Parameter identification of a differentiable Bouc-Wen model using constrained extended Kalman filter

Hysteresis is of critical importance to structural safety under severe dynamic loading conditions. One of the widely used hysteretic models for civil structures is the Bouc-Wen model, the effectiveness of which depends on suitable model parameters. The locally non-differentiable governing equation of the conventional Bouc-Wen model poses difficulty on existing identification algorithms, especially the extended Kalman filter, which relies on linearized system equations to propagate state estimates and covariance. In addition, the standard extended Kalman filter usually does not incorporate parameter constraints, and therefore may result in unreasonable estimates. In this article, a modified and differentiable Bouc-Wen model, together with a constrained extended Kalman filter (CEKF), is proposed to identify the hysteretic model parameters in a reliable way. The partial derivatives of the differentiable Bouc-Wen model with respect to hysteretic parameters can be easily calculated for implementing the identification algorithm. Constrained extended Kalman filter restricts the Kalman gain to ensure that the estimates of parameters satisfy constraints from physical laws. Parameter identification using simulated and experimental data collected from a four-story structure demonstrates that constrained extended Kalman filter can achieve more reliable identification results than the standard extended Kalman filter.