Unscented Kalman filter with performance recovery strategy for parameter estimation of isolation structures

After a strong earthquake, it is crucial to evaluate accurately the health of structures in order to decide whether they can continue to be used. Isolation techniques are well known for enhancing the seismic performance of structures; however, a large response displacement anticipated in the design will likely impact the expansion joints. The occurrence of any damage or impact involves a large disturbance in the system or measurement equations. The Kalman filter (KF) is effective and reliable under proper conditions, but a simple simulation may show disrupted stability conditions after a large disturbance, causing a temporary filter divergence. If the filter design cannot be rapidly adjusted, an overall filter divergence may occur, preventing an accurate evaluation of structural health. This study proposes a performance recovery strategy for the unscented KF (UKF). Rather than identifying optimal parameter estimates at the current instant, the filter meets the stability conditions and asymptotically approaches the true estimates. The measurement noise is adaptively adjusted to bound the true noise covariance. Once the filter divergence is identified based on the expected measurement residual error, the state covariance is adjusted by a covariance-matching technique to bound the true error covariance. After sufficient measurements are obtained, the state covariance is reduced to a low level, indicating filter convergence and a reliable estimation. The effectiveness of the proposed approach is numerically validated for an isolation bridge and building under several scenarios, and two existing UKF variants, which adaptively estimate the system and measurement noise covariances, are compared.