A generalized numerical framework of imprecise probability to propagate epistemic uncertainty

A generalized numerical framework is presented for constructing computational models capable of processing inputs defined as sets of probability distribution functions and sets of intervals. The framework implements a novel solution strategy that couples advanced sampling-based methods and optimization procedures, and provides a credible tool for calculating imprecise measure of failure probability. In this paper, the tool is utilized to perform epistemic uncertainty propagation and to identify the extreme case realizations leading to the bounding values of the failure probability. It has to be noted that the proposed strategy, is insensitive both to the dimension of the problem and to the targeted failure probability, so far as the performance function displays a single failure mode. It is shown by means of examples that the numerical tool is significantly more efficient than a naive approach to the problem of epistemic uncertainty propagation.