Otimização bi-objetivo aplicada à estimação de parâmetros de modelos não-lineares: caracterização e tomada de decisão

Abstract

The system identification consists of a group of techniques for dynamic system modeling. Usually, these techniques are classified according to the use or not of information presented in measured data. Generally, the system identification is composed by four parts: (i) selection of representation, (ii) structure detection, (iii) parameters estimation and (iv) model validation. The basic theory is well structured and there is considerable number of works that use this theory to develop mathematical and computational tools. Normally, the analysis of residues, that is the one step ahead error, is used for structure detection as performance index. Although this approach is still used, some works suggest that this presents an inclination to structural error. In this work, it is suggested, that these indexes are used based on simulation error and not residual. The present work intends to use a bi-objective approach to parameter estimation. The analysis of the simulation error of the model is used as performance index in the decision stage. The structure will be considered known and equal to the system. This work aims to plead, with base in simulations and mathematical analysis, that bi-objective estimators, with certain structural characteristics, such as, linearity in the parameters and convexity, are able to yield a set of models, which are statically similar. It is also possible to estimate the closest parameters to real values of the models. These estimated parameters are unbiased. The decision stage is taken into account by means of correlation techniques. Several examples in the text are used to validate the developed techniques. The characterization and the decision stage of bi-objective unbiased estimator are the main contributions of this thesis.