Identification of Hysteresis Dynamics Using Duffing-Like and Bouc-Wen Models

Abstract

Two methods of identifying hysteresis behavior for dynamic systems is introduced and compared in this paper, which are Duffing-like and Bouc-Wen models. Many structural and mechanical systems including the unwanted hysteresis dynamics, such as rubber isolators, magnetoresistive sensors, and magnetorheological dampers, complicate the design, analysis, control, and application work. Hysteresis can be said a general property of dynamic systems, and many mathematical models have been proposed in the material, mechanical, and civil engineering literature, in order to identify the hysteresis dynamics. However, some of the models used in literature, including discontinuous and piecewise terms, are not able to duplicate the hysteresis dynamics accurately. In addition, the complicated and coupling effects of the parameters renders the identification work inefficient and inaccurate. As a result, these models still present difficulty in the process of mechanical design, parameter analysis, and control implementation. The innovative Duffing-like model has been proposed, which is developed based on the original Duffing equation and is a second-order nonlinear ordinary differential equation. Parameters are decoupled in the model, such that the linear and nonlinear effects of the parameters on the hysteresis curve can be investigated. By adjusting the parameters individually, the stiffness, damping, and yielding dynamics are observed. By understanding the influence of each parameter, it is able to advance a standard process for identifying the hysteresis behavior for different dynamic systems. Therefore, in order to reflect the advantages of Duffing-like model, this paper compares the Duffing-like and Bouc-Wen models. Bouc-Wen model was proposed in literature since 1997, and a variety of modification, identification, and application work based on the Bouc-Wen model haven been discussed. However, the Bouc-Wen model is essentially a discontinuous equation and the parameters do not have explicit physical meaning. Therefore, the efficacy of control application using the Bouc-Wen model is very limited. In order to show can compare the Duffing-like and Bouc-Wen models, the parameter identification procedure and numerical simulation results are presented in the paper. In addition, the hysteresis system of a 400-N magnetorheological damper is used as an example for the identification and simulation study. The simulation results show that the Bouc-Wen model, which contains discontinuous functions and difficult-to-track parameters, is not able to provide a reliable basis for parameter tuning. In contract, the Duffing-like model allows the physical meaning of the parameters to be defined in a systematic manner.