Optimization of parameters for a calculated result having an experimental result

Hello everyone, I have a function

Hc=par1.*(x.^par2).*(y.^par3).*(z.^par4).*exp(par5.*w).*exp(par6.*v)

I have the inputs x, y, z, w and v (they are number arrays of equal quantity of elements) and the initial values for par1, par2... par6, so I have multiple outputs of Hc. I also have the experimental values of H. I have the relative deviation for each one and the average relative deviation as follows:

RD=(H-Hc)./H.*100;
 ARD=100*(sum(RD))/q; %where q is the number of elements

Now, I need to optimize those 6 parameters so that the relative deviation is as close to zero (0) as possible. How could I do that?

Answer 1

[Alan Weiss]

Perhaps along the lines of Curve Fitting via Optimization. Before fitting, you might want to take the logarithm of both sides of your equation in order to get a simpler expression to optimize.

Alan Weiss

MATLAB mathematical toolbox documentation

[Torsten]

To get starting values for the parameters, you should try to fit

log(Hc)

against

log(par1)+par2*log(x)+par3*log(y)+par4*log(z)+par5*w+par6*v

That's a linear fit in the parameters - thus easily accomplished.

Best wishes

Torsten.

[Eduardo Chacin]

@Alan Weiss @Torsten I'm a beginner with MatLab and I'm having a really hard time with it. I'm gonna share what I've got and if someone could please explain me how to optimize (and if I need other files for example) I'd really appreciate it

      function Hc = myfunction( P_k, T_k, c, z, w, v, IFexp )

      y=T_k;
      q=length(P_k);

      %Initial values for parameters
      par1=0.1442;
      par2=2.6388;
      par3=2.2083;
      par4=0.2168;
      par5=0.2;
      par6=0.4;

      %Ecuations
      a=1.28+55.*(1./P_k+0.04).*exp(50.22./(T_k+230));

      g=0.4+2084.69.*(1./P_k-0.002).*exp((-986.95)./(T_k+230));

      x=(g./a).*c;

      Hc=par1.*(x.^par2).*(y.^par3).*(z.^par4).*exp(par5.*w).*exp

      (par6.*v);
      disp(Hc)

      RD=(IFexp-IFc)./IFexp.*100;
      display(RD)

      ARD=100*(sum(RD))/q;
      display(ARD)

      end

This far the program works, but I'm still stuck with the optimization. 
I need that the average relative deviation (ARD) tends to 0.
How could I do that? Already having what I have