Mixed aleatory and epistemic uncertainty propagation using Dempster–Shafer theory

Abstract

In this paper, we deal with epistemic uncertainty in the framework of Dempster–Shafer theory, where basic belief assignments are used to characterize the uncertain parameters. To propagate the mixed epistemic and aleatory uncertainties, we introduce the relevant theoretical basics of DS theory, present the numerical approach based on DS theory combined with generalized polynomial chaos expansion, and conduct the error analysis for the numerical approach. Specifically, to analyze the convergence rate of the numerical solution represented with basic belief assignments, we define a measure based on the Hausdorff distance to quantify the difference between two basic belief assignments. The convergence of the numerical approximation is demonstrated with a few simple examples under different scenarios, and the presented numerical approach is applied to quantify the mixed types of uncertainty in quasi-one-dimensional flow.