Non Linear curve fitting

Hi,

I have an equation of the following form.

Y = K1 * (( x1 - (K2*x2) + (K3*x3)) * (x4 - x2))

x1 is fixed at 1.5. The models accounts for behavior in a nonlinear region. Its a current equation which has a slight nonlinear behavior.

The points I have are the following.. x4 varies from 0.51 - 0.6 and for each x4 I have x3 varying from a nominal value +/- 75mV. The nominal value of x3 will be different for different x4. And again for each x3+/- 75mV I have x2 varying from 0.25-0.5.

Essentially there are two nested loops. x2 always runs from 0.25-5 for every x3+/-75mV for every x4 between 0.51 - 0.6 .

Since I will have a Y for every combination of x2,x3,x4. I read it as a matrix with the input combinations of x2,x3,x4 as say INP and the output Y as a matrix OUT.

Then I used the following to find my coefficients.

Z = (INP' * INP ) \ (INP' * OUT )

The error I am getting is around 15% but I want to have less than 5% error. Could someone please help me in this?

Thanks in advance for the help.

Thanks, Venkat

[Venkatesa]

Hi,

Anyone any suggestions?

Thanks,

Venkat

Answer 1

[Walter Roberson]

Sounds like fmincons() might perhaps be suitable for this, but if you have the curvefitting toolbox or optimization toolbox then there are more specific tools there.

[Venkatesa]

Hi Walter,

Thanks for your suggestion. But I am not so conversant with Matlab. I tried using fmincon but Not sure how and what options I should be using. How do I give my constraints et all.

I am not sure how to know if I am having a constraint in my problem or not.

Some advice would help.

Thanks,

Venkat

[Walter Roberson]

Saying that "x4 varies from 0.51 - 0.6" is a constraint on x4; likewise you have a constraint on x2 I think (I might be misreading.) You might be able to program some of the other constraints through the A*x<=b parameter to fmincon() -- if not exactly then perhaps close enough as to meaningfully reduce the search domain.