Response surface method in Matlab

Hi.

I have 6 independent variable and one dependent variable. I want to fit a response surface to the data by for exp a second order polynomial, when I open curve fitting toolbox, There is only two space for the input variable. can anyone help me about this. How can I do this fit in matlab?

Thank you in advance for your time.

Answer 1

[darova]

Look here

[Arash]

Thank you for your help, But if I understand correctly, this means that I must know the form of the equation and it will compute for me the coefficient of the equation. Is there any way that matlab fits a surface based on any algorithm (not linear) to my data?

[darova]

Of course! Look this:

[Arash]

Here you have two independent variable X and Y and Z as the dependent variable. How can I apply this to a four independent variable for example [x1 x2 x3 x4 ];

I don't know my equation to use the custom option. I want to get the euqation from thisw method [polynomial with degree of 2] from my data.

[darova]

fit toolbox can't handle such task. Maybe you want griddedInterpolant

Answer 2

[Thonn Homsnit]

I faced the same problem as the author. But I have just figured it out !

I use the 'fitnlm' function with the user defined function with handle like this

modelFun = @(b1,x1)( ...
    +b1(1).*x1(:,1) ...  
    +b1(2).*x1(:,2) ...
    +b1(3).*x1(:,3)...
    +b1(4).*x1(:,4)...
    +b1(5).*x1(:,1).*x1(:,2) ...
    +b1(6).*x1(:,1).*x1(:,3) ...
    +b1(7).*x1(:,1).*x1(:,4) ...
    +b1(8).*x1(:,2).*x1(:,3) ...
    +b1(9).*x1(:,2).*x1(:,4) ...
    +b1(10).*x1(:,3).*x1(:,4) ...
    +b1(11).*x1(:,1).*x1(:,1) ...
    +b1(12).*x1(:,2).*x1(:,2) ...
    +b1(13).*x1(:,3).*x1(:,3) ...
    +b1(14).*x1(:,4).*x1(:,4) ...
    +b1(15) ...
    );

beta0   = zeros(15,1); %%% initial coefficient value %%%%
mdl1    = fitnlm(x1,y1,modelFun,beta0);
b1 = table2array(mdl1.Coefficients(:,"Estimate"));

x1 is predictor matrix and y1 is target vector. you can solve the b1 matrix which is the coefficient of this function. Another tool is using MBC toolbox. But the documentation is very old and i cannot find the algorithm behind the toolbox.

Hope it helps.