Identification of Hysteretic Systems Using NARX Models, Part I: Evolutionary Identification

Abstract

Although there has been considerable work on the identification of hysteretic systems over the years, there has been comparatively little using discrete NARX or NARMAX models. One of the reasons for this may be that many of the common continuous-time models for hysteresis, like the Bouc-Wen model are nonlinear in the parameters and incorporate unmeasured states, and this makes a direct analytical discretisation somewhat opaque. Because NARX models are universal in the sense that they can model any input–output process, they can be applied directly without consideration of the hysteretic nature; however, if the polynomial form of NARX were to be used for a Bouc-Wen system, the result would be input-dependent because of the non-polynomial (indeed discontinuous) nature of the original model. The objective of the current paper is to investigate the use of NARX models for Bouc-Wen systems and to consider the use of non-polynomial basis functions as a potential means of alleviating any input-dependence. As the title suggests, the parameter estimation scheme adopted will be an evolutionary one based on Self-Adaptive Differential Evolution (SADE). The paper will present results for simulated data.