Structure detection of nonlinear dynamic systems using bootstrap methods [and biomedical application]

Identification of NARMAX models involves estimating unknown parameters and detecting its underlying structure, which entails selecting a set of parameters to give a parsimonious description of the system. In the present study a bootstrap based structure detection algorithm is investigated. The bootstrap method is a numerical procedure for estimating parameter statistics that requires few assumptions. Its use for structure detection maintains the simplicity of routines developed for linear regression estimators but requires a less restrictive set of assumptions. The performance of this bootstrap structure detection technique was evaluated by using it to estimate the structure of a simple NARMAX model and comparing the results to those with the t-test and stepwise regression. Applicability of the method to more complex systems such as ones encountered in biomedical applications, was shown by identifying a parsimonious system description of the ankle model. Moreover, we showed that the bootstrap method yields parameter statistics that are closer to optimal than using traditional methods. The proposed method is simple to use and is robust in the presence of noise.