The current structural health monitoring (SHM) system still cannot effectively and directly monitor most of the loads acting on the structure. Therefore, the state-input joint identification algorithm based on augmented Kalman filtering (AKF) has become one of the best choices. Due to the need to construct an augmented state vector, existing AKF algorithms must impose an evolutionary model on unknown input, such as the famous random walk assumption, which often does not match the actual situation. This paper proposes a novel implicit state augmented Kalman filter (ISAKF) algorithm with broad applicability and clear physical meaning. Its biggest difference compared to traditional AKF is that it eliminates any prior models imposed on the input. The components of the augmented state vector are mathematically independent of each other, so it essentially weakens the connection between the input and the state, which leads to a decrease in the robustness of the algorithm. The proposed algorithm utilizes the Newmark-β method to establish system independent constraint to compensate for the loss of robustness. In the proposed algorithm, the form of the discrete-time recursive equation is completely different from the traditional one, so the traditional Kalman filtering (KF) framework is no longer applicable, and a new filtering framework is derived in this paper. Two numerical cases were presented, the first demonstrating the performance of ISAKF in jointly identifying structural states and inputs in displacement-only observation scenarios, and the second demonstrating the performance of ISAKF in identifying seismic input and equivalent nonlinear force when structures exhibit nonlinear behavior under earthquake conditions. Finally, the effectiveness of the proposed ISAKF algorithm was validated through experiments on a scaled five story shear type building model.

augmented Kalman filter,implicit state,robustness,unknown input,real time