De Dados Medidos até Avaliação de Modelos: Modelamento de Sistemas através de Galerkin-Jacobi Personalizado (From Measure Data to Evaluation of Models: System Modeling through Custom Galerkin-Jacobi)

Igor Santos Peretta (iperetta@ieee.org)1, Keiji Yamanaka (keiji@ufu.br)2, Pierre Collet (pierre.collet@unistra.br)3


1Universidade Federal de Uberlândia (BR); Université de Strasbourg (FR)
2Universidade Federal de Uberlândia
3Université de Strasbourg

This paper appears in: Revista IEEE América Latina

Publication Date: May 2015
Volume: 13,   Issue: 5 
ISSN: 1548-0992


Abstract:
This work presents a method to evaluate the quality of candidate models for a given observed system in terms of fitness. Taking a candidate model, i.e. a proposed differential equation, this work uses the Galerkin method with a Jacobi/Legendre polynomial basis to approximate solve it. After, this method computes the mean square error between the approximate solution and the measure data. It ends with a relative grade for the fitness of the model to the system to enable comparisons between other possible candidates. The proposed method is intended to aid evolutionary algorithms to evolve fit models to systems based on their measure data.

Index Terms:
system modeling, differential equations, Galerkin method, Jacobi polynomials, Legendre polynomials, measured data, univariate domain, multivariate domain   


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