Non-probabilistic reliability analysis with both multi-super-ellipsoidal input and fuzzy state

In real-world engineering scenarios, incomplete uncertainty information and ambiguous failure states persist and pose significant challenges for structural reliability analysis. This paper introduces a non-probabilistic fuzzy reliability analysis (NPFRA) model featuring fuzzy output states, where the input uncertainties are quantified by a multi-super-ellipsoidal model. Initially, we define both reliability and failure indices of NPFRA, and provide the corresponding Monte Carlo simulation (MCS) solution. Additionally, an extended variable space (EVS) method is established to transform the NPFRA problem into a conventional non-probabilistic reliability analysis (NPRA) one, and MCS based on EVS is derived accordingly. To address the efficiency issue of MCS, a novel method called active learning kriging with norm-constrained expected risk function (ALK-NERF) is developed explicitly for NPFRA. Four examples are adopted to verify the rationality and effectiveness of the proposed ALK-NERF for NPFRA.