Fast Bayesian approach for modal identification using free vibration data, Part II - Posterior uncertainty and application

A Bayesian statistical framework has been developed for modal identification using free vibration data in the companion paper (Zhang et al., Mech. Syst. Sig. Process. (2015)). Efficient strategies have been developed for evaluating the most probable value (MPV) of the modal parameters in both well-separated mode and general multiple mode cases. This paper investigates the posterior uncertainty of the modal parameters in terms of their posterior covariance matrix, which is mathematically equal to the inverse of the Hessian of the negative log-likelihood function (NLLF) evaluated at the MPVs. Computational issues associated with the determination of the posterior covariance matrix are discussed. Analytical expressions are derived for the Hessian so that it can be evaluated accurately and efficiently without resorting to finite difference method. The proposed methods are verified with synthetic data and then applied to field vibration test data.