Hierarchical Bayesian Model Updating for Nonlinear Structures Using Response Time Histories

This paper presents a novel hierarchical Bayesian modeling (HBM) framework for the model updating and response predictions of dynamic systems with material nonlinearity using multiple data sets consisting of measured response time histories. The proposed framework is capable of capturing the uncertainties originating from both structural and prediction error parameters. To this end, a multilevel probabilistic model is proposed aiming to characterize the variability of both model and noise parameters. Moreover, a new Laplace approximation is formulated within the HBM framework to reduce the computational burden up to a great extent. Finally, a multidegree of freedom (MDOF) nonlinear system modeled by Bouc-Wen hysteresis elements is employed to demonstrate the effectiveness of the method. © 2022, The Society for Experimental Mechanics, Inc.