lsqnonlin data plotting and verification

Hello, I've been spending a lot of time with my data lately.

To optimize Fick's second low and my data, I made an objective function and ran it, and the data value was calculated, but I wasn't sure if it worked correctly.

I am attaching the function I wrote.

function equation = myobjective(D_in)

   c_m = zeros(6,1);
   c_m(1,1) = 0.47683;
   c_m(2,1) = 0.00108063;
   c_m(3,1) = 0.00005262;
   c_m(4,1) = 0.00000709;
   c_m(5,1) = 0.00000158;
   c_m(6,1) = 0.00000047;
   
   q_m = zeros(6,1);
   q_m(1,1) = 2.79224;
   q_m(2,1) = 22.54350400;
   q_m(3,1) = 62.07328340;
   q_m(4,1) = 121.29189583;
   q_m(5,1) = 200.25023496;
   q_m(6,1) = 298.94340840;
      
   t_n = zeros(6,1);
   t_n(1,1) = 900;
   t_n(2,1) = 1800;
   t_n(3,1) = 3600;
   t_n(4,1) = 5400;
   t_n(5,1) = 7200;
   t_n(6,1) = 10800;
   
   
   X_exp = zeros(6,1);
   X_exp(1,1) = 0.3640;
   X_exp(2,1) = 0.3048;
   X_exp(3,1) = 0.1785;
   X_exp(4,1) = 0.1230;
   X_exp(5,1) = 0.0736;
   X_exp(6,1) = 0.0595;
   
 
   a = 0.01;
    
   equation = zeros(6,1);
   x_comp = zeros(6,1);
         
   for n=1:6
      for m=1:6
          x_comp(1,1) = c_m(m,1)*exp(-D_in*t_n(n,1)*q_m(m,1)*3*10000);
          x_comp(2,1) = x_comp(2,1) + c_m(m,1).^3*exp(-D_in*t_n(n,1)*q_m(m,1)*3*10000);
          x_comp(3,1) = x_comp(3,1) + c_m(m,1).^3*exp(-D_in*t_n(n,1)*q_m(m,1)*3*10000);
          x_comp(4,1) = x_comp(4,1) + c_m(m,1).^3*exp(-D_in*t_n(n,1)*q_m(m,1)*3*10000);
          x_comp(5,1) = x_comp(5,1) + c_m(m,1).^3*exp(-D_in*t_n(n,1)*q_m(m,1)*3*10000);
          x_comp(6,1) = x_comp(6,1) + c_m(m,1).^3*exp(-D_in*t_n(n,1)*q_m(m,1)*3*10000);
      end
      
      equation(n,1) = X_exp(n,1) - x_comp(n,1);
   end
   
   
end

options = optimoptions(@lsqnonlin,'Algorithm', 'trust-region-reflective','Display', 'iter', 'MaxFunctionEvaluations', 1000000, 'MaxIterations', 100000);

D_in = zeros(1,1);
lower_bound = 10^(-10);
upper_bound = 10^(-8);
output_with_bound = lsqnonlin(@myobjective, D_in, lower_bound, upper_bound, options)
output_without_bound = lsqnonlin(@myobjective, D_in,[], [], options)

There are two things I want to ask you.

1. Is there a way to verify that my results were calculated correctly?

(in graph form if possible)

2. Can I plot D_in and T_n in my function result?

I've spent a lot of time trying to study MATLAB, but I still don't know much. I hope you all can help.

+ I use an English translator, so there may be some awkwardness in the text. Sorry in advance.

thank you.

Answer 1

[Matt J]

If you use lsqcurvefit instead of lsqnonlin, any of the examples here,

https://www.mathworks.com/help/optim/ug/lsqcurvefit.html#buuhcjo-4

will show you how to do what you want. However, one problem I see already is in the code below. It appears that x_comp(2:6) are identical to one another, so it is unlikely that the result will match X_exp(2:6), which are not identical.

          x_comp(1,1) = c_m(m,1)*exp(-D_in*t_n(n,1)*q_m(m,1)*3*10000);
          x_comp(2,1) = x_comp(2,1) + c_m(m,1).^3*exp(-D_in*t_n(n,1)*q_m(m,1)*3*10000);
          x_comp(3,1) = x_comp(3,1) + c_m(m,1).^3*exp(-D_in*t_n(n,1)*q_m(m,1)*3*10000);
          x_comp(4,1) = x_comp(4,1) + c_m(m,1).^3*exp(-D_in*t_n(n,1)*q_m(m,1)*3*10000);
          x_comp(5,1) = x_comp(5,1) + c_m(m,1).^3*exp(-D_in*t_n(n,1)*q_m(m,1)*3*10000);
          x_comp(6,1) = x_comp(6,1) + c_m(m,1).^3*exp(-D_in*t_n(n,1)*q_m(m,1)*3*10000);