Hidden-state unscented Kalman filter with unknown input for the joint identification of 3D structural parameters and unknown excitation

The unscented Kalman filter with unknown input (UKF-UI) is an effective method for the identification of structural system and unknown excitation, but for three-dimensional multi-degree-of-freedom structures, the joint identification of structural state-parameter-unknown excitation often leads to high dimensions of extended state vector. To address this issue, a hidden-state unscented Kalman filter with unknown input is proposed for the joint identification of structural parameters and unknown excitation of three-dimensional structures. In the proposed method, only the time-invariant structural parameters are included in the structural state vector, while the displacements and velocities of all structural degrees of freedom are defined as hidden states and excluded from the state vector. This explicitly avoids the conventional extended state vector containing displacement, velocity and structural parameters. By reducing the state vector dimension, the identification of joint structural state-parameter is reduced to parameter-only identification. Moreover, the unbiased minimum variance estimation is used to achieve synchronous identification of unknown excitation. It avoids prior assumptions about unknown excitation and enhances the applicability in practical engineering. The identification of a three-dimensional frame structure under unknown excitation is used to verify the effectiveness of the proposed method. Through the observation of partial acceleration and displacement response data, structural element parameters of the three-dimensional structure and the unknown excitation acting on the three-dimensional structure can be identified.