On the Hysteretic Bouc–Wen Model

Abstract

This paper deals with the problem of identifying the parameters of the hysteretic Bouc–Wen model. In the existing literature, the methods devoted to this problem rely mainly on numerical simulations and do not have, to a very large extent, a rigorous mathematical justification. Our method consists in exciting the hysteretic system with a periodic input and obtain the desired parameters from the resulting limit cycle. The identification method that we propose has a rigorous mathematical basis as it based on the analytic description of the limit cycle, and, unlike existing identification methods for the Bouc–Wen model, gives guaranteed relative errors between the (unknown) exact model parameters and their corresponding estimates. We also prove that this method is robust with respect to constant and T-periodic disturbances commonly present in any laboratory experiment. A numerical simulation example illustrates the use of our identification method.