Optimization of multiple input variable to a model

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

[Alex Sha]

Hi, if possible, post out all data please, including lp data.

[Kabir Shariff]

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

Answer 1

[Alan Weiss]

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