A nonlinear unbiased minimum-variance filter for structural identification with unknown external excitations

Excitations identification and structural identification are two pivotal factors in the field of structural health monitoring. The extended Kalman filter (EKF) is widely used for identifying structural dynamic systems. However, it has been demonstrated that an inevitable linearization error exists, which can make it difficult to deal with situations when external excitations are unknown. To address this issue, this paper proposes a novel derivative-free version of the nonlinear unbiased minimum variance filter for structural identification with unknown external excitations (NUMVF-UEE) based on the unscented Kalman filter (UKF). This method derives optimal estimations of structural parameters and unknown external excitations by minimizing the traces of the covariance matrices with respect to the augment vectors. To demonstrate the effectiveness of the proposed method, several numerical examples are introduced. The results show that NUMVF-UEE can simultaneously provide accurate estimations of both structural system parameters and unknown external excitations in real-time.