Title: Use of self-consistency in the structure selection of NARX polynomial models

Authors: Marcela Andrade Alves; Marcelo Vieira Corrêa; Luis Antonio Aguirre

Addresses: Curso de Engenharia Elétrica, Centro Universitário do Leste de Minas Gerais (Unileste-MG), Av. Tancredo Neves 3500, Coronel Fabriciano, Brazil. ' Curso de Engenharia Elétrica, Centro Universitário do Leste de Minas Gerais (Unileste-MG), Av. Tancredo Neves 3500, Coronel Fabriciano, Brazil. ' Departamento de Engenharia Eletrônica, Universidade Federal de Minas Gerais (UFMG), Av. Antônio Carlos 6627, Belo Horizonte, Brazil

Abstract: This paper addresses the choice of regressors in non-linear polynomial models. Because the starting point is a tentative model, the procedure can be interpreted as a model structure simplification scheme. Given a tentative model y(k | k – 1) estimated from a set of data Z, it is shown how simple analytical manipulations yield a corresponding two-step-ahead polynomial y_a(k + 1 | k – 1). On the other hand, using the data Z and classical structure selection algorithms it is possible to choose the structure of a data-driven two-step-ahead polynomial y(k + 1 | k – 1). The common terms in y_a(k + 1 | k – 1) and y(k + 1 | k – 1) are called self-consistent. If the tentative model has any terms that produce non-self-consistent terms in y_a(k + 1 | k – 1), such terms should be removed. The new procedure was tested on simulated and measured data in cases where the classical structure selection algorithms selected spurious terms. Results show that using self-consistency, one is able to detect such spurious terms.

Keywords: system identification; structure selection; prediction error minimisation; NARX models; self-consistency; polynomial modelling.

DOI: 10.1504/IJMIC.2012.043935

International Journal of Modelling, Identification and Control, 2012 Vol.15 No.1, pp.1 - 12

Published online: 29 Nov 2014 *

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