Comparative assessment of stabilizing techniques for joint input-state estimation via Augmented Kalman Filter

In the context of Structural Health Monitoring, the accurate estimation of the state of a structural system subjected to various sources of dynamic loads can be beneficial for assessing the current structural performance and for predicting the future one. In case of linear systems, for example, the estimation of the state can provide valuable information about unmeasured strains and corresponding stresses that, in turn, can favor the prediction of fatigue damage. Additionally, state estimation of structural systems responding in the nonlinear regime can facilitate the identification of damages that occurred during an extreme event (e.g., excessive wave, earthquake and strong wind). A major challenge in the state estimation task stems from the unavailability of the external input loads. Therefore, several joint input-state estimation techniques have already been developed to address this issue; among them, the Augmented Kalman Filter (AKF) is one of the most commonly employed. Despite the advantages of the AKF, a critical aspect of this joint input-state estimation technique is associated with the instability that the estimation can experience when only noisy acceleration time series are available. Heretofore, several approaches have been proposed aiming to stabilize the estimation in case of linear systems. In this work, some of the most commonly employed approaches for stabilizing the AKF-based joint-input state estimation (e.g., dummy displacement measurements, dummy load measurements, and Gaussian process latent force model) are adopted and thoroughly compared. Two five-DOF linear systems subjected to dynamic loads are simulated, while the calculated responses are used to assess and compare the performance of various existing techniques for stabilizing the estimation.