Unscented Kalman Filter empowered by Bayesian model evidence for system identification in structural dynamics

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 and can lead to bias or even divergence of the estimates if they cannot catch correctly the real system behaviour. Indeed, the adoption of either excessively simplified or too complex models may have a detrimental effect on tracking of the system state: oversimplified models may underestimate the effect of a physical process taking place; complex models may lead to good data fitting but, possibly, to poor predictions. For this reason, we propose an Unscented Kalman Filter (UKF) empowered with online Bayesian model evidence computation. This approach employs more than one model to track the state of the system and associates to each model a plausibility measure, updated whenever new measurements are exploited. In this way, the filter outcomes obtained for different models are put in comparison and a quantitative confidence value is associated to each of them. While the coupling of Extended Kalman Filter (EKF) and Bayesian model evidence was already addressed, it still lacks robustness in case of severe nonlinearities in system response to the external stimuli; we therefore modified the approach to exploit the most striking features of the UKF, namely the ease of implementation (as it does not require the computation of model Jacobian) and the higher-order accuracy in the description of the evolution of the state statistics. A few challenging identification problems related to structural dynamics are discussed, to show the effectiveness of the proposed methodology.