Four-parameters optimization of a 1D function: wrong values

Question

Maja 2024-2-23

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2085938-four-parameters-optimization-of-a-1d-function-wrong-values

评论： Maja 2024-2-24

采纳的回答： Matt J

Hello everybody,

I have some data (see file data.txt) that I have to fit with a function equal to:

function = p1*e^(-p2*ln((t-p4)/p3)^2)+p5, with t>p4

t is the time (hours), p are the 5 parameters to be optimized.

t is expressed in hours, so I defined it as t=((0:1:length(data(:,1))-1)/60)'.

The optimizaiton should be based on the minimization of the square error between data and the fit. I defined the error as:

error_function = @(params) sum((fun(params, t) - funzy).^2), where funzy is the vector with values coming from data-txt divided per 10.

I tried using fminsearch, however, the fourth parameter p4 results being negative and this does not have a physical meaning. Expected values of the parameters should be p1 = max value of the data function, p2 = curvature of the fit (0.5 to 5), p3 = time at which the ppeak occurs (starting from d), p4 = time at which values in data are not zero ( to 2), and p5 = offset y-axis (around -0.002).

I tired fmincon but it seemed not working and after that I tried even to use the genetic algorithm, but without any satisfactory results.

Can someone please help me?

Thanks a lot!