Asked by madhuri dubey
on 9 Jul 2018

My equation is y=a(1-exp(-b(c+x)) x=[0,80,100,120,150] y=[2195,4265,4824,5143.5,5329] When I am solving it in matlab, I am not getting a proper fit in addition, sse=6.5196e+05 and r square=0.899. Although the r square value is acceptable, the sse is too high. Therefore kindly help to get minimum sse. Further I have tried in curve fitting tool but I got same thing.

Star Strider
님의 답변 9 Jul 2018

채택된 답변

I get good results with this:

yf = @(b,x) b(1).*(1-exp(-b(2)*(b(3)+x)));

B0 = [5000; 0.01; 10];

[Bm,normresm] = fminsearch(@(b) norm(y - yf(b,x)), B0);

SSE = sum((y - yf(Bm,x)).^2)

Bm =

6677.76372320411

0.0084077646869843

47.1622210493944

normresm =

195.173589996072

SSE =

38092.7302319547

Star Strider
10 Jul 2018

As always, my pleasure.

I would be tempted to use polyfit to get initial estimates of ‘a’, ‘c’, and ‘d’ (estimated as [-0.09, 34, 2200] when I did it) , then let your nonlinear parameter estimation routine (similar to my code) estimate them and ‘b’ (that I would initially estimate as 10).

I usually create my own initial population for ga. I would be tempted here to use a matrix of 500 individuals, defined as:

init_pop = randi(5000, 500, 4);

using the appropriate options function (linked to in the See Also section in the ga documentation) to define it as such. The ga function is efficient, however since it has to search the entire parameter space, it will take time for it to converge.

Note that you have 5 data pairs and you are now estimating 4 parameters.

madhuri dubey
11 Jul 2018

Star Strider
11 Jul 2018

There isn’t. You’re ignoring the constant multiplication factor 1.0E+03. The full result:

p =

1.0e+03 *

-0.000088159928538 0.034559355475118 2.180742845451099

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Image Analyst
님의 답변 11 Jul 2018

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