Tightening the bound estimate of structural reliability under imprecise probability information

Structural reliability analysis is typically performed based on the identification of distribution types of random inputs. However, this is often not feasible in engineering practice due to limited available probabilistic information (e.g., limited observed samples or physics-based inference). In this paper, a linear programming-based approach is developed to perform structural reliability analysis subjected to incompletely informed random variables. The approach converts a reliability analysis into a standard linear programming problem, which can make full use of the probabilistic information of the variables. The proposed method can also be used to construct the best-possible distribution function bounds for a random variable with limited statistical information. Illustrative examples are presented to demonstrate the applicability and efficiency of the proposed method. It is shown that the proposed approach can provide a tighter estimate of structural reliability bounds compared with existing interval Monte Carlo methods which propagate probability boxes.