Using Levenberg-Marquardt algorithm in the optimization

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RAPHAEL OWENS
RAPHAEL OWENS 2020-4-22
评论： Robert U 2020-5-5
How can I use the optimization tool preferable to find a given value in an equation. This is the main equation I=i_ph-Is.*(exp(U./(m_1*Ut))-1) and I have a IU curve, but i want to get the value of 'c_01' in the sub equation Is=c_01*T^(3)*exp((-e_g*eV)/(k*T)).

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Robert U
Robert U 2020-4-23
Hi RAPHAEL OWENS,
there are several solvers and methods available. One of the available functions in Matlab is lsqcurvefit(). Below there is a sketch of how to apply the function on your (supposedly) available data.
% known parameters
T
e_g
eV
k
i_ph
m_1
Ut
% underlying equation
Is = @(c_01) c_01 * T^3 * exp((-e_g*eV)/(k*T));
I = @(c_01,U) i_ph - Is(c0_1) .* (exp(U./(m_1*Ut))-1);
% start value(s) for optimization
c_01_guess = 1;
% choose algorithm, and possibly other options for optimization solver
opt = optimoptions('lsqcurvefit');
opt.Algorithm = 'levenberg-marquardt';
% run optimization
c_01_opt = lsqcurvefit(I,c_01_guess,U_measured,I_measured,[],[],opt);
Kind regards,
Robert
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RAPHAEL OWENS
RAPHAEL OWENS 2020-4-28
Hallo Robert, I need further clarity. How can i get the value of a parameter using optimization.
I=i_ph - (c_01 * T^3 * exp(-((e_g*e)/(k*T)))) .* (exp(U./(m_1*Ut))-1);
The parameter is c_01
The real value of c_01 is 170.8
So the optimized value will be also the real value.
Can you kindly break down the explanation also, because the genral idea is to get a parameter when we are just given the vectors that makes up the curve.
If we were just given UI value and the curve, and also some constants, how will i get an X parameter.
I hope my question is clear enough. Thanks
t=25; %temperature (C)
T=t+273; %temperature (K)
i_ph=3.113; %phase current [A]
e_g=1.12; %band gap [eV]
m_1=1.00; %diode factor
e=1.6*10^-(19); %electronvolt [j]
k=1.38*10^-(23); %Boltzmann constant [JK^(-1)]
U=(0:0.001:0.6); %voltage [V]
Ut=(k*T)/e;
Ut=0.0257
I=i_ph - (c_01 * T^3 * exp(-((e_g*e)/(k*T)))) .* (exp(U./(m_1*Ut))-1);
Robert U
Robert U 2020-5-5
Hi RAPHAEL OWENS,
I am not sure whether I understood your question correctly: Where do I acquire xdata and ydata on real data?
Usually you are measuring the U-I-curve by supplying U and measuring I. In that case the real data are "U" (xdata) and "I" (ydata). The grid does not matter since you are trying to fit the data to a model function. It just needs to be fine enough to cover the overall model function characteristics.
In a nutshell:
  1. Supply U (xdata)
  2. Measure I (ydata)
  3. Give known parameters
  4. Fit to model funcion.
Kind regards,
Robert

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