7. Bayesian Methods for Uncertainty Quantification in Multi-level Systems

This paper develops a Bayesian methodology for uncertainty quantification and test resource allocation in multi-level systems. The various component, subsystem, and system-level models, the corresponding parameters, and the model errors are connected efficiently using a Bayes network. This provides a unified framework for uncertainty analysis where test data can be integrated along with computational models and simulations. The Bayes network is useful in two ways: (1) in a forward problem where the various sources of uncertainty are propagated through multiple levels of modeling to predict the overall uncertainty in the system response; and (2) in an inverse problem where the model parameters of multiple subsystems are calibrated simultaneously using test data. The calibration procedure leads to a decrease in the variance of the model parameters, and hence, in the overall system performance prediction. Then the Bayes network is used for test resource allocation where an optimization-based procedure is used to identify tests that can effectively reduce the uncertainty in the system model prediction are identified. The proposed methods are illustrated using two numerical examples: a multi-level structural dynamics problem and a multi-disciplinary thermally induced vibration problem.