Nonlinear model updating through a hierarchical Bayesian modeling framework

A new time-domain probabilistic technique based on hierarchical Bayesian modeling (HBM) framework is proposed for calibration and uncertainty quantification of hysteretic type nonlinearities dynamical systems. Specifically, hyper models are introduced respectively material model parameters as well prediction error variance parameters, aiming to consider both the due unmodeled dynamics. asymptotic approximation developed simplify process nonlinear updating substantially reduce computational burden HBM framework. This further employed provide insightful expressions parameters. Given a large number data points within dataset, formulated be independent parameter. Two numerical examples conducted verify accuracy performance method considering Bouc–Wen (BW) nonlinearities. Model manifested variability in measured from multiple datasets. Results five-story structure indicate that main source can affect experimental data. It also demonstrated parameter arising depends sensor locations. shown approach robust not only quantifying uncertainties structural but predicting system quantities interests (QoI) with reasonable providing reliable bounds, opposed conventional which often severely underestimates bounds.