Hierarchical Bayesian learning framework for multi-level modeling using multi-level data

A hierarchical Bayesian learning framework is proposed to account for multi-level modeling in structural dynamics. In the system considered as a hierarchy of lower-level models, starting at lowest material level, progressing component then subsystem before ending up level. and uncertainty quantification techniques based on measurements that rely data collected only level cover quite limited number component/subsystem operating conditions are far from representing full spectrum conditions. addition, large models parameters involved lower higher levels system, constitutes this approach inappropriate simultaneously reliably quantifying uncertainties different levels. work, comprehensive tools through process. The embedded within model by introducing probability these depend hyperparameters. An important issue has be accounted shared This necessitates parameter inference process takes into Accurate insightful asymptotic approximations developed, substantially reducing computational effort required procedure. inferred datasets available propagated predict confidence output quantities interest. simple dynamical consisting components subsystems employed demonstrate effectiveness method.