A Bootstrap Term Selection Method for the Identification of Time-Varying Nonlinear Systems

Abstract

Most physical systems are nonlinear and often time-varying. Constructing accurate models for nonlinear systems require specialized model structures that include their nonlinearities, whereas models of time-varying systems must include the time courses of the model's parameters. This contribution implements a technique in which the time dependence of the system's parameters are modeled by projecting them onto one or more expansion bases. However, unless an appropriate set of bases is chosen, it is likely that many of the basis functions used in the expansion will not contribute appreciably to the final model and may cause inaccuracy in the parameter estimates. Our study addresses the selection of a minimal number of parameters for optimization from a basis expansion of a system's time variations. The bootstrap method is used to select significant basis coefficients and hence basis functions in order to improve the overall accuracy of the model. The performance of the algorithm is demonstrated on simulated data from a system used to model the reflex contribution to joint stiffness.