Problem using nlinfit for multiple non-linear regression - poor fit

Dear all,

I am tryng to validate a model for an electrochemical cell potential using experimental data for different operating conditions (Temperature, Current density, Concentrations).

My model equation (Vnum) contains several terms: quadratic + logaritmic + asinh including exponentials and exponentials + constant.

I have tried to use the nlifit function for multiple non-linear regression:

%Experimental Voltage [V]

Vexp_800_1 = [1.3012, 1.2767, 1.2426, 1.2398, 1.1977, 1.1351, 0.878];

Vexp_850 = [1.2069, 1.1773, 1.1443, 1.1431, 1.1074, 1.0677, 0.859];

Vexp_750 = [1.3814, 1.3649, 1.3369, 1.3344,1.2723, 1.2285, 0.897];

Vexp_800_2 = [1.31, 1.2871, 1.2526, 1.2514, 1.2093, 1.148, 0.878];

Vexp_800_3 = [1.2947, 1.2679, 1.2349, 1.2334, 1.1889, 1.1663, 0.878];

beta1= [Aan Eact_an Bcat Eact_cat Rcc]; %Guess fitting parameters (from literature)

x=[Idens_test, Texp_test, H2_exp_test, H2O_exp_test, O2_exp_test];

Vnum=@(beta0,x)(((244800-49.18*x(:,2)-0.00272*x(:,2).^2)/(Z*F)+R*x(:,2)/(Z*F).*log(x(:,3)./x(:,4).*x(:,5).^0.5*P^0.5) ...

+R*x(:,2)/F.*asinh(x(:,1)./(beta0(1)*exp(-beta0(2)./(R*x(:,2)))))+R*x(:,2)/F.*asinh(x(:,1)./(beta0(3)*exp(-beta0(4)./(R*x(:,2)))))+x(:,1).*(1./(69200*exp(-9681./x(:,2))*0.01))*S_SSZ+beta0(5)));

beta=nlinfit(x,Vexp_test,Vnum,beta1);

But i receive the following warning:

Warning: Some columns of the Jacobian are effectively zero at the solution, indicating that the model

is insensitive to some of its parameters. That may be because those parameters are not present in

the model, or otherwise do not affect the predicted values. It may also be due to numerical

underflow in the model function, which can sometimes be avoided by choosing better initial parameter

values, or by rescaling or recentering. Parameter estimates may be unreliable.

I am struggling in understanding the error. I have checked my model equation and I do not see parameters that are not present in the model. I have already tried to change better initial parameters from literature. Is this issue related to rescaling or recentering of Jacobian?

I do not know if this could help, but I noticed that reducing fitting terms deleting one of the asinh terms message error disappears. Unfortunately I need both terms in my model.

beta2= [Aan Eact_an Rcc]; %Guess fitting parameters (from literature)

Vnum=@(beta0,x)(((244800-49.18*x(:,2)-0.00272*x(:,2).^2)/(Z*F)+R*x(:,2)/(Z*F).*log(x(:,3)./x(:,4).*x(:,5).^0.5*P^0.5) ...

+R*x(:,2)/F.*asinh(x(:,1)./(beta0(1)*exp(-beta0(2)./(R*x(:,2)))))+x(:,1).*(1./(69200*exp(-9681./x(:,2))*0.01))*S_SSZ+beta0(3)));

I attach the full code so you could have a closer view on the problem.

Thank you in advance

[Torsten]

You don't use the fourth and fifth parameter in your model function. Thus you should remove the two parameters from your initial guess vector.