Fitting uneven data to a function

Question

Hashim 2022-9-1

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1792785-fitting-uneven-data-to-a-function

编辑： Torsten 2022-9-2

Data.txt

Hi!

So, I recently asked a question as to how to solve a summation (link) and I think I have the function working but I am having issues fitting it to my unevenly spaced data. I have attached the data file (column 4 is x data and 3 is y data). I am scaling the data as you can see in the figure (by taking an inverse square root of the x data) attached at the bottom. Is this a data problem? Or can I make a good fit by adding something like weights? Or do I need to use a different function altogether?

Function itself is as such:

MATLAB function I wrote to give as an input to the fitting function.

function I_num = CurveFitD(x, t)
%CurveFitD We want to fit the I(t)=f(t) to a custom function. 
%   For a bounded layer we have an expression which can yield us the
%   thickness of the polymer layer (in centimeters). We have to fit the transient to this
%   equation to calculate the layer thickness. 
% Constants
I_num       = zeros(size(t));
% Bounded Cottrell
for i    = 1:length(t)
    for k = 1:42
        I_num(i) = I_num(i) + (-1).^k.*exp(-((k*x(1))^2)./(x(2).*t(i)));  
    end
    I_num(i) = sqrt(x(2)./(pi.*t(i))).*(x(3)./x(1)).*(1+2.*I_num(i));
end 
end

I am calling this function using lsqcurvefit as given. As you can see I have an idea of the parameters I want to extract.

%% Nonlinear Curve-Fitting (Data-Fitting 'lsq')
%%
t              = E3PS_Whole.CorrectedTimes; 
I_exp          = E3PS_Whole.WE1CurrentA;
invsqrt        = 1./sqrt(t);
options = optimoptions('lsqcurvefit','Algorithm','trust-region-reflective',...
           'OptimalityTolerance',1e-12,...
           'StepTolerance', 1e-12,...
           'FunctionTolerance',1e-12,...
           'FiniteDifferenceType',"central");
%                x(1)=d; x(2)=D_e; x(3)=deltaQ
lb             = [1e-07;    1e-10;        1e-09];
ub             = [1e-03;    1e-06;        1e-05]; 
x_0            = [4e-05;    1e-07;        1e-06];
[x,resnorm,residual,exitflag,output]=lsqcurvefit(@CurveFitD, x_0, t, I_exp, lb, ub, options);
I_num = CurveFitD(x, t);
% I vs E for Experimental and Calculated 
figure(4); 
plot(invsqrt, I_exp, 'ro', 'LineWidth', 1);
hold on; 
plot(invsqrt, I_num, 'b--', 'LineWidth',2);
xlabel('1/{\surd{t}} / s^{-1/2}'); ylabel('I / A'); 
legend('Experimental', 'Numerical'); 

Output looks like this.

4 个评论
显示 2更早的评论隐藏 2更早的评论

Matt J 2022-9-1

I don't yet have the grasp of how to run code here but will try to learn about it.

Use the Run button,

Torsten 2022-9-2

Define x(1) = sqrt(D)/d and x(2) = deltaq as your model parameters and write your model in these two parameters.

Using three parameters as you do makes your model overfitted.

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Answer 1

Matt J 2022-9-1

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1792785-fitting-uneven-data-to-a-function#answer_1039915

编辑：Matt J 2022-9-1

Or do I need to use a different function altogether?

The first thing I notice is that your model is over-parametrized. You are writing it in terms of 3 parameters when in fact there are only 2 degrees of freedom, since the model depends on d and D only through the ratio d^2/D.

Also, one of the parameters

is merely a linear scaling constant, and can be eliminated from the iterative fitting process as well if you do the curve fit using fminspleas,

https://www.mathworks.com/matlabcentral/fileexchange/10093-fminspleas

Solving for 1 unknown should be pretty robust, without the need for data weighting, but fminspleas does let you provide weights if desired.