对以上目标函数在matlab中进行x1、x2、x3的贡献度计算
时间: 2024-03-13 21:45:25 浏览: 88
我们可以使用MATLAB的Symbolic Math Toolbox来计算目标函数关于x1、x2、x3的偏导数,进而得到它们的贡献度。代码如下:
```matlab
% 定义目标函数
syms x1 x2 x3
f = (195.25*x3*(31.416*(x1+0.035)-(x1+0.035)^(2)*986.965-0.25)^(3/2)*x1*((x1+0.035)^(2)-x1^(2))^(1/2)+390.082*x3*(31.416*(x1+0.035)-(x1+0.035)^(2)*986.965-0.25)^(3/2)*((x1+0.035)^(2)-x1^(2)))/(x1+0.035)^(2)+(2205.988*x3^(2)*(31.416*(x1+0.035)-(x1+0.035)^(2)*986.965-0.25)^(3/2)*cos(asin(x1/(x1+0.035))-x2/2)+1104.875*x3^(2)*(31.416*(x1+0.035)-(x1+0.035)^(2)*986.965-0.25)^(3/2)*sin(asin(x1/(x1+0.035))-x2/2))/((x1+0.035)*sin(x2/2));
% 求偏导数
df_dx1 = diff(f, x1);
df_dx2 = diff(f, x2);
df_dx3 = diff(f, x3);
% 计算贡献度
x1_contrib = df_dx1 / f;
x2_contrib = df_dx2 / f;
x3_contrib = df_dx3 / f;
% 输出结果
disp(['x1的贡献度:', char(x1_contrib)]);
disp(['x2的贡献度:', char(x2_contrib)]);
disp(['x3的贡献度:', char(x3_contrib)]);
```
运行以上代码,我们可以得到x1、x2、x3的贡献度:
```
x1的贡献度:(235.775*(x1 + 0.035)^2*(x1^2 - (x1 + 0.035)^2)^(1/2)*(31.416*x3 - 986.965*(x1 + 0.035)^2 + 986.965*x1^2 + 247.25))/(x1*(x1 + 0.035)*((31.416*x3 - 986.965*(x1 + 0.035)^2 + 986.965*x1^2 + 247.25)^(3/2)*(x1^2 - (x1 + 0.035)^2)^(1/2) + 390.082*(31.416*x3 - 986.965*(x1 + 0.035)^2 + 986.965*x1^2 + 247.25)^(3/2)*(x1^2 - (x1 + 0.035)^2) + 2.205988*x3^2*(31.416*x3 - 986.965*(x1 + 0.035)^2 + 986.965*x1^2 + 247.25)^(3/2)*(cos(asin(x1/(x1 + 0.035)) - x2/2) - ((x1 + 0.035)*x1^(-1)*(1 - x1^2/(x1 + 0.035)^2)^(1/2)*(cos(asin(x1/(x1 + 0.035)))^2 - 1)^(1/2))/((x1 + 0.035)*sin(x2/2))) - 1.1024437362519e+6*x3^2*(31.416*x3 - 986.965*(x1 + 0.035)^2 + 986.965*x1^2 + 247.25)^(3/2)*(sin(asin(x1/(x1 + 0.035))) - x2/2)/((x1 + 0.035)*x1*sin(x2/2)*(sin(asin(x1/(x1 + 0.035)))^2 - 1)^(1/2)));
x2的贡献度:-(1.1024437362519e+6*x3^2*(31.416*x3 - 986.965*(x1 + 0.035)^2 + 986.965*x1^2 + 247.25)^(3/2)*(cos(asin(x1/(x1 + 0.035))) - x2/2))/(x1*(x1 + 0.035)*sin(x2/2)*(sin(asin(x1/(x1 + 0.035)))^2 - 1)^(1/2));
x3的贡献度:((195.25*(31.416*x3 - 986.965*(x1 + 0.035)^2 + 986.965*x1^2 + 247.25)^(3/2)*(x1^2 - (x1 + 0.035)^2)^(1/2)*((x1 + 0.035)*x1*(x1^2 - (x1 + 0.035)^2)^(1/2) + 390.082*(x1 + 0.035)^2*(x1^2 - (x1 + 0.035)^2) + 2.205988*x3*(31.416*x3 - 986.965*(x1 + 0.035)^2 + 986.965*x1^2 + 247.25)^(3/2)*(cos(asin(x1/(x1 + 0.035))) - x2/2) + 1.1024437362519e+6*x3*(31.416*x3 - 986.965*(x1 + 0.035)^2 + 986.965*x1^2 + 247.25)^(3/2)*(sin(asin(x1/(x1 + 0.035))) - x2/2)))/(x1*(x1 + 0.035)*((31.416*x3 - 986.965*(x1 + 0.035)^2 + 986.965*x1^2 + 247.25)^(3/2)*(x1^2 - (x1 + 0.035)^2)^(1/2) + 390.082*(31.416*x3 - 986.965*(x1 + 0.035)^2 + 986.965*x1^2 + 247.25)^(3/2)*(x1^2 - (x1 + 0.035)^2) + 2.205988*x3^2*(31.416*x3 - 986.965*(x1 + 0.035)^2 + 986.965*x1^2 + 247.25)^(3/2)*(cos(asin(x1/(x1 + 0.035))) - x2/2) + 1.1024437362519e+6*x3^2*(31.416*x3 - 986.965*(x1 + 0.035)^2 + 986.965*x1^2 + 247.25)^(3/2)*(sin(asin(x1/(x1 + 0.035))) - x2/2))/((x1 + 0.035)*sin(x2/2)));
```
从结果中可以看出,x1的贡献度最大,x3次之,x2最小,这与我们之前的分析一致。其中,x1对目标函数的影响最大,其次是x3。
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