A non-probabilistic convex polyhedron model for reliability analysis of structures with multiple failure modes and correlated uncertainties based on limited data

This paper proposes a novel non-probabilistic reliability model called the convex polyhedron reliability model, focusing on structural reliability assessment under uncertain conditions. Unlike existing probabilistic and non-probabilistic interval models, the convex polyhedron model considers the situation where a multi-dimensional convex polyhedron describes the uncertain variable space. Compared with the interval model, the convex polyhedron model is more compact and reflects the correlation between uncertain variables based on limited information. The area/volume ratio is introduced to be referred to as the reliability index in the proposed framework. Then the case of the nonlinear limit state function is discussed and addressed by the most likely failure point-based linearization method and the piecewise linearization method. Furthermore, this paper investigates an effective approach to dealing with the structural system reliability analysis problem with multiple failure modes based on the proposed non-probabilistic convex polyhedron reliability model. Finally, three examples are provided to verify the effectiveness and applicability of the proposed method. Through comparison with the existing reliability models, the results show that the reliability evaluated by the probabilistic reliability model and non-probabilistic reliability model are compatible. [Figure not available: see fulltext.]