Identification of Bouc-Wen hysteretic systems based on a joint optimization approach

Abstract

Hysteresis phenomena are commonly encountered in structural systems. To describe hysteresis behaviors, the Bouc-Wen model is intensively leveraged to reconstruct hysteresis loops in mechanical engineering owing to its versatility. However, the internal hysteretic restoring force is usually not measurable, which is a critical challenge in nonlinear system identification. A novel identification method based on a joint optimization approach is proposed in this paper to identify Bouc-Wen hysteretic systems. Considering the effect of measurement errors, the Duhamel’s integral is introduced to rewrite the Bouc-Wen hysteretic system identification problem, which can effectively avoid calculating the second derivative of the displacement measurement. In addition, a jointly optimized objective function is developed to calibrate the system parameters and internal hysteretic force by imposing joint physics constraints on the system parameters and states. To improve the computational efficiency of the joint optimization problem, an iteratively alternating procedure is proposed to update the state and parameter estimations. The simulation and experimental studies validate the effectiveness of the new identification method for hysteretic systems.