1 Hierarchical Bayesian Modeling Framework for Model Updating and Robust Predictions in Structural Dynamics using Modal Features Xinyu Jia 1 , Omid Sedehi 2 , Costas Papadimitriou 1,* , Lambros S. Katafygiotis 2 , Babak Moaveni 3 1 Department of Mechanical Engineering, University of Thessaly, Volos, Greece 2 Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology, Hong Kong, China 3 Department of Civil and Environmental Engineering, Tufts University, MA, USA ABSTRACT The hierarchical Bayesian modeling (HBM) framework has recently been developed to tackle the uncertainty quantification and propagation in structural dynamics inverse problems. This new framework characterizes the ensemble variability of structural parameters observed over multiple datasets together with the identification uncertainty obtained based on the discrepancy between the measured and model outputs. The present paper expands on this framework, developing it further for model inference based on modal features. It generalizes the HBM framework by considering an additional hyper distribution to characterize the uncertainty of prediction error variances across different datasets. Moreover, computationally efficient approximations are developed to simplify the computation of the posterior distribution of hyper-parameters. Conditions are presented under which the approximations are expected to be accurate. The asymptotic approximations provide insightful information on the relation of the estimates of the hyper-parameters and their uncertainties with the variability of the estimations and identification uncertainties. Introducing the HBM formulation is beneficial, particularly for the propagation of uncertainty based on both structural and prediction error parameters providing reasonable uncertainty bounds. The posterior uncertainty of the structural and prediction error parameters is propagated to estimate data-informed output quantities of interests, including failure probabilities, which offers robustness to the variability over datasets. The proposed approximations are tested and verified using simulated and experimental examples. The effects of the uncertainty due to dataset variability and the prediction error uncertainty are illustrated in these examples. Keywords: Hierarchical Bayesian modeling; parameter variability; prediction error uncertainty; model updating; response prediction; modal properties 1. Introduction Updating models and predicting responses using data-driven approaches has been substantially investigated in structural dynamics using deterministic [1] and probabilistic approaches [2-5]. Due to a rigorous probabilistic framework, Bayesian tools can rationally integrate data and physics-based models in order to select the most appropriate models among alternative competing ones [6-8], estimate the parameters of these models and their uncertainties [5,9,10], as well as propagating uncertainties to predict important quantities of interest (QoI) in operation and safety of structural systems [11-14]. Undoubtedly, the Bayesian framework offers an indispensable and powerful mathematical tool for quantifying and propagating uncertainties in simulations. However, challenges still remain. For example, owing to the redundant information carried in the data, the conventional Bayesian approach often underestimates the uncertainty, resulting in an inherent reduction of the parameter uncertainty as the number of data increases [2]. Furthermore, standard Bayesian procedures do not properly take into account the uncertainty in the parameters attributed to the variability in experimental data, environmental conditions, material properties, manufacturing process, assembling process, and nonlinear mechanisms activated under different loading conditions [15-19]. In light of above, a comprehensive hierarchical Bayesian modeling (HBM) framework has been further developed in various scientific disciplines [20-24] to properly quantify the uncertainties within the model parameters. Specifically in the field of structural dynamics, the HBM approach was used to * Corresponding Author Email Address: costasp@uth.gr