topic Re: Nonlinear fitting nonoptimal solution in Discussions

Nonlinear fitting nonoptimal solution

Rutuger85 — Fri, 09 Aug 2024 13:40:18 GMT

I'm trying to use the nonlinear modeling tool to solve the following equation.

Parameter(
{Ea = 35, A = 0.25},
Root(
Exp( -(1000 * Ea) / (:R * :"Test Temperture (K)"n) + A ) *
:"Test Time (hrs)"n
)
);

Ea and A are parameters

R is a constant

Time and Temperature are two columns in my table and I have a column that I set as y, that I'm trying to solve for.

I get a solution for Ea and A but when I plot the predicted vs. the experimental, I don't get a great 1:1 fit (i.e. slope of ~1.5). I have found better solutions to this problem using two separate linearization methods to solve for Ea and A but I would like to run it this way to be able to get the upper and lower bounds for the estimate.

It seems like the software is getting stuck at some local minima vs. driving to an optimal solution. Is there anything I can do to improve upon this method?

Thank you,

JMP version 16.0.0

Re: Nonlinear fitting nonoptimal solution

peng_liu — Fri, 04 Oct 2024 02:40:02 GMT

Are you trying to solve this equation:

Maybe, your starting values (35, 0.25) for Ea and A are too far from the optimal.

Look at the equation, after algebraic manipulation, it is equivalent to this:

Log(Y^2 / Time) = A - 1000/(R*Temp) * Ea.

That is a simple linear relationship. And you may run a regression to get an estimate about A (intercept) and Ea (slope). Then put the estimate back to solve your nonlinear regression. Maybe this can help, but no guarantee. Still depend on your data.

Re: Nonlinear fitting nonoptimal solution

Victor_G — Fri, 04 Oct 2024 07:57:11 GMT

Hi @Rutuger85,

Welcome in the Community !

It may be hard to help you without a sample data set to test. Could you share an anonymized one ?

@peng_liu already gave you a good starting point with the possible transformation of your equation and the different starting points for your parameters values Ea and A.

If you read the documentation Statistical Details on Effective Nonlinear Modeling, there might be other options as well to try :

Specify paramater bounds (red triangle from Nonlinear Fit, "Parameter Bounds" Nonlinear Platform Options) to reduce the search space,
Change optimization method (red triangle from Nonlinear Fit, "Iteration options", and try to use Newton, QuasiNewton SR1, QuasiNewton BFGS, ...),
Change stop conditions : number of iterations (you can increase it to improve the chance of finding an optimum), Obj change, ...

You can also at the end use the sliders linked to the parameters to try improving the fit manually and/or find more acceptable starting values for the solver chosen.

Another option could be to try using the "Fit Curve" platform and try finding an appropriate model Statistical Details for Fit Curve Models.

Hope these few additional suggestions will help you,