Técnicas de otimização bi-objetivo para a determinação da estrutura de modelos NARX

Abstract

The system identification aims to obtain a mathematical model that describes the behavior of a dynamic system from measurements.There are some typical steps in the process of building mathematical models from data: i) tests realization and data collection, ii) selection of the class of models, iii) structure detection, iv) parameters estimation and v) model validation. In this study we investigated the problem of structure detection. In this work, one criterion based on multiobjective techniques was developed to help to determine the structure of polynomial NARX models. Multiobjective techniques, unlike the mono-objective approach, are able to find intermediate solutions that take into account the compromise between the goals, not just individual solutions. This set of solutions is called Pareto-optimal. Therefore, the aim was to determine the structure of a polynomial NARX model, using Pareto curves. The curves were generated by the combination of possibles structures of the model. The methodology proposed in this work was applied to identify three simulated examples and two experimental examples: a buck converter and a pneumatic valve. Simulation results have shown that it is possible to distinguish between under and overparametrization scenarios and to classify spurious from genuine regressors in a model. Experimental results showed that the bi-objective method can assist in the selection of polynomial NARX model structures.