Unscented Kalman Filter Empowered by Bayesian Model Evidence for System Identification in Structural Dynamics

Abstract

System identification is often limited to parameter identification, while model uncertainties are disregarded or accounted for by a fictitious process noise. However, modelling assumptions may have a large impact on system identification. For this reason, we propose to use an unscented Kalman filter (UKF) empowered by online Bayesian model evidence computation for the sake of system identification and model selection. This approach employs more than one model to track the state of the system and associates with each model a plausibility measure, updated whenever new measurements are available. The filter outcomes obtained for different models are then compared and a quantitative confidence value is associated with each of them. Only the system identification outcomes related to the model with the highest plausibility are considered. While the coupling of extended Kalman filters (EKFs) and Bayesian model evidence was already addressed, we modify the approach to exploit the most striking features of the UKF, namely, the ease of implementation and higher-order accuracy in the description of the evolution of the state mean and variance. A challenging identification problem related to structural dynamics is discussed to show the effectiveness of the proposed methodology.