Modified Strong Tracking System Identification Method Based on Square Root Center Difference Kalman Filter for Civil Structures

Abstract

Civil engineering structures will exhibit hysteretic behavior due to damage caused by dynamic loads. Identifying the hysteretic behavior of structures is a practical and challenging problem that involves observing vibration data to determine strength and stiffness degradation. This paper proposes a modified square root central difference Kalman filter (MSRCD-KF) method to track this behavior. By combining the QR decomposition and strong tracking filtering technology, the proposed method makes the recursive calculation process unconditionally stable, while enabling the tracking of abrupt changes in structural parameters. A three degree-of-freedom (3-DOF) Duffing system is used in the simulation to verify the effectiveness of the proposed method. Numerical results show that the proposed method can converge to the true value quickly and accurately. Then, the proposed method is used to identify the structural parameters of a two-story concrete frame structure under different seismic loading sequences. In the first example, the structure is simplified as a 2-DOF linear system for which the equivalent stiffness and damping under different damage levels are identified. This information is then used to obtain the stiffness variation trend, damping ratio, and frequency. The second example uses the Bouc–Wen model to consider the stiffness and strength degradation of the structure. Finally, the experimental results demonstrate that the proposed method can accurately identify the structural parameters of nonlinear systems, and the identified hysteresis curves are in good agreement with the experimental ones.