Alternating state-parameter identification of Bouc-Wen hysteretic systems from steady-state harmonic response

Abstract

• A novel identification method for Bouc-Wen systems based on harmonic balance method is proposed. • An effective initialization method is developed to predetermine the parameters of linear subsystem and Bouc-Wen parameters. • To update the estimation of parameters in linear subsystem and hysteretic force, an iteratively alternating method is further developed. • The simulation and experimental studies validate the effectiveness of the new method. Describing hysteresis behaviors in mechanical engineering has attracted increasing research interest. Among the numerous models that characterize hysteretic nonlinearities, the Bouc-Wen model stands out owing to its versatility. However, there is a critical challenge for Bouc-Wen hysteretic systems identification that the internal hysteretic restoring force is usually not measurable. A novel alternating state-parameter identification method is proposed in this paper to identify Bouc-Wen hysteretic systems from steady-state harmonic response. Based on the interpretation that system response and restoring force can be analytically approximated via Fourier series, the harmonic balance method is leveraged to reconstruct the hysteretic force. To implement the reconstruction process, an effective initialization procedure is developed to predetermine the parameters of linear subsystem and Bouc-Wen parameters. In the initialization procedure, the Duhamel's integral is leveraged to represent the Bouc-Wen hysteretic system identification problem, which avoids the high-order derivative of measured displacement and further reduces the effect of noise. Additionally, to update the estimation of system parameters and hysteretic force, an iteratively alternating procedure is further developed in this paper. The numerical simulation and dynamic experiment validate the effectiveness of the new identification method for Bouc-Wen hysteretic systems.