Parameter Estimation of a model

I have experimental data of application of current profile to a battery and have quantiies like time, current, voltage, temperature. From this data I calculate SoC based on Coloumb counting.

I have created a model that calculates terminal voltage but have some parameters i want to determine. Equation is in the picture attached.

Parameters are E0, r, k0, k1, k2, k3.

How can i estimate these parameters so that th voltage output of the equation matches with the expermiental data.

Answer 1

[Star Strider]

I would do something like this —

Data = [(0:10).' rand(11, 3)];                                  % Data = [Time Current Voltage Temperature
SOC = rand(11,1);
fcn = @(E0, r, k0, k1, k2, k3, Iin, Vm, SOC) E0 + Iin.*r - k0./SOC - k1.*SOC + k2.*log(SOC) + k3.*log(1-SOC) - Vm;
objfcn = @(b) norm(fcn(b(1),b(2),b(3),b(4),b(5),b(6),Data(:,2),Data(:,3),SOC));

B0 = rand(1,6);
Parms = fminunc(objfcn, B0)

Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.

Parms = 1×6

-0.4379 -0.2098 0.2440 -1.0951 -1.3480 -0.0587

fprintf(1,'E0 = %6.3f\nr  = %6.3f\nk0 = %6.3f\nk1 = %6.3f\nk2 = %6.3f\nk3 = %6.3f\n',Parms)

E0 = -0.438
r  = -0.210
k0 =  0.244
k1 = -1.095
k2 = -1.348
k3 = -0.059

Make appropriate changes for your data.

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