Fitting uneven data to a function

7 次查看（过去 30 天）
Hashim
Hashim 2022-9-1
编辑： Torsten 2022-9-2
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
Matt J
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
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.

请先登录，再进行评论。

请先登录，再回答此问题。

回答（1 个）

Matt J
Matt J 2022-9-1
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.
  4 个评论
显示 2更早的评论
Hashim
Hashim 2022-9-2
out=1+2*sum( (-1).^k.*exp(-k.^2.*B./t) ,2);
What does the 2 at the end mean?
Torsten
Torsten 2022-9-2
编辑：Torsten 2022-9-2
S = sum(A,dim) returns the sum along dimension dim. For example, if A is a matrix, then sum(A,2) is a column vector containing the sum of each row.
So it's the sum over k, not over t.

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Get Started with Curve Fitting Toolbox 的更多信息

标签

产品

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by