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附 錄 A
Genetic Algorithm Optimization On Crane
Transmission In Neural Network
Abstract：The fuzzy optimization mathematic model is established to design crane transmission. The method of second-class comprehensive evaluation was used by the optimal level cut set, thus the optimal level value of every fuzzy constraint can be attained, and the fuzzy optimization is transformed into the usual optimization. The Fast Back Propagation of neural network algorithm is adopted to train feed-forward networks so as to fit relative coefficient. Then the fitness function with penalty terms is built by penalty strategy, neural networks program is recalled, solver functions of Genetic Algorithm Toolbox of Matlab software are adopted to solve the optimization mathematic model.
Index ：Terms-Crane Mechanism; Genetic Algorithm Optimization; Neural Networks.
FUZZY OPTIMIZATION MATHEMATICAL MODEL OF TRACTION MECHANISM
Design sample: A involute helicoidal worm gearing is adopted in crane transmission, which has principal parameters as follows: rated power Pe=1.5kw, output speed 28.4r/min, output torque T2=295.87N.m, gear ratio u=49.3, working load factor k=1.05. The worm is machined and heat-treated 45 steel and the tooth corona of gear is made of machined ZQA1 9-4
A. Specifying objective function
In order to economize nonferrous metal of tooth corona of worm gear, the objective function should be specified that the volume of tooth corona of worm gear in traction
mechanism incline to minimum=1.5. According to Fig.1, d0, di2 and b are outer diameters, inner diameters and face width of tooth corona of worm gear respectively, thus the volume of tooth corona is;
where
Therefore the objective function is
where m-module of gear;
d1-reference diameter of gear;
z1-number of start of worm.
Fig.1.the configure drawing of worm gear
B. Selecting design variables
According to equation of the objective function, Z1 ,m,d1should be selected as design variables, that is:
C. Establishing fuzzy constraints
Considering the random character of the value of design parameters and some factors whose value is very indefinite such as loading property and material quality, the fuzzy
constraints are set up, including the property and boundary constraints.
1)Limit of number of start of worm: to power
drive, z1=1~2;
2)Limit of module of gear:2≤m≤8;
3)Limit of the lead angle γ of the worm for guaranteeing
the efficiency of the worm gearing:
3≤γ≤8,tan γ=mz1/d1;
4)Constraint of contact strength of worm gear:
Where Ze-the material elasticity factor,
σh-the contact stresses of worm gear;
[σh]-the fuzzy value of the allowable contact stresses of worm gear.
5)Constraint of tooth beam strength of worm gear:
Where σf the beam stress of gear teeth;
[σf]-fuzzy value of the allowable bending stress of worm gear teeth;
Yf -the profile factor for worm gear teeth.
6)Constraint of the stiffness of worm:
The worm is supported between two bearings, if the worm shaft bends too much, that is, the teeth will not mesh properly, and the result will be excessive wear and early failure. So the maximum deflection is
Where Ft1-the tangential force of the worm(N),
F r1-the radial force of the worm(N),
E-the modulus of elasticity(Mpa),
I-the inertia moment of the dangerous cross-section of worm(mm4)
L-the distance of the worm bearings (mm),
L=0 .9muz1.
IV.FUZZY OPTIMIZATION MATHEMATICAL MODEL OF TRACTION MECHANISM
The key of this method is how to decide the optimal level value. Several factors, such as factor class, factor fuzziness and the different influence of the factors on the different optimal level values, were considered and the method of second-class comprehensive evaluation was used based on the optimal level cut set, thus the optimal level value
λ*of every fuzzy constraint can be attained, that is λ*=0.71.Therefore the fuzzy optimization problem is converted into the usual optimization problem.
