Sequential Refinement of Uncertainty Through Bayesian Inference and Global Sensitivity Analysis

Abstract

This paper presents a computational framework for uncertainty characterization and propagation, as well as sensitivity analysis under the presence of aleatory and epistemic uncertainties, and it develops a rigorous methodology for efficient refinement of epistemic uncertainty by identifying important epistemic variables that significantly affect the overall performance of an engineering system. The proposed methodology is illustrated using the NASA Langley Research Center Uncertainty Quantification Challenge problem that deals with an uncertainty analysis of a generic transport model. First, Bayesian inference is used to infer subsystem-level epistemic quantities using the subsystem-level model and corresponding data. Second, tools of variance-based global sensitivity analysis are used to identify four important epistemic variables (this limitation, specified in the NASA Langley Research Center Uncertainty Quantification Challenge, is reflective of practical engineering situations where not all epistemic variables can be refined due to time/budget constraints) that significantly affect system-level performance. The most significant contribution of this paper is the development of the sequential refinement methodology, where epistemic variables for refinement are not identified all at once. Instead, only one variable is first identified, and then, Bayesian inference and global sensitivity calculations are repeated to identify the next important variable. This procedure is continued until all four variables are identified and the refinement in the system-level performance is computed. The advantages of the proposed sequential refinement methodology over the all-at-once uncertainty refinement approach are explained and numerically demonstrated, before being applied to the NASA Langley Research Center Uncertainty Quantification Challenge problem.

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