Improved force identification with augmented Kalman filter based on the sparse constraint

To ensure the accurate analysis and evaluation of structural integrity and vibration responses, a novel technique is required for load identification with minimal error. Accordingly, this paper presents an augmented Kalman filter (AKF) based on sparse constraint theory for solving state and input estimation problems. In the scheme developed in this study, the space-sparse characteristic of the force (as prior information) is introduced into the AKF via a pseudo- measurement equation. The unconstrained optimization of the AKF is transformed into constrained optimization based on the l1-norm. The proposed method solves the force drift problem in AKF more effectively than classical dummy measurements. Moreover, the stability of the system and its estimation accuracy are significantly increased. Additionally, a new augmented state-space model was established based on the augmented precise integration method, which can be applied more extensively than the zero-order hold model. To assess the performance of the proposed method, three cases were examined, namely, two numerical simulations and an experiment involving a three-story shear building. The results indicated that the proposed method outperforms the traditional dummy measurement method under a non-underdetermined and collocated sensor configuration.