Computationally efficient hierarchical Bayesian modeling framework for learning embedded model uncertainties

Abstract

A hierarchical Bayesian modeling (HBM) framework has recently been developed for estimating the uncertainties in the parameters of physics-based models of systems, as well as propagating these uncertainties to estimate the uncertainty in output quantities of interest. According to the framework, uncertainties due to model error are embedded into the model parameters by assigning a parameterized probability distribution and inferring the hyper-parameters of this distribution using multiple sets of experimental data. Herein the framework is extended to properly account for the uncertainty in the prediction error model. The error term is modeled by a Normal distribution with hyper parameters to be estimated by the multiple sets of data. This generalization allow making consistent uncertainty propagation for response quantities of interest. New asymptotic approximations for estimating the uncertainties in the hyper-parameters, as well as propagating these uncertainties to model parameters and observed and unobserved output quantities of interest are developed. The proposed framework provide realistic account of model uncertainties that are insensitive to large number of data sets, avoiding severe underestimation of uncertainty arising from conventional Bayesian learning techniques. Problems drawn from structural dynamics applications are used to demonstrate the effectiveness of the proposed framework. © 2020 European Association for Structural Dynamics. All rights reserved.