Efficient Bayesian model class selection of vector autoregressive models for system identification

We develop an efficient Bayesian model class selection method for vector autoregressive (VAR) model order selection, so that uncertainties of system identification can be rigorously quantified, and structural dynamic properties can be well captured. The general theory of Bayesian model class selection is first derived in terms of a VAR model to construct the evidence of a model class that is used as the criterion for model order selection. We then approximate the extremely high dimensional integral involved in calculating the evidence based on the Laplace asymptotic approximation. The fast calculation is thus feasible using only the most probable values of VAR parameters. Numerical problems are solved for practical applications. The propagation of uncertainties from VAR parameters to modal parameters is also discussed. A laboratory shear building and a full-scale old factory building are used to demonstrate the good performance of the proposed method in model class selection, system identification, and uncertainty quantification.