhì)量，溫差，面積作為輸出。用神經(jīng)網(wǎng)絡(luò)擬合變量與輸出的數(shù)學(xué)模型，首相必須要有數(shù)據(jù)來源，這里我用復(fù)合中心設(shè)計(jì)法則構(gòu)造設(shè)計(jì)點(diǎn)，根據(jù)規(guī)則，八個(gè)變量將構(gòu)造出81個(gè)設(shè)計(jì)點(diǎn)。然后在ansys

workbench中進(jìn)行81次仿真(先在proe建模并設(shè)置變量，將模型導(dǎo)入wokbench中進(jìn)行相應(yīng)的設(shè)置，那么就會(huì)自動(dòng)的完成81次仿真，將結(jié)果導(dǎo)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?yàn)楸救俗隽?1組仿真試驗(yàn)，這里的矩陣后面有轉(zhuǎn)置符號(hào)，在神經(jīng)網(wǎng)絡(luò)模型中，輸入P的是8X81的矩陣(把程序復(fù)制過來之后格式?jīng)]對(duì)齊，大家自己調(diào)整一下啦)，對(duì)應(yīng)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(biāo)矢量

[PP,ps]=mapminmax(P,-1,1); %把P歸一化處理變?yōu)閜p，在范圍(-1,1)內(nèi)

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

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

% 創(chuàng)建三層前向神經(jīng)網(wǎng)絡(luò),隱層神經(jīng)元為15輸出層神經(jīng)元為3

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

%

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

% 訓(xùn)練函數(shù)：traingdm，功能：以動(dòng)量BP算法修正神經(jīng)網(wǎng)絡(luò)的權(quán)值和閾值。

% 它的相關(guān)特性包括：

% epochs：訓(xùn)練的次數(shù)，默認(rèn)：100

% goal：誤差性能目標(biāo)值，默認(rèn)：0

% lr：學(xué)習(xí)率，默認(rèn)：0.01

% max_fail：確認(rèn)樣本進(jìn)行仿真時(shí)，最大的失敗次數(shù)，默認(rèn)：5

% mc：動(dòng)量因子，默認(rèn)：0.9

% min_grad：最小梯度值，默認(rèn)：1e-10

% show：顯示的間隔次數(shù)，默認(rèn)：25

% time：訓(xùn)練的最長(zhǎng)時(shí)間，默認(rèn)：inf

%

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

inputWeights=net.IW{1,1}?%當(dāng)前輸入層權(quán)值和閾值

inputbias=net.b{1}

% 當(dāng)前網(wǎng)絡(luò)層權(quán)值和閾值

layerWeights=net.LW{2,1}

layerbias=net.b{2}

% 設(shè)置網(wǎng)絡(luò)的訓(xùn)練參數(shù)

net.trainParam.show = 2;

net.trainParam.lr = 0.05;

net.trainParam.mc = 0.9;

net.trainParam.epochs =10000;

net.trainParam.goal =

1e-3;

% 調(diào)用 TRAINGDM 算法訓(xùn)練 BP 網(wǎng)絡(luò)(在構(gòu)建net中有說明)

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

A = sim(net,PP) ; % 對(duì) BP 網(wǎng)絡(luò)進(jìn)行仿真，

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

對(duì)A矩陣進(jìn)行反歸一化處理()

% 計(jì)算仿真誤差

E = T - A

MSE=mse(E)

echo off

按上面的運(yùn)行之后結(jié)果如圖所示。

如果輸出值與目標(biāo)值完全相等則R=1，這里已經(jīng)非常接近了，說明效果擬合效果還是可以的，右圖是訓(xùn)練過程的平方和誤差變化，達(dá)到我們指定的誤差0.001時(shí)候，訓(xùn)練停止。

總結(jié)

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