Curve fitting to data using fit

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Editor 2022-10-11

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1822303-curve-fitting-to-data-using-fit

评论： Cris LaPierre 2022-10-11

采纳的回答： Matt J

在 MATLAB Online 中打开

I have data x sampled at times t. I would like to fit my function to this data. Below is a code.

clear; close all

x=[100; 85.4019292604501; 77.9310344827586; 79.3365583966828; 70.3524533;

13.213644524237; 24.5654917953199; 12.6526340272125;

9.71822886716503; 9.99113213124446; 10.525];

t=[0; 24; 24; 24; 24; 48; 48; 48; 72; 72; 72;];

mdl=fittype('A*exp((-C.*(1-exp(-lambda.*t))/lambda)-(D*(exp(-lambda.*t)-1+lambda.*t)/lambda^2))','indep','t');

fittedmdl = fit(t,x,mdl,'start',[0.1 0.1 0.1 0.1])

fittedmdl =

General model: fittedmdl(t) = A*exp((-C.*(1-exp(-lambda.*t))/lambda)-(D*(exp(-lambda.*t) -1+lambda.*t)/lambda^2)) Coefficients (with 95% confidence bounds): A = 100 (84.3, 115.7) C = -120.9 (-9.45e+09, 9.45e+09) D = 6.135 (-4.793e+08, 4.793e+08) lambda = 105.9 (-8.273e+09, 8.273e+09)

plot(fittedmdl,'k.')

hold on

plot(t,x,'.m', MarkerSize=20)

And I obtain the following figure:

I am not impressed with the fitting. Can someone please check where I could be going wrong. Thanks in anticipation.

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Editor 2022-10-11

Thank you all for your constructive comments. I can tell that one of the problem could be the poor choice of initial conditions for this complex model. I will try though to play around with the initial condtions to see whether anything good can come out.

Thank you once again

Cris LaPierre 2022-10-11

Just responding about the missing negative sign. The negative sign before C has been applied to the contents inside parentheses. So it is there.

-C(1-exp(

t)) is the same as C(exp(

t)-1)

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采纳的回答

Matt J 2022-10-11

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1822303-curve-fitting-to-data-using-fit#answer_1071538

编辑：Matt J 2022-10-11

在 MATLAB Online 中打开

x=[100; 85.4019292604501; 77.9310344827586; 79.3365583966828; 70.3524533;

13.213644524237; 24.5654917953199; 12.6526340272125;

9.71822886716503; 9.99113213124446; 10.525];

t=[0; 24; 24; 24; 24; 48; 48; 48; 72; 72; 72;];

mdl=fittype('A*exp((-C.*(1-exp(-lambda.*t))/lambda)-(D*(exp(-lambda.*t)-1+lambda.*t)/lambda^2))','indep','t');

fittedmdl = fit(t,x,mdl,'start',[100 0.1 0.1 0.1],'Lower',[0 0 0 0])

fittedmdl =

General model: fittedmdl(t) = A*exp((-C.*(1-exp(-lambda.*t))/lambda)-(D*(exp(-lambda.*t) -1+lambda.*t)/lambda^2)) Coefficients (with 95% confidence bounds): A = 108.1 (88.32, 128) C = 4.114e-14 (fixed at bound) D = 0.001322 (0.0002522, 0.002393) lambda = 8.823e-07 (-0.0381, 0.0381)

H=plot(fittedmdl,t,x);

H(1).MarkerSize=20; H(1).Color='m';

H(2).Color='k';H(2).LineWidth=2;