Optimization of multiple input variable to a model

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Kabir Shariff on 19 Aug 2021
Answered: Alan Weiss on 22 Aug 2021
Hello Community,
I am relatively new to matlab, I have a optimization problem detailed below;
1. the aim is to develop an analytical model for a measured data for a range of thrust coeffict Ct and ambient turbulence Iamb
My measured data 'Ip' depends on both Ct and Iamb along x.
Ct = [0.64 0.89 0.98];
Iamb = [0.08 0.15 0.2 0.23];
2. For a Ct, say Ct =0.64, I have I have 4 sets of data for Ip corresponding to Iamb.
In total I have 12 sets for data
3. I use a cftool to fit the data, using a custom model equation
Ip = a*exp(-b*x) +c;
This model equation fits all the data as shown below
4. My question: How can I the extract the dependence of Ct and Iamb in the constant a,b,c?
I want to have a generalize model equation of the form say,
Ip = a1*Iamb* exp(-b1*x) + c1;
for 0.08<Iamb<0.23 and 0.64 < Ct < 0.98
where a1, b1 and c1 are function of Iamb and Ct
5. What optimization tool is suited for this application?, I tried fmincon as follows but not getting the the correct model
c0 = [ 1 1 1 ]; % initiaal values
Ip = @(c) *c(1)*exp(-c(2)*x) +c(3) % optimization func
obj = @(c) sum(((Ip(c) - Im)./Im).^2); % obj func
copt = fmincon(obj,c0)
resulting to the values a1,b1, & c1
how can I develop Ct and Iamb relation from the set of values (a,b,c)?
6. Thank you for your assistance, I can provide more clarification if needed
Kabir Shariff on 20 Aug 2021
Hi Alex,
Please find attached the data. I combine it into a single file for easy access.
If needed, I can provide my working code also.
Thanks

Alan Weiss on 22 Aug 2021
Usually you should use a least-squares solver for nonlinear fitting. See Nonlinear Data-Fitting and Nonlinear Least -Squares, Problem-Based for examples.
Alan Weiss
MATLAB mathematical toolbox documentation

R2019a

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