Epistemic Uncertainty in the Calculation of Margins

Epistemic uncertainty, characterizing lack-of-knowledge, is often prevalent in engineering applications. However, the methods we have for analyzing and propagating epistemic uncertainty are not as nearly widely used or well-understood as methods to propagate aleatory uncertainty (e.g. inherent variability characterized by probability distributions). In this paper, we examine three methods used in propagating epistemic uncertainties: interval analysis, Dempster-Shafer evidence theory, and second-order probability. We demonstrate examples of their use on a problem in structural dynamics, specifically in the assessment of margins. In terms of new approaches, we examine the use of surrogate methods in epistemic analysis, both surrogate-based optimization in interval analysis and use of polynomial chaos expansions to provide upper and lower bounding approximations. Although there are pitfalls associated with surrogates, they can be powerful and efficient in the quantification of epistemic uncertainty.