V.TRAINING RELATION COEFFICIENT BY NEURAL NETWORKS
Neural networks are composed of simple element operating in parallel. These elements are inspired by biological nervous systems. As in nature, the network function is determined largely by the connections between elements. We can train a neural network to perform a particular function by adjusting the values of the connections
(weights)between elements. Commonly neural networks are adjusted, or trained, so that a particular input leads to a specific target output based on a comparison of the output and the target, until the network output matches the target. Some points on relation curve between teeth number Z2 and the profile factor Yf of worm gear are selected as training sample data, the Fast Back Propagation are adopted to train feed-forward networks, the weights and biases of the network are updated. Then neural networks is simulated by the function of Neural Networks Toolbox in MATLAB. Program as follows:
Z2=0:10:90;YF=[2.58,2.5176,2.4566,2.3972,2.3392,2.2825,2.2273,2.1734,2.1208,2.0695]
n1=5;[W1,b1,W2,b2]= initff(Z2,n1,’tansig’,YF,’purelin’);
fpd=100;mne=20000;sse=0.001;lr=0.01;tp=[fpd, mne, sse, lr];
[W1,b1,W2,b2,te,tr]=trainbpx(W1,b1,’tansig’,W2,b2,’purelin’,Z2,YF,tp)
y=simuff(Z2,W1,b1,’tansig’,W2,b2,’purelin’)
VI..SOLVING USUAL OPTIMIZATION MATHEMATICAL MODEL BY GENETIC ALGORITHM TOOLBOX
One key to successfully solving many types of optimization problems is choosing the method that best suits the problem. The Genetic Algorithm and Direct Search Toolbox is a collection of functions that extend the capabilities of the Optimization Toolbox and the MATLAB? numeric computing environment. The Genetic Algorithm Toolbox includes routines for solving optimization problems using Genetic algorithm Direct search. These algorithms enable you to solve a variety of optimization problems that lie outside the scope of the standard Optimization Toolbox. Firstly the fitness function with penalty terms is built by penalty strategy with addition type, and the fitness function is programmed in MATLAB language, and above neural networks program fitting the profile factor of worm gear teeth is recalled, then the nonlinear constraints function are
programmed and the solver functions of Genetic Algorithm Toolbox are adopted. Program as follows:
options= gaoptim set (‘PopulationSize’,20);
options=gaoptimset(‘Generations',100);
options=gaoptimset(‘CrossoverFraction’0.95, ’MigrationFraction’0.01);
options=gaoptimset('SelectionFcn', selection-tournament,
’CrossoverFcn’, cross over scattered,’ Mutation Fcn’,
Mutation gaussian); nvars=3;lb=[1;2;10];ub=[2;8;150];
[x, Fval, exit Flag, Output]=ga(@fitnessfun, nvars,
[],[],[],[],lb, ub, @yueshufun, options)
After function counting 108 times and iterating 326
times, the final running output of above programming is:
x1=1.0102,x2=4.8889,x3=78.2222,f(X)=1090628.
VII..CONCLUSION
This paper explored the methods available in the Genetic Algorithm and Neural Networks Toolbox. Compared with standard optimization algorithms(f(X)=1269257.5),
the objective function optimum in the genetic algorithm is about16 .37%less than the former. Therefore we saw that the genetic algorithm is an effective solver for non smooth problems. Additionally, we found that the genetic algorithm can be combined with other solvers, such as fuzzy logic and neural networks, to efficiently find a more accurate solution.
TABLE I
OUTPUT OF STANDARD OPTIMIZATION AND GENETIC ALGORITHM
附 錄 B
在神經(jīng)網(wǎng)絡(luò)中起重機(jī)傳輸遺傳算法最佳化
摘要：那失真的適宜數(shù)學(xué)模型在設(shè)計(jì)起重機(jī)傳輸建立。那方法的二等的綜合評(píng)價(jià)被那最佳的把割集弄平整使用經(jīng)由，那方法的二等的綜合評(píng)價(jià)是使用經(jīng)由那最佳的把割集弄平整，因此每個(gè)模糊約束那最佳的價(jià)值可以是獲得弄平整，并且那模糊的最佳化是被變成那通常的最佳化。神經(jīng)網(wǎng)絡(luò)算法那背面加固增長(zhǎng)的將采用到連續(xù)性前饋網(wǎng)絡(luò)如此適合相關(guān)系數(shù)。然后那用罰款期限是構(gòu)成由罰款策略裝配功能、神經(jīng)網(wǎng)絡(luò)計(jì)劃是召回、解算機(jī)功能的遺傳算法工具箱的matlab軟件是采用到解決那最佳化數(shù)學(xué)模型。
索引詞：起重機(jī)機(jī)構(gòu)；遺傳算法最佳化；神經(jīng)網(wǎng)絡(luò)。
模糊的最佳化數(shù)學(xué)模型的牽引機(jī)構(gòu)
設(shè)計(jì)漸開(kāi)線螺旋狀的蝸輪傳動(dòng)裝置是采民用在起重機(jī)傳輸，哪個(gè)有主參數(shù)如下：額定功率Pe=1.5kw、輸出速度28.4r／min、輸出轉(zhuǎn)矩T2=2 295.87n.m、齒輪比U=49.3、工作負(fù)荷因素k=1.05, 那螺旋是機(jī)器和經(jīng)加熱處理材45鋼和那由ZQA19-4構(gòu)成的齒輪的齒輪冠.
