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.

中文翻译：

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多超椭球输入和模糊状态的非概率可靠性分析


在现实工程场景中，不完整的不确定性信息和模糊的失效状态持续存在，给结构可靠性分析带来了重大挑战。本文介绍了一种具有模糊输出状态的非概率模糊可靠性分析（NPFRA）模型，其中输入不确定性通过多超椭球模型进行量化。首先，我们定义了NPFRA的可靠性和失效指数，并提供了相应的蒙特卡罗模拟（MCS）解决方案。此外，还建立了一种扩展变量空间（EVS）方法，将NPFRA问题转化为传统的非概率可靠性分析（NPRA）问题，并相应地推导了基于EVS的MCS。为了解决 MCS 的效率问题，专门为 NPFRA 开发了一种称为具有范数约束预期风险函数的主动学习克里金法 (ALK-NERF) 的新方法。采用四个例子验证了所提出的 NPFRA ALK-NERF 的合理性和有效性。