Targeted Reduction of p-Boxes in Risk Assessments With Mixed Aleatory and Epistemic Uncertainties

Abstract

The treatment of uncertainty using extra-probabilistic approaches, like intervals or p-boxes, allows for a clear separation between epistemic uncertainty and randomness in the results of risk assessments. This can take the form of an interval of failure probabilities; the interval width W being an indicator of “what is unknown.” In some situations, W is too large to be informative. To overcome this problem, we propose to reverse the usual chain of treatment by starting with the targeted value of W that is acceptable to support the decision-making, and to quantify the necessary reduction in the input p-boxes that allows achieving it. In this view, we assess the feasibility of this procedure using two case studies (risk of dike failure, and risk of rupture of a frame structure subjected to lateral loads). By making the link with the estimation of excursion sets (i.e., the set of points where a function takes values below some prescribed threshold), we propose to alleviate the computational burden of the procedure by relying on the combination of Gaussian process (GP) metamodels and sequential design of computer experiments. The considered test cases show that the estimates can be achieved with only a few tens of calls to the computationally intensive algorithm for mixed aleatory/epistemic uncertainty propagation.