A framework for global reliability sensitivity analysis in the presence of multi-uncertainty

In reliability analysis with numerical models, one is often interested in the sensitivity of the probability of failure estimate to changes in the model input. In the context of multi-uncertainty, one whishes to separate the effect of different types of uncertainties. A common distinction is between aleatory (irreducible) and epistemic (reducible) uncertainty, but more generally one can consider any classification of the uncertain model inputs in two subgroups, type A and type B. We propose a new sensitivity measure for the probability of failure conditional on type B inputs. On this basis, we outline a framework for multi-uncertainty-driven reliability sensitivity analysis. A bi-level surrogate modelling strategy is designed to efficiently compute the new conditional reliability sensitivity measures. In the first level, a surrogate is constructed for the model response to circumvent possibly expensive evaluations of the numerical model. By solving a sequence of reliability problems conditional on samples of type B random variables, we construct a level 2-surrogate for the logarithm of the conditional probability of failure, using polynomial bases which allow to directly evaluate the variance-based sensitivities. The new sensitivity measure and its computation are demonstrated through two engineering examples.