A computational algorithm for the multiple generation of nonlinear mathematical models and stability study

This paper presents an algorithm that generates families of mathematical models with nonlinear parameters, and includes the study of linear models, based on the experimental data of the intervening variables. The implementation of this algorithm has been named polymodel and is based on the application of the Gauss–Newton algorithm for obtaining the parameters of nonlinear models [Verdú F. Un Algoritmo para la construcción múltiple de modelos matemáticos no lineales y el estudio de su estabilidad. Doctoral Tesis. Universidad de Alicante, 2004]. One of its characteristics is a search among different nonlinear models within the parameters; unlike the methods found in the scientific literature [Camacho Rosales J. Estadística con SPSS para windows. Ed. Ra-Ma, 2002; Mathsoft Inc. Splus-4. Guide to Statistics. Seattle, 1997], the user does not intervene in their generation. A pruning criteria has also been introduced that is based on the stability analysis of models generated from perturbations, applying studies carried out by the authors and published in [Verdú F, Villacampa Y. A computer program for a Monte Carlo analysis of sensitivity in equations of environmental modelling obtained from experimental data. Advances in Engineering Software, 2002]. Object-oriented Pascal has been used in Delphi 6.