Extended model set, global data and threshold model identification of severely non-linear systems

This article maybe used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. New parameter estimation algorithms, based on an extended model set, a global data model and a threshold model formulation, are derived for identifyingseverely non-linear systems. It is shown that in each case an integrated structure determination and parameter estimation algorithm based on an orthogonal decomposition of the regression matrix can be derived to provide procedures for identifying parsimonious models of unknown systemswith complexstructure. Simulation studies are included to illustrate the techniques discussed. 1. Introduction If the response of a system is dominated by non-linear characteristics it is often necessary to use a non-linear model and this immediately raises the problem of what class of models to use. The non-linear autoregressive moving average with exogenous inputs (NARMAX) model which was first introduced by Billings and Leontaritis (1981) and rigorously derived by Leontaritis and Billings (1985) provides a unified representation for a wide class of discrete-time non-linear stochastic systems. Model structure determination is often vital for identification of non-linear systems. Even if attention is restricted to polynomial expansions of the NARMAX model, a difficulty quickly arises because the number of terms can increase rapidly leading to an excessively complex model and numerical ill-conditioning in the identification procedure. In order to find an adequate model that uses only a few terms it is necessary to select only the significant terms from a large set of candidate terms. An orthogonal algorithm (Korenberg et al. 1988, Billings et al. 1988) has proved to be very efficient in determining the significant terms and providing corresponding parameter estimates. Chen et al. (1989) have shown that this estimator is in fact an orthogonal least-squares algorithm based on the classical Gram-Schmidt method and have derived several equivalent estimators by using different orthogonal decomposition techniques such …