A layer assigned probability space partition method for structural small failure probability problem结构小失效概率问题的分层概率空间剖分方法
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Bai Y, Ning CL, Li J, 2024. A layer assigned probability space partition method for structural small failure probability problem. Probabilistic Engineering Mechanics, 76: 103633.DOI: 10.1016/j.probengmech.2024.103633
摘要 | Abstract
物理综合法 (physical synthesis method, PSM) 因其明确的概念基础，成为进行结构可靠性分析的强大框架。然而，在处理小失效概率情形时，该方法通常需要大量计算成本。为应对这一挑战，本研究提出了一种分层概率空间剖分方法，用于在物理综合法框架下，根据结构构件的极限承载力失效准则识别关键点。该方法借鉴了 Harbitz β 球，采用构件最小可靠性指标，来识别概率空间中的重要代表性点，从而简化计算。通过两个案例研究展示了该方法的有效性：一是简支梁，二是六层钢筋混凝土框架。结果表明，与传统蒙特卡罗方法相比，结合物理综合法，该方法在效率上有显著提高。此外，在相同计算资源下，该方法的计算精度优于重要性抽样方法，尤其在处理小失效概率情形时表现突出。此外，通过引入共同安全域的概念，该方法解决了多个失效面下结构可靠性分析的难题。关键词: 概率密度演化方法, β 球, 赋得概率, 结构系统可靠性, 物理综合法, χ 方分布The Physical Synthesis Method (PSM) stands out as a robust framework for conducting structural reliability analyses due to its clear conceptual foundation. However, this approach often necessitates significant computational resources when addressing scenarios with small failure probabilities. In response to this challenge, this study introduces a layer assigned probability space partition method designed to identify pivotal points based on the ultimate bearing capacity failure criterion of structural components within the PSM framework. Drawing inspiration from Harbitz's β-sphere, this method effectively utilizes the minimum reliability index of components to discern essential representative points within the probability space, thus streamlining computations. The efficacy of this approach is showcased through two case studies: a simply supported beam and a six-story reinforced concrete frame. The outcomes demonstrate that the proposed method, when integrated with PSM, exhibits a substantial enhancement in efficiency compared to the conventional Monte Carlo method. Besides, under equivalent computational resources, it achieves superior computational accuracy compared to the importance sampling method, particularly in scenarios with small failure probabilities. Furthermore, by introducing the notion of a common safe domain, this method addresses challenges in structural reliability analyses involving multiple failure surfaces.Keywords: Probability density evolution method; β-sphere; Assigned probability; Structural system reliability; Physical synthesis method; Chi-square distribution![]()
Fig. 1. Harbitz's β-sphere
Fig. 2. Concept of common safe domain
Fig. 3. Relationship between probability and the radius of common safe domain
Fig. 4. Assigned probability of representative points
图 5: 第 1 层与第 2 层代表性点的赋得概率Fig. 5. Assigned probability of representative points in layer 1 and layer 2
Fig. 6. Flowchart of the proposed method
Fig. 7. A simply supported RC beam
Fig. 8. Structural failure probability evolution along generalized loading time
Fig. 9. 3D model of a RC frame structure
Fig. 10. Location of the examined beams in the first floor
作者信息 | Authors
同济大学 (Tongji University) 土木工程学院
同济大学 (Tongji University) 土木工程学院
李杰 Jie Li, 通讯作者 (Corresp.)
同济大学 (Tongji University) 土木工程学院Email: lijie@tongji.edu.cn
律梦泽 M.Z. Lyu | 编辑 (Ed)
P.D. Spanos | 审校 (Rev)
陈建兵 J.B. Chen | 审校 (Rev)
彭勇波 Y.B. Peng | 审校 (Rev)