A指定目標(biāo)函數(shù)
為了節(jié)省有色金屬的齒輪冠的螺旋齒輪，那目標(biāo)函數(shù)將應(yīng)指定那那大量的齒輪冠的螺旋齒輪在牽引機(jī)構(gòu)向最小的按照?qǐng)D1傾斜，d0、 di2,b分別是外徑、內(nèi)徑和螺旋齒輪的齒面寬冠，因此那是大量的牙齒冠；
由
所以那目標(biāo)函數(shù)是
m齒輪模數(shù)；d1齒輪分度圓直徑；z1螺旋開(kāi)始的齒數(shù)。
圖1.渦輪傳動(dòng)裝置圖
B反面選擇設(shè)計(jì)參數(shù)按照等式的那目標(biāo)函數(shù)、,m、d1將應(yīng)雖然設(shè)計(jì)參數(shù)選擇，但是簡(jiǎn)而言之：
C建立模糊約束
認(rèn)為Φ值的隨機(jī)特性設(shè)計(jì)參數(shù)和一些因素誰(shuí)的價(jià)值很不定的比如負(fù)荷性質(zhì)和材料品質(zhì)、那模糊約束是建立、包括那性質(zhì)和邊界約束在內(nèi)。
1）極限的開(kāi)始的螺旋的齒數(shù)：z1=1~2;；
2）極限的齒輪的模數(shù):2≤m≤8；
3）極限的那導(dǎo)程角螺旋的因?yàn)楸ＷC蝸輪傳動(dòng)裝置的效率：3≤γ≤8,tan γ=mz1/d1;
4）約束的接觸強(qiáng)度的螺旋齒輪：
那材料彈性因素、
σh那接觸應(yīng)力的螺旋齒輪；
[σh]-那模糊的Φ值那容許接觸應(yīng)力的螺旋齒輪。
5）約束的牙齒梁強(qiáng)度的螺旋齒輪：
那橫梁強(qiáng)調(diào)的輪齒；
[σf]-模糊的Φ值那容許彎曲應(yīng)力的螺旋齒輪牙齒；
Yf-那輪廓因素因?yàn)槁菪X輪牙齒。
６）約束稠的的的螺旋：那螺旋信息系統(tǒng)支持
在...之間二軸承、如果那蝸桿軸彎曲多，那就是說(shuō)，那牙齒不會(huì)適當(dāng)?shù)鼐W(wǎng)孔，那么，那結(jié)果將要成為...的過(guò)度磨損和過(guò)早損壞所以極限偏轉(zhuǎn)是
ft1-螺旋的切向力（N）、
F r1-螺旋的徑向力（N）、
E-那彈性模數(shù)（Mpa)、
I-危險(xiǎn)截面的慣性矩的螺旋（mm4）
L-蝸桿軸承的距離（毫米）、L=9muz1
IV.模糊的最佳化數(shù)學(xué)模型的牽引機(jī)構(gòu)
這個(gè)的鍵方法是如何決定那最佳的把價(jià)值個(gè)別的因素弄平整、比如因素通信鏈路分析器系統(tǒng)、因素模糊和因素的不同的影響上去那不同的最佳的把價(jià)值弄平整、是認(rèn)為和那方法的二等的綜合評(píng)價(jià)是使用以那最佳的把割集弄平整為基礎(chǔ)，因此那最佳的把價(jià)值＊的每模糊約束可以是獲得弄平整、簡(jiǎn)而言之＊那模糊的優(yōu)化問(wèn)題是變?yōu)槟峭ǔ５膬?yōu)化問(wèn)題。
V.連續(xù)性相關(guān)系數(shù)由神經(jīng)網(wǎng)絡(luò)
神經(jīng)網(wǎng)絡(luò)由...組成簡(jiǎn)單的元件并行操作這個(gè)元件被生物學(xué)的神經(jīng)的體系當(dāng)做本質(zhì)上鼓舞、那網(wǎng)絡(luò)函數(shù)決意大量地由那關(guān)系在...之間元件我們可以訓(xùn)練一神經(jīng)網(wǎng)絡(luò)執(zhí)行一特定函數(shù)由調(diào)整那Φ值那關(guān)系（重量）在...之間元件通常神經(jīng)網(wǎng)絡(luò)是調(diào)整，否則連續(xù)性，結(jié)果一特別的輸入導(dǎo)致一具體任務(wù)產(chǎn)量以一比較產(chǎn)量的和那靶子為基礎(chǔ)、直到那網(wǎng)絡(luò)產(chǎn)量相配那靶子。
