Improved Structure Detection For Polynomial NARX Models Using a Multiobjective Error Reduction Ratio

Abstract

This paper addresses the problem of structure detection for polynomial NARX models. It develops MERR, a multiobjective extension of a methodology well-known as the error reduction ratio (ERR). It is shown that it is possible to choose terms which take into account dynamics of prediction error and other types of affine information, such as fixed points or static curve. Two examples are included to illustrate the proposed methodology. A numerical example shows that the technique is able to reconstruct the structure of a system, known a priori. The identification of a pilot DC–DC buck converter shows that the proposed approach is capable to find models valid over a wide range of operation points. In this latter example, MERR is compared with ERR in two forms: (i) affine information is applied only in the structure selection for MERR and (ii) affine information is applied for structure selection for MERR and for parameter estimation for both MERR and ERR. In both comparisons, MERR presented nondominated solutions of Pareto set