Tuning of Kalman Filter Noise Parameters for Uncertainty Quantification in Input-State Estimation of MDOF Systems

The current research work deals with uncertainty quantification aspects in the problem of joint input-state estimation in structural dynamics. Specifically, it focuses on methodologies that can facilitate the tuning of the noise covariance matrices within the framework of Bayesian filtering techniques. These covariance matrices reflect the uncertainties of the estimation scheme and their proper calibration can reinforce the reliability of the estimated dynamic response. In this work, the performance of two approaches is investigated in the case of linear systems. First, a state-of-the-art methodology from the literature called Bayesian Expectation Maximization is implemented. The purpose of this optimization scheme is to identify the optimal noise covariance matrices based on the available observations of the dynamic response quantities. After evaluating the performance of this methodology, an adaptive time-varying noise Augmented Kalman Filter is proposed for updating the noise characteristics. The proposed scheme is expected to reduce the uncertainty of the input-state estimation. The two methods are applied on a 2D multi-story and multi-bay steel moment resisting frame subjected to earthquake-induced ground excitation. The performance of the different methods is evaluated and discussed.</p