Advanced Line Sampling for efficient robust reliability analysis

• A novel numerical strategy to compute interval failure probabilities is presented.
• Credal sets and bounded sets are utilized for the robust reliability analyses.
• The cost of a robust reliability analysis is reduced by orders of magnitude.
• We develop an adaptive algorithm to increase the speed of a reliability analysis.
• The proposed strategy demonstrates high efficiency on real-scale applications.

A numerical strategy for the efficient estimation of set-valued failure probabilities, coupling Monte Carlo with optimization methods, is presented in this paper. The notion of uncertainty is generalized to include both aleatory and epistemic uncertainties, allowing to capture gaps of knowledge and scarcity of data. The proposed formulation of the generalized uncertainty model allows for sets of probability distribution functions, also known as credal sets, and sets of bounded variables. The developed Advanced Line Sampling method is combined with the generalized uncertainty model, in order to both speed up the reliability analysis, and provide a better estimate for the lower and upper bounds of the failure probability. The proposed strategy knocks down the computational barrier of computing interval failure probabilities, and reduces the cost of a robust reliability analysis by many orders of magnitude. The efficiency and applicability of the developed method is demonstrated via numerical examples. The solution strategy is integrated into the open-source software for uncertainty quantification and risk analysis OpenCossan, allowing its application on large-scale engineering problems as well as broadening its spectrum of applications.