A framework for global reliability sensitivity analysis in the presence of multi-uncertainty. (March 2020) - Ehre, Max; Papaioannou, Iason; Straub, Daniel
Highlights: We propose a set of new global reliability-oriented sensitivity measures. The indices are tailored to multi-uncertainty scenarios (e.g. aleatory/epistemic). The quantities of interest are log-transformed conditional failure probabilities. We devise a bi-level surrogate-based approach to efficiently estimate the indices. The efficacy of the approach is demonstrated in two engineering examples. Abstract: 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.