A nonlinear state-space approach to hysteresis identification. (1st February 2017) - Noël, J.P.; Esfahani, A.F.; Kerschen, G.; Schoukens, J.
Abstract: Most studies tackling hysteresis identification in the technical literature follow white-box approaches, i.e. they rely on the assumption that measured data obey a specific hysteretic model. Such an assumption may be a hard requirement to handle in real applications, since hysteresis is a highly individualistic nonlinear behaviour. The present paper adopts a black-box approach based on nonlinear state-space models to identify hysteresis dynamics. This approach is shown to provide a general framework to hysteresis identification, featuring flexibility and parsimony of representation. Nonlinear model terms are constructed as a multivariate polynomial in the state variables, and parameter estimation is performed by minimising weighted least-squares cost functions. Technical issues, including the selection of the model order and the polynomial degree, are discussed, and model validation is achieved in both broadband and sine conditions. The study is carried out numerically by exploiting synthetic data generated via the Bouc–Wen equations. Abstract : Highlights: A general framework to identify hysteresis in dynamic systems is introduced. State-space models with polynomial nonlinear terms are selected to support this framework. They are fitted to data using a rigorous two-step weighted least-squares methodology. A numerical study is conducted to demonstrate the fitting accuracy of the proposed approach. The identified black-box models are also found to be reasonably parsimonious.