Probability box propagation: benchmarking challenge problems

Probability boxes are an effective tool for the quantification of epistemic uncertainty in structural reliability analysis. However, it has been acknowledged that their propagation through a typical structural reliability analysis problem is in general non-trivial, due to the large number of samples of the limit state function required. The challenges are threefold: firstly minimising the computational time required, secondly robustness of the obtained bounds on the failure probability of the structure, and finally the tightness of the obtained bounds. Many methods have emerged in the literature which claim to solve the problem of efficient sampling, but in general the relative efficiency of the proposed methods is currently not well understood. It is likely that the efficiency and robustness of the methods is a function of the type of problem being studied. Therefore, we propose a range of test cases which can be applied to new algorithms which aim to solve this problem. The test cases consist of varying numbers of probability box inputs, rare and common failure events and linear and highly non-linear limit state functions.