How can I find maximum value of this function???

Question

youn chan choi 2022-4-28

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1707190-how-can-i-find-maximum-value-of-this-function

回答： David Hill 2022-4-28

P1 = 25;
P2 = 37.5;
P3 = 20;
W1 = [5, 10];
W2 = [5, 10];
W3 = [5, 10];
L1 = [40, 60];
L2 = [25, 40];
L3 = [15, 25];
r1 = [6, 15];
r2 = [6, 15];
r3 = [6, 15];
T2 = [0.25*pi, 0.5*pi];
T3 = [0, 0.5*pi];
Fa = 1000
% Each moment arms
M1 = (P1^2+W1^2)/P1;
M2 = (P2^2+W2^2)/P2;
M3 = (P3^2+(sqrt((2*W3)^2-(P3-(L3-2*W3))^2)-W3)^2)/P3;
% Each contact Forces
PA = P3 + L2*cos(T3) + L1*cos(T2 + T3);
PB = P2 + L1*cost(T2);
F1 = (Fa*r1-F2*PB-F3*PA)/M1;
F2 = (Fa*r2-F3(P3+L2*cos(T3)))/M2;
F3 = (Fa*r3)/M3;
Favg = (F1+F2+F3)/3;
% Objective functions for the dimension optimization
d1 = F1+F2+F3;
d2 = (Favg-F1)^2+(Favg-F2)^2+(Favg-F3)^2;
fdim = (d1 + 1000/(1 + d2))

I need to find maximum value of 'fdim' when there are 8 variables have to considering.

Honestly, I have no idea of how to find it... I tried many times with several methods. But, I finally couldn't do this.

So, let me know how to find the maximum value of 'fdim'.

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youn chan choi 2022-4-28

Oh,, i'm sorry. I just miss it. Now, I add them. Thank you so much

David Hill 2022-4-28

在 MATLAB Online 中打开

PB = P2 + L1*cost(T2);
% I assume you mean:
PB = P2 + L1*cos(T2);

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Answer 1

David Hill 2022-4-28

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1707190-how-can-i-find-maximum-value-of-this-function#answer_953110

在 MATLAB Online 中打开

This is a brute force method.

P1 = 25;
P2 = 37.5;
P3 = 20;
W1 = [5, 10];
W2 = [5, 10];
W3 = [5, 10];
L1 = [40, 60];
L2 = [25, 40];
L3 = [15, 25];
r1 = [6, 15];
r2 = [6, 15];
r3 = [6, 15];
T2 = [0.25*pi, 0.5*pi];
T3 = [0, 0.5*pi];
Fa = 1000;
[p1,p2,p3,w1,w2,w3,l1,l2,l3,R1,R2,R3,t2,t3,fa]=ndgrid(P1,P2,P3,W1,W2,W3,L1,L2,L3,r1,r2,r3,T2,T3,Fa);
M1 = (p1.^2+w1.^2)./p1;
M2 = (p2.^2+w2.^2)./p2;
M3 = (p3.^2+(sqrt((2*w3).^2-(p3-(l3-2*w3)).^2)-w3).^2)./p3;
PA = p3 + l2.*cos(t3) + l1.*cos(t2 + t3);
PB = p2 + l1.*cos(t2);
F3 = (fa.*R3)./M3;
F2 = (Fa.*R2-F3.*(p3+l2.*cos(t3)))./M2;
F1 = (fa.*R1-F2.*PB-F3.*PA)./M1;
Favg = (F1+F2+F3)/3;
d1 = F1+F2+F3;
d2 = (Favg-F1).^2+(Favg-F2).^2+(Favg-F3).^2;
fdim = (d1 + 1000./(1 + d2));
Max=max(fdim,[],'all');%did you expect your calculations to go complex?