How to design a proper script/code for estimating multiple parameters (more than three) for a model, without using 'lsqnonline'?

Hello everyone.

I wanted to ask if there is a proper way for designing a script to estimate multiple parameters for a model.

My problem is that I have a model function - let say 'My_model(a,b,c,d)' - that needed 4 different parameters, and I want to fit the model with the measured data. I wanted to estimate the best 4 parameters that will give the least Root-Mean-Square-Error (RMSE). I have designed my codes using for loops. I would like to find a better way to design the code, and would like to ask your help, comments or suggestions on what should I do to improve it.

Below is the scripts:

% Script Example
load('Data');       %load the 'Data_measured' with size 1 x n

% Parameters to estimate
a = 0.12:0.08:4.1;     %the estimated range for 'a'
b = 0.01:0.01:1;       %the estimated range for 'b'
c = 0.0:0.01:1;        %the estimated range for 'c'
d = 1.2:0.02:2;        %the estimated range for 'd'

% Declare initial error
RMSEr = 100;

% The Estimation 
for i1=1:size(a,2) 
  for i2=1:size(b,2) 
      for i3=1:size(c,2) 
          for i4=1:size(d,2) 
              Data_Predict = My_model(a(i1), b(i2), c(i3), d(i4));   % Having size 1 x n
              Er = sqrt(nansum((Data_measured - Data_Predict).^2)) * 100 / (size(Data_measured,2));
              if Er < RMSEr  
                  RMSEr  = Er;  
                  a_best = a(i1);    
                  b_best = b(i2);  
                  c_best = c(i3); 
                  d_best = d(i4);                                                         
              end 
          end
      end
  end
end

This script takes a long time to estimates all the best parameters for the model. I would like to know if there is a more suitable way, method, and/or built-in function that can help me to improve this code.

Thank you very much.

Note: I have looked 'lsqnonline' and 'lsqcurvefit' functions, but I don't know how to use it to estimate multiple parameters, or whether it is suitable for my problem.

Answer 1

[Stephen23]

You could use lsqnonlin. Its application is quite straightforward, the only important thing to be aware of is that the function must accept a vector of values, not separate inputs (in the example below I used an anonymous function to allow this).

You need to carefully read the lsqnonlin documentation, but here is some untested code to get you started:

S = load('Data'); % best practice is to load into a variable.
lb = [0.12;0.01;0;1.2];
ub = [4.10;1.00;1;2.0];
x0 = (lb + ub) / 2;
fun = @(varargin)My_model(varargin{:})-S.Data_measured;
x = lsqnonlin(fun,x0,lb,ub);

It will need some tweaking, and you should also look at the optimization options.

[HADI AFFENDY DAHLAN]

Thank you for the example code. I will try it on my model.