This study opens up new horizons in data-driven structural identification methods offering extensive improvements and enhancements over the existing time-/frequency-domain probabilistic methods. It pushes forward a holistic Bayesian statistical framework to integrate the existing formulations under a hierarchical setting aiming to quantify both the identification precision and the ensemble variability prompted due to model errors. Since the computation of the posterior distributions in hierarchical models is expensive and cumbersome, novel marginalization strategies, asymptotic approximations, and maximum a posteriori estimations are proposed and outlined under mathematical formulations and computational algorithms so as to handle the uncertainty quantification and propagation. For the...[ Read more ]

This study opens up new horizons in data-driven structural identification methods offering extensive improvements and enhancements over the existing time-/frequency-domain probabilistic methods. It pushes forward a holistic Bayesian statistical framework to integrate the existing formulations under a hierarchical setting aiming to quantify both the identification precision and the ensemble variability prompted due to model errors. Since the computation of the posterior distributions in hierarchical models is expensive and cumbersome, novel marginalization strategies, asymptotic approximations, and maximum a posteriori estimations are proposed and outlined under mathematical formulations and computational algorithms so as to handle the uncertainty quantification and propagation. For the first time, the connection between the ensemble covariance matrix and hyper distribution parameters is characterized through approximate estimations. This interesting finding addresses relevant concerns relating to the outcome of the mainstream Bayesian methods in capturing the stochastics variability from multiple data sets. Moreover, the joint estimation of the state and input in linear time-invariant dynamical systems is revisited proposing novel sequential Bayesian formulations. An appealing feature of the proposed method is the promise it holds up for updating the covariance matrices of the process and measurement noise in a real-time fashion using asymptotic approximations. Experimental and numerical examples are employed to illustrate the efficacy and efficiency of the proposed methodologies. Contrary to the present methods that produce significant low-frequency drifts while using noisy acceleration response-only measurements, the proposed method offers drift-free perfect predictions. This Bayesian filtering-technique proposed for the reconstruction of the state and input forces can next be established in the emerging fatigue prognosis frameworks.