Non linear function parameter estimation - matlab, lsqnonlin, fzero

Question

I'm having difficulty with a fitting problem. From the errors that I get I imagine that the boundaries are not defined correctly and I haven't managed to find a solution. Any help would be very much appreciated.

Alternative methods for the solution of the same problem are also accepted.

Description

I have to estimate the parameters of a non-linear function of the type:

A*y(x) + B*EXP(C*y(x)) + g(x,D) = 0

subjected to the parameters PAR = [A,B,C,D] being within the range

LB < PAR < UB

Code

To solve the problem I'm using the Matlab functions lsqnonlin and fzero. The simplified code used is reported below.

The problem is divided in four functions:

1. parameterEstimation - (a wrapper for the lsqnonlin function)
2. objectiveFunction_lsq - (the objective function for the param estimation)
3. yFun - (the function returing the value of the variable y)
4. objectiveFunction_zero - (the objective function of the non-linear equation used to calculate y)

Errors

Running the code on the data I get the this waring

Warning: Length of lower bounds is > length(x); ignoring extra bounds

and this error

Failure in initial user-supplied objective function evaluation. LSQNONLIN cannot continue

This makes me to think that the boundaries are not correctly used or not correctly called, but maybe the problem is elsewhere.

---

function Done = parameterEstimation()
    %read inputs
    Xmeas = xlsread('filepath','worksheet','range');
    Ymeas = xlsread('filepath','worksheet','range');

    %inital values and boundary conditions
    initialGuess = [1,1,1,1]; %model parameters initial guess
    LB = [0,0,0,0]; %model parameters lower boundaries
    UB = [2,2,2,2]; %model parameters upper boundaries

    %parameter estimation
    calcParam = lsqnonlin(@objectiveFunction_lsq_2,initialGuess,LB,UB,[],Xmeas,Ymeas);
    Done = calcParam;

function diff = objectiveFunction_lsq_2(PAR,Xmeas,Ymeas)
    y_calculated = yFun(PAR,Xmeas);
    diff = y_calculated-Ymeas;

function result = yFun(PAR,X)
    y_0 = 2;
    val = fzero(@(y)objfun_y(y,PAR,X),y_0);
    result = val;

function result = objfun_y(y,PAR,X)
    A = PAR(1);
    B = PAR(2);
    A = PAR(3);
    C = PAR(4);
    D = PAR(5);

    val = A*y+B*exp(y*C)+g(D,X);
    result = val;

Answer 1

I don't have the optimization toolbox, but are you sure you can pass the constants like that?

I would do this instead:

calcParam = lsqnonlin(@(PAR) objectiveFunction_lsq_2(PAR,Xmeas,Ymeas),initialGuess,LB,UB);