一些漲若干點(diǎn)相關(guān)曲線在齒數(shù)和那輪廓因素的螺旋齒輪被選為連續(xù)性樣本數(shù)據(jù)之間、那背面加固繁殖將采用到連續(xù)性前饋網(wǎng)絡(luò)、網(wǎng)絡(luò)的重量和偏見(jiàn)是更新然后神經(jīng)網(wǎng)絡(luò)被那功能的神經(jīng)網(wǎng)絡(luò)工具箱在matlab模擬。計(jì)劃如下：
Z2=0:10:90;YF=[2.58,2.5176,2.4566,2.3972,2.3392,2.28 25,2.2273,2.1734,2.1208,2.0695];
n1=5;[W1,b1,W2,b2]= initff(Z2,n1,’tansig’,YF,’purelin’);
fpd=100;mne=20000;sse=0.001;lr=0.01;tp=[fpd, mne, sse, lr];
[W1,b1,W2,b2,te,tr]=trainbpx(W1,b1,’tansig’,W2,b2,’purelin’,Z2,YF,tp)
y=simuff(Z2,W1,b1,’tansig’,W2,b2,’purelin’)
VI..解決通常的最佳化數(shù)學(xué)模型由遺傳算法工具箱
單密鑰到成功地解決許多種優(yōu)化問(wèn)題是選擇那方法那井衣服那問(wèn)題那遺傳算法和直接檢索工具箱是許多功能那伸展那做...的能力那最佳化工具箱和那matlab？數(shù)字計(jì)算環(huán)境那遺傳算法工具箱包括常規(guī)因?yàn)榻鉀Q優(yōu)化問(wèn)題與罰款期限是用加法類型造由罰款策略一起使用遺傳算法直接檢索這算法使你解決種種的優(yōu)化問(wèn)題那謊言超出那標(biāo)準(zhǔn)最佳化工具箱范圍。第一那適合功能，并且那適合功能是編制matlab語(yǔ)言、和在神經(jīng)網(wǎng)絡(luò)計(jì)劃適合那輪廓因素的螺旋齒輪牙齒是召回上、然后那非直線型限制功能是程序和那解算機(jī)功能的遺傳算法工具箱是采用。
程序如下：
選擇權(quán)gaoptimset（總體大小 ,20）；
選擇權(quán)gaoptimset（世代,100）；
選擇權(quán)gaoptimset（交叉分?jǐn)?shù)'0.95,' 分?jǐn)?shù)0.01）；
選擇權(quán)gaoptimset（s選擇完全約束的非晶網(wǎng)、選擇錦標(biāo)賽、、交叉分散、變化高斯型曲線）；nvars=3;lb=[1;2;10];ub=[2;8;150];[x,Fval, exitFlag, Output]=ga(@fitnessfun, nvars,[],[],[],[],lb, ub, @yueshufun, options)）
在功能計(jì)算108次并重復(fù)次時(shí)以后，那最后的焊道上面程序的產(chǎn)量是：
x1=1.0102,x2=4.8889,x3=78.2222,f(X)=1090628.
VII..結(jié)論
這個(gè)紙?zhí)綔y(cè)那方法有效范圍那遺傳算法和神經(jīng)網(wǎng)絡(luò)工具箱和...相比標(biāo)準(zhǔn)最優(yōu)化算法f(X)=1269257.5)、那目標(biāo)函數(shù)在遺傳算法的最佳的是 大概16 .37%少于比前者.因此我們努力設(shè)法使那遺傳算法是一有效的解算機(jī)因?yàn)閚onsmooth問(wèn)題.加之、我們發(fā)現(xiàn)那遺傳算法可以與...化合其他的解算機(jī)、比如模糊邏輯和神經(jīng)網(wǎng)絡(luò)、有效地發(fā)現(xiàn)一更精確的解答。
表格1標(biāo)準(zhǔn)最佳化的產(chǎn)量和遺傳算法
解算機(jī)
X1
X2
X3
F(X)
標(biāo)準(zhǔn)最佳化
1.0501
4.3574
78.4517
1269257.5
遺傳算法
1.0102
4.8889
78.2222
1090628