Meta-