Bayesian Methodology for Uncertainty Quantification in Complex Engineering Systems

Abstract

This chapter presents a Bayesian methodology for system-level uncertainty quantification and test resource allocation in complex engineering systems. The various component, subsystem, and system-level models, the corresponding parameters, and the model errors are connected efficiently using a Bayesian network. This provides a unified framework for uncertainty analysis where test data can be integrated along with computational models across the entire hierarchy of the overall engineering system. The Bayesian 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-level response; and (2) in an inverse problem where the model parameters of multiple subsystems are calibrated simultaneously using test data. Test data available at multiple data are first used to infer model parameters, and then, this information is propagated through the Bayesian network to compute the overall uncertainty in the system-level prediction. Then, the Bayesian network is used for test resource allocation where an optimization-based procedure is used to identify tests that can effectively reduce the overall uncertainty in the system-level prediction. Finally, the overall Bayesian methodology for uncertainty quantification and test resource allocation is illustrated using three different numerical examples. While the first example is mathematical, the second and third examples deal with practical applications in the domain of structural mechanics.