Hierarchical Bayesian Model Updating via Conditional Normalizing Flows

Recently, data-driven Bayesian approaches, such as conditional normalizing flows (CNFs), have begun to attract attention as a means of probabilistic model updating without explicitly defined likelihoods. Motivated by these recent developments, this study proposes a hierarchical Bayesian model updating framework based on CNF, which enables efficient likelihood-free inference from limited observations. The CNF is trained in an offline data-driven manner to learn the joint density of structural responses and model parameters, allowing direct evaluation of likelihood terms without additional simulations, thus effectively acting as a surrogate model within the Bayesian inference process. To estimate the posterior distributions of both model and hyperparameters, a hybrid Gibbs–Metropolis sampling strategy is introduced, achieving computational efficiency even in high-dimensional spaces. The proposed approach is validated through 2-DOF and 3-DOF benchmark problems, showing that it can accurately reproduce theoretical posterior distributions and quantify uncertainties with only a few observations. The results indicate that the CNF-based hierarchical Bayesian updating provides a robust and flexible framework for stochastic model calibration and uncertainty quantification in structural dynamical systems.