Trial and error problem

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Learner
Learner 2018-4-11
评论： Sunil Raiyani 2022-7-14
Dear Matlab Community Members
As shown in the flowchart, My objective is to find the values b and c for the given value a, Both the values b and c lies in the range 0.000001 to 2 (Approximately), I wrote a simple code in matlab to search for the values (i.e. a = 0.000001:0.000000:2 and b = 0.000001:0.000000:2), that means for each value of a it will search for the value of b, when condition 1 is less the toleratnce, it will check conditon 2, if it also less than the toleracnce, it will break the loop and return the values. But my problem here is
  1. It is taking too much time (Approximately, for each value of a, it is taking almost 30 Minutes) I have nearly about 1000 values of a.
  2. I want to know, is there any better way or techniques to find the values (b and c).
Thanks you very much
* |Simplified version of flowchart|*
*
Original flowchart*
Code is really big, it involves multiple functions, This is the real flowchart of the code (This is softened membrane model, reinforced concrete)
This code will not run, since it has supported funciton files.
eps_2 = -[linspace(0.01, 0.1, 20), linspace(0.1, 5, 30)]*10^-3;
eps_1_initial = [linspace(0.01,1, 200), linspace(1, 100, 200)]*10^-3;
Gamma_12_initial = [linspace(0.01,1, 200), linspace(1, 100, 200)]*10^-3;
Tol = 1e-3;
%%SMM (Softened Membrane Model) Model
for i = 1:length(eps_2)
eps_2_trail = eps_2(i);
eps_1 = eps_1_initial;
Gamma_12 = Gamma_12_initial;
TotalError = [];
for m = 1:6
for j = 1:length(Gamma_12)
Gamma_12_trail = Gamma_12(j);
for k = 1:length(eps_1)
eps_1_trail = eps_1(k);
eps_l = eps_1_trail*(cosd(Alpha_1))^2 + eps_2_trail*(sind(Alpha_1))^2 - Gamma_12_trail*cosd(Alpha_1)*sind(Alpha_1);
eps_t = eps_1_trail*(sind(Alpha_1))^2 + eps_2_trail*(cosd(Alpha_1))^2 + Gamma_12_trail*cosd(Alpha_1)*sind(Alpha_1);
[v12, v21] = HsuZhuRatios(eps_l, eps_t, eps_yl, eps_yt);
eps_1_bar = eps_1_trail/(1 - v12*v21) + v12*eps_2_trail/(1 - v12*v21);
eps_2_bar = v21*eps_1_trail/(1 - v12*v21) + eps_2_trail/(1 - v12*v21);
eps_l_bar = eps_1_bar*(cosd(Alpha_1))^2 + eps_2_bar*(sind(Alpha_1))^2 - Gamma_12_trail*cosd(Alpha_1)*sind(Alpha_1);
eps_t_bar = eps_1_bar*(sind(Alpha_1))^2 + eps_2_bar*(cosd(Alpha_1))^2 + Gamma_12_trail*cosd(Alpha_1)*sind(Alpha_1);
Beta = 0.5*atand(Gamma_12_trail/(eps_1_trail - eps_2_trail));
Sigma_2c = ConcreteComp(fcDash, eps_c0, eps_2_bar, eps_1_bar, Beta);
Sigma_1c = ConcreteTension(fcDash, eps_c0, eps_cr, Ec, eps_2_bar, eps_1_bar);
Tau_12c = ConcreteShear(Sigma_1c, Sigma_2c, eps_1_trail, eps_2_trail, Gamma_12_trail);
% Longitudinal Steel:
fl = Steel(fcDash, rho_l, fyl, Esl, eps_l_bar);
ft = Steel(fcDash, rho_t, fyt, Est, eps_t_bar);
[SumError, DiffError] = Check( rho_l, rho_t, fl, ft, Sigma_l, Sigma_t, Sigma_1c, Sigma_2c, Tau_12c, Alpha_1 );
TotalError(j, k) = SumError^2 + DiffError^2;
Tau_lt_trial(j, k) = (Sigma_1c - Sigma_2c)*sind(Alpha_1)*cosd(Alpha_1) + Tau_12c*((cosd(Alpha_1))^2 - (sind(Alpha_1))^2);
Gamma_lt_trial(j, k) = 2*((eps_1_trail - eps_2_trail)*sind(Alpha_1)*cosd(Alpha_1) + 0.5*Gamma_12_trail*((cosd(Alpha_1))^2 - (sind(Alpha_1))^2));
end
end
[a, b] = find(TotalError == min(min(TotalError)));
Gamma_12_iterative = Gamma_12(a(1));
eps_1_iterative = eps_1(b(1));
if (min(min(TotalError)) >= Tol) && (m ~= 6)
eps_1 = [linspace(eps_1_iterative/10, eps_1_iterative, 100), linspace(eps_1_iterative, eps_1_iterative*10, 100)];
Gamma_12 = [linspace(Gamma_12_iterative/10, Gamma_12_iterative, 100), linspace(Gamma_12_iterative, Gamma_12_iterative*10, 100)];
TotalError = [];
Tau_lt_trial = [];
Gamma_lt_trial = [];
else
break;
end
end
Tau_lt(i) = Tau_lt_trial(a(1), b(1));
Gamma_lt(i) = Gamma_lt_trial(a(1), b(1));
eps_1_final = eps_1(b(1));
Gamma_12_final = Gamma_12(a(1));
fprintf('%d Out of %d Values of eps_2 completed \n', i, length(eps_2))
Values = table(eps_2_trail, eps_1_final, Gamma_12_final, Tau_lt(i), Gamma_lt(i), TotalError(a(1), b(1)))
end
%%Plotting
plot(Gamma_lt, smooth(Tau_lt))
  4 个评论
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Learner
Learner 2018-4-11
Added, Please find the code in the question
Sunil Raiyani
Sunil Raiyani 2022-7-14
Have you got the solution for the same. Actually I am also stuck with the same problem.

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回答（1 个）

Torsten
Torsten 2018-4-12
Condition 1 and Condition 2 hide two equations that must be fulfilled to accept eps1 and gamma1 as solutions. So you have two equations in two unknowns that can be solved using MATLAB's "fsolve".
Best wishes
Torsten.
  1 个评论
Learner
Learner 2018-6-1
编辑：Learner 2018-6-1
I cannot use fsolve(), since for solving variables b and c, I need to calculate other variables such as fl, ft etc..., as shown in "Original flowchart" diagram, these variables comes from a series of equations and I have to select an equation out of several equations based on the values of b and c, i.e. it is a nonlinear problem.
That's why I tried with a linear search and bisection methods. Recently I tried with finsearch() tool in matlab, it is satisfying my requirement but, Initial guess is the problem.
Do you have any idea how to give initial guess??

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