Optimization of parameters for a calculated result having an experimental result

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Eduardo Chacin 2018-9-4

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评论： Eduardo Chacin 2018-9-6

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?

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Answer 1

Alan Weiss 2018-9-4

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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

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Torsten 2018-9-5

在 MATLAB Online 中打开

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 2018-9-6

在 MATLAB Online 中打开

@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