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Most studies tackling hysteresis identification in the technical literaturefollow white-box approaches, i.e. they rely on the assumption that measureddata obey a specific hysteretic model. Such an assumption may be a hardrequirement to handle in real applications, since hysteresis is a highlyindividualistic nonlinear behaviour. The present paper adopts a black-boxapproach based on nonlinear state-space models to identify hysteresis dynamics.This approach is shown to provide a general framework to hysteresisidentification, featuring flexibility and parsimony of representation.Nonlinear model terms are constructed as a multivariate polynomial in the statevariables, and parameter estimation is performed by minimising weightedleast-squares cost functions. Technical issues, including the selection of themodel order and the polynomial degree, are discussed, and model validation isachieved in both broadband and sine conditions. The study is carried outnumerically by exploiting synthetic data generated via the Bouc-Wen equations.

A nonlinear state-space approach to hysteresis identification