Trial and error problem

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))

[Geoff Hayes]

Vijay - can you post your code so that we can get an idea of what you have attempted?

[Torsten]

How do b and c depend on a, i.e. what are the conditions to decide whether b and c are the correct values for the given a ?

[Learner]

Added, Please find the code in the question

[Sunil Raiyani]

Have you got the solution for the same. Actually I am also stuck with the same problem.

Answer 1

[Torsten]

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.

[Learner]

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??