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.
Highlights
Kalman filters (KFs) are well-known tools for system identification
We propose a way to tackle this aspect by calculating a quantitative estimate, referred to as model evidence, measuring how much the model employed by the KF is plausible with respect to other possible parametrizations
From the results reported above, M2 seems to lead to the best system identification; we reached this conclusion by knowing the mechanical properties of the reference system
Summary
In civil and mechanical engineering, different model classes, consisting of different parametrizations of the structure to be identified, can be formulated. They are built upon different levels of complexity in the description of the system mechanics and uncertainty in the formulation of the modelling assumptions. Emphasis is usually placed on improving the quality of the parameter estimate, especially whenever nonlinear dynamic systems are handled. With this goal, KF extensions such as the extended Kalman filter (EKF) or the unscented Kalman filter (UKF) have been introduced. While a similar estimate was discussed in [2]
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