A Distributionally Robust Approach for Mixed Aleatory and Epistemic Uncertainties Propagation

A study focuses on the generalized global non-intrusive imprecise stochastic simulation (NISS) method, as it can propagate both the imprecise probability models and nonprobabilistic models at the same time. The staircase distributions are theoretically ready to be used in this method by constructing parametric p-boxes defining their hyper parameters as interval values. The feasibility of the proposed method is demonstrated by solving the reliability analysis subproblem of the NASA uncertainty quantification (UQ) challenge problem 2019. The Gaussian distribution-based p-box naturally contains Gaussian distributions, whereas the staircase distribution-based p-box contains a broad range of distributions, including skewed and bimodal distributions. A hybrid NISS method is developed, where the staircase distribution-based p-boxes are propagated by the local NISS method to significantly suppress the computational cost to estimate the component functions over the hyperparameters.