Response surface method in Matlab

Question

Arash 2020-3-2

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回答： Thonn Homsnit 2022-5-10

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.

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Answer 1

darova 2020-3-2

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Look here

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Arash 2020-3-4

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 2020-3-4

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

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Answer 2

Thonn Homsnit 2022-5-10

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在 MATLAB Online 中打开

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.