A bootstrap method for structure detection of NARMAX models

Abstract

Many systems may be described by NARMAX models using only a few terms. However, depending on the order of the system the number of candidate terms can become very large. Selection of a subset of these candidate terms is necessary for an efficient system description. This is an unresolved issue in system identification for over-parameterized models. Therefore, in this paper, we develop a bootstrap structure detection (BSD) algorithm as a means of determining the structure of highly over-parameterized models. The performance of this BSD technique was evaluated by using it to estimate the structure of a (1) simple NARMAX model, (2) moderately over-parameterized NARMAX model and (3) highly over-parameterized NARMAX model. The results demonstrate that the BSD algorithm is a robust method for detecting the structure of NARMAX models. This method provides accurate estimates of parameter statistics without relying on assumptions made by traditional procedures and yields a parsimonious description of the system.

Acknowledgments

Supported by grants from the Natural Sciences Engineering Research Council of Canada, the Canadian Institutes of Health Research and the Max Stern Fellowship of McGill University.

The authors would like to dedicate this work in loving memory of Margherita B. Rapagna (25 August, 1968–20 May, 2002).

Notes

‡ Present address: McConnell Brain Imaging Center, Montréal Neurological Institute, 3801 University Street, Montréal, Québec H3A 2B4, Canada.

Additional information

Notes on contributors

Robert E. Kearney

‡ Present address: McConnell Brain Imaging Center, Montréal Neurological Institute, 3801 University Street, Montréal, Québec H3A 2B4, Canada.