Uncertainty Quantification and Integration in Engineering Systems
A comprehensive framework for the treatment of uncertainty is essential to facilitate decision-making in engineering systems at every stage of the life cycle, such as design, manufacturing/construction, operations, system health assessment and risk management. This dissertation advances the state of the art in uncertainty quantification methods by systematically accounting for the various sources of uncertainty (natural variability, data uncertainty, and model uncertainty) in order to compute the overall uncertainty in the system-level prediction. First, a likelihood-based methodology is developed in order to represent epistemic uncertainty (due to sparse/imprecise data) using probability distributions, thereby facilitating combined treatment of aleatory and epistemic uncertainty. Second, computational methods are developed to systematically include the various sources of uncertainty in model verification, validation and calibration activities. Third, a Bayesian network-based methodology is developed for integrating the results of various uncertainty quantification activities in hierarchical system models. Different types of hierarchical system models, including multi-physics and multi-level models, are considered. Fourth, the Bayesian methodology is used to guide decision-making with respect to test resource allocation for uncertainty quantification. Finally, a methodology for inverse sensitivity analysis is developed in order to analyze the effect of various sources of uncertainty on the variance of posterior estimation and thereby aid in design of experiments and dimension reduction. The proposed methods are applied to civil, mechanical, and aerospace structures.