A suboptimal bootstrap method for structure detection of non-linear output-error models with application to human ankle dynamics

Abstract

Identification of non-linear systems involves estimating unknown parameters and structure detection, selection of a subset of candidate terms that best describe the observed output. This is a necessary procedure to compute an efficient system description which may afford greater insight into the functionality of the system or a simpler controller design. For non-linear systems simple output additive noise can generate multiplicative terms between the input, output and noise. The terms associated with noise need to be modelled to obtain unbiased parameter estimates, significantly increasing the number of candidate terms to be estimated and considered. In special cases, it may be possible to use an output error (OE) model structure and the instrumental variable (IV) estimator to obtain unbiased parameters without modelling the noise. This significantly reduces the dimensionality of the structure computation problem. Therefore, in this paper, we propose a suboptimal bootstrap structure detection (SOBSD) algorithm for non-linear OE models.

Performance of this SOBSD algorithm was evaluated by using it to estimate the structure of (i) a simulated NARMAX model describing ankle dynamics and (ii) application to experimental data. The results demonstrate that the SOBSD method is simple to use and provides good results for non-linear OE models.

Acknowledgments

Supported by grants from Vetenskapsrådet, The Swedish Research Council. The author would like to dedicate this work in loving memory of Margherita B. Rapagna (August 25, 1968–May 20, 2002).

Notes

Email: [email protected]

Additional information

Notes on contributors

Sunil L. Kukreja *

Email: [email protected]