Identification of time-varying stiffness with unknown mass distribution based on extended Kalman filter

Although the extended Kalman filter (EKF) provides a promising way for structural state estimation, it cannot effectively track time -varying parameters online. Besides, the structural mass distribution is usually assumed to be known in advance for many EKF-based methods, limiting their applications. In this paper, by using limited observations, an adaptive EKF with unknown mass coefficients (AEKF-UM) approach is proposed for the identification of time -variant parameters and mass distribution at the same time. A real-time updating procedure is presented for improving the process and measurement noise covariance matrices at each time step to assure the stability and accuracy of convergence results. Based on the dramatic increase of measurement noise covariance, an index is defined for determining the damage instant. A covariance resetting technique is then used to enhance the tracking capability for the purpose of effectively capturing the time -varying parameters. The unknown mass coefficients can be estimated at the same time by adding them into the extended state vector. To validate the effectiveness of the proposed approach, two numerical cases are considered, i.e. (i) the Phase I ASCE structural health monitoring benchmark building structure, and (ii) a four-story nonlinear structure equipped with a magneto-rheological (MR) damper. Experimental tests on a four-story building model subject to base excitation are also conducted to investigate the performance of the proposed approach. Results show that the proposed approach is capable of satisfactorily tracking abrupt changes of stiffness parameters with unknown mass distributions.