A two-stage and two-step algorithm for the identification of structural damage and unknown excitations: numerical and experimental studies

Extended Kalman Filter (EKF) has been widely used for structural identification and damage detection. However, conventional EKF approaches require that external excitations are measured. Also, in the conventional EKF, unknown structural parameters are included as an augmented vector in forming the extended state vector. Hence the sizes of extended state vector and state equation are quite large, which suffers from not only large computational effort but also convergence problem for the identification of a large number of unknown parameters. Moreover, such approaches are not suitable for intelligent structural damage detection due to the limited computational power and storage capacities of smart sensors. In this paper, a two-stage and two-step algorithm is proposed for the identification of structural damage as well as unknown external excitations. In stage-one, structural state vector and unknown structural parameters are recursively estimated in a two-step Kalman estimator approach. Then, the unknown external excitations are estimated sequentially by least-squares estimation in stage-two. Therefore, the number of unknown variables to be estimated in each step is reduced and the identification of structural system and unknown excitation are conducted sequentially, which simplify the identification problem and reduces computational efforts significantly. Both numerical simulation examples and lab experimental tests are used to validate the proposed algorithm for the identification of structural damage as well as unknown excitations for structural health monitoring.