Error lsqnonlin reaching values using nested functions - matlab

Question

I want to fit two parameters using lsqnonlin. I have set up my system of ODE and want to solve them with my new parameters that are found after I performed the lsqnonlin.
function [dcdt] = CSTRSinSeries(t,c,par)
for i=1:par.n
if i==1
dcdt(i) = 1/par.tau_per_tank * (par.c0-c(i))+par.kf*(par.c0_meth-c(i))- ...
par.kb*c(i).^2;
else
dcdt(i) = 1/par.tau_per_tank * (c(i-1)-c(i))+par.k*(par.c0_meth-c(i))- ...
par.kb*c(i).^2;
end
end
dcdt = dcdt';
end
% fitcrit function
function error = fitcrit(curve_fit_parameters,time_exp,conc_exp, par, init)
[time_model_fit,conc_model_fit] = ode45(#(t,c) CSTRSinSeries(t,c,par),time_exp,init,[]);
error = (conc_exp-conc_model_fit);
end
I think the problem has to do with the fact that my parameters are in parameter struct par and that I don't want to fit on all of these parameters, but just on basis of two of those.
This is my main script for performing the curve fitting:
% initial guesses for model parameters, no. of indeces is number of fitted % parameters
k0 = [0.028 0.002];
% lower and upper bounds for model parameters, this can be altered
LB = [0.00 0.00];
UB = [Inf Inf];
% Set up fitting options
options = optimset('TolX',1.0E-6,'MaxFunEvals',1000);
% Perform nonlinear least squares fit (note that we store much more
% statistics than just the final fitted parameters)
[curve_fit_parameters,RESNORM,RESIDUAL,EXITFLAG,OUTPUT,LAMBDA,JACOBIAN] = ...
lsqnonlin(#(k) fitcrit(k,time_exp, conc_exp, par, init),k0,LB,UB,options);
The code now does not give an error, however the output of my curve_fit_parameters is now the same as my initial values (also when I change my initial value, it stays the same).
The error is:
>> PackedBed
Initial point is a local minimum.
Optimization completed because the size of the gradient at the initial point
is less than the default value of the optimality tolerance.
<stopping criteria details>
The stopping criteria gives a relative first-order optimality 0.00+00, so I think that the parameters lsqnonlin changes have no influence on my error.
I think that the mistake is the lsqnonlin function, where I refer to 'k' instead of 'par.kb and par.kf'. However, I don't know how to refer to these as these are nested functions. Replacing 'k' by 'par.kb, par.kf' gives me the error: Unexpected matlab operator.
Could anyone help me with my problem?

Answer 1

As suggested by Adriaan in the comments, you can easily make a copy of the par struct in your fitcrit function, and assign the parameters to optimize to this par_tmp struct. The fitcrit function then becomes:
function error = fitcrit(curve_fit_parameters,time_exp,conc_exp, par, init)
par_tmp = par;
par_tmp.kf = curve_fit_parameters(1); % change to parameters you need to fit
par_tmp.kb = curve_fit_parameters(2);
[time_model_fit,conc_model_fit] = ode45(#(t,c) odefun(t,c,par_tmp),time_exp,init,[]); % pass par_tmp to ODE solver
error = (conc_exp-conc_model_fit);
end
In the script calling lsqnonlin, you will have to change the par struct to include the converged solution of the parameter subset to optimize:
% initial guesses for model parameters, no. of indeces is number of fitted % parameters
k0 = [0.028 0.002];
% lower and upper bounds for model parameters, this can be altered
LB = [0.00 0.00];
UB = [Inf Inf];
% Set up fitting options
options = optimset('TolX',1.0E-6,'MaxFunEvals',1000);
% Perform nonlinear least squares fit (note that we store much more
% statistics than just the final fitted parameters)
[curve_fit_parameters,RESNORM,RESIDUAL,EXITFLAG,OUTPUT,LAMBDA,JACOBIAN] = ...
lsqnonlin(#(k) fitcrit(k,time_exp, conc_exp, par, init),k0,LB,UB,options);
% make par_final
par_final = par;
par_final.kf = curve_fit_parameters(1);
par_final.kb = curve_fit_parameters(2);
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