Use of self-consistency in the structure selection of NARX polynomial models Online publication date: Sat, 29-Nov-2014
by Marcela Andrade Alves; Marcelo Vieira Corrêa; Luis Antonio Aguirre
International Journal of Modelling, Identification and Control (IJMIC), Vol. 15, No. 1, 2012
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 ya(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 ya(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 ya(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.
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