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Curve fitting multiple parameters function

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Kabir Shariff
Kabir Shariff 2021-8-13
评论： Kabir Shariff 2021-8-18
Hello,
I have a set of data that fits a defined curve fitting function model as
I = a*exp(-bx)+c;
the parameters a, b and c depends on a function r, say (a,b,c) = f(r)
My defined function I also depends on another parameter k , say (a,b,c) = f(k)
How can I define single function that that depends on both k and r, say
I = f(a,b,c)
I = a*exp(-bx)+c
(a,b,c) = f(k,r)
Thank you
  2 个评论
Sambit Supriya Dash
Sambit Supriya Dash 2021-8-15
Could you elaborate more the question with funs. or with some similar examples ?
Kabir Shariff
Kabir Shariff 2021-8-15
I want to develop an analytical modelfor turbulence from numerical sumulation data. I know the turbulence depends on three different parameters, the thrust const (r) , the ambient const (k) and the position (x).
I use an exponential function model to fit the numerical data as shown in the figure
The model equation is of the form
I = a*exp(-bx)+c;
where a, b and c are linear functions that depend on the ambinent const (k),
I maintain a value of r and simulate for different values of k to have different values of (a,b and c) to develop a relation. e.g
The same model is also used to obtain a similar parameters a, b, and c that depends on the thrust coeffcient (r) ( keeping k constant)
I want to to have an expression that combines both r and k in a, b and c parameters something like

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回答（1 个）

Sulaymon Eshkabilov
You can write a function file or function handle, e.g.:
F=@(k, r, x)(2*r*k*exp(0.576*k*x)+c); % etc.
% OR
function F = MyFun(k,r, x)
F = (2*r*k*exp(0.576*k*x)+c);
end
  2 个评论
Kabir Shariff
Kabir Shariff 2021-8-17
I think the function handle will not do the job.
I dont have the model with variation of both r and k, but I have a model for each separate variable (i.e model eqn for r and model eqn for k)
I want to have a single model that account for both variables
NB: the equations given are for example purpose
Kabir Shariff
Kabir Shariff 2021-8-18
Hello,
I would like to give more calrification on my case please.
  1. My objective is to develop analytical model from a measured data for range of k and r
My measured data is dependent on both thrust const (r) and ambient constant (k) and varies along x
r = [0.64 0.89 0.98];
k = [0.08 0.15 0.2 0.23];
I use a defined model equation to fit the data; my model equation of the form;
I = a*exp(-bx)+c;
2. with cftool, I fix r say 0.64, and find the parameters a, b, and c in the model equation for all values of k ( meaning i have 4 different values of a,b, and c correspoding to k)
3. I repeat the same step for r = 0.89 and r = 0.98 (each case obtaining a different coefficent of the model equation)
4. Then, I ploted k Vs a, k vs b and k vs c. to obtain the relationship between k and (a,b,c) which is linear relation
5. I did a similar plot this time with r, say r vs a, r vs b and r vs c ( also obtaining a linear dependance)
6. I have two different models, one with variable r (k constanrt) and the other with variable k (r constant)
Is there any way to optimize the model to be in the form?
I = a*r*kexp(-b*kx)+c*r;
for 0.064 < r < 0.98;
0.08 < k < 0.23
a, b,c constant
Thank you in advance

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