How do I curve fit the data set

Question

Prajwal Magadi 2023-7-29

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2002157-how-do-i-curve-fit-the-data-set

评论： Sam Chak 2023-7-29

采纳的回答： Sam Chak

curve_fit.mat

Hello all,

I'm facing difficulty in fitting the data.

The red ones are from the data set, and I want to fit that as like blue one (Experimental Data). How can I do that. I have also attached the data set for your reference.

Thank You.

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Sam Chak 2023-7-29

Hi @Prajwal Magadi

What is the mathematical function of the blue curve? Is it a skewed normal distribution function?

Can you also suggest some candidate functions for fitting into the red data? Look up some Kernel functions.

Red data seems to have discontinuities at multiple intervals. Is it acceptable to have a piecewise function to fit the data?

Prajwal Magadi 2023-7-29

The blue curve is also a data set from an experimental obervation.

The red data is from the simulation.

And I have no idea of the function type of blue data.

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Answer 1

Sam Chak 2023-7-29

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2002157-how-do-i-curve-fit-the-data-set#answer_1280462

在 MATLAB Online 中打开

curve_fit.mat

Hi @Prajwal Magadi

Not sure if this is what your want. But you can try finding the best math function to fit.

data = load('curve_fit.mat');

x = data.theta_degree';

y = data.x';

skewEqn = 'a/(sqrt(2*pi))*exp(- b*(x - c)^2)*((1/2)*(1 + erf(e*(x - c)/sqrt(2)))) + d';

fo = fitoptions('Method', 'NonlinearLeastSquares',...

'Lower', [ 0, 0, 5, 0, 0.1],... % {a, b, c, d, e}

'Upper', [100, 1, 20, 10, 1.0],...

'StartPoint', [50 0.5 10 5 0.5]);

ft = fittype(skewEqn, 'options', fo);

[yfit, gof] = fit(x, y, ft)

yfit =

General model: yfit(x) = a/(sqrt(2*pi))*exp(- b*(x - c)^2)*((1/2)*(1 + erf(e*(x - c)/sqrt(2) ))) + d Coefficients (with 95% confidence bounds): a = 85.15 (84.38, 85.93) b = 0.003494 (0.003423, 0.003564) c = 7.162 (7.116, 7.209) d = 2.461 (2.241, 2.681) e = 0.3845 (0.3752, 0.3937)

gof = struct with fields:

sse: 9.7227e+04 rsquare: 0.9063 dfe: 9995 adjrsquare: 0.9062 rmse: 3.1189

plot(yfit, x, y)

grid on, xlabel('\theta'), ylabel('x')

legend('Data', 'Fitted Skew Dist Fcn')

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Prajwal Magadi 2023-7-29

Thank you Sam.

Sam Chak 2023-7-29

@Prajwal Magadi, Don't mention it. Have a nice weekend!

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Answer 2

Alex Sha 2023-7-29

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2002157-how-do-i-curve-fit-the-data-set#answer_1280532

在 MATLAB Online 中打开

@Prajwal Magadi, one more function:

Sum Squared Error (SSE): 75571.6557870726
Root of Mean Square Error (RMSE): 2.74902993412354
Correlation Coef. (R): 0.962878352853849
R-Square: 0.927134722394541
Parameter	Best Estimate    
---------	-------------    
y0       	3.57509887406416 
a        	10210313.7484567 
xc       	17.1109591760412 
w1       	18.7010167618592 
w2       	-1.38399464317597
w3       	-1.49504622174935

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Alex Sha 2023-7-29

Hi, your data chart looks like peak-type function chart, so just try some typical peak functions, "Asym2Sig" function, shown above, gives more better outcomes.

Sam Chak 2023-7-29

Hi @Alex Sha, thanks for sharing the information about the Asymmetric Double Sigmoidal function. I don't have Origin Pro, and I have never seen many of those functions before.

https://www.originlab.com/doc/en/Origin-Help/Peak-Analyzer-Functions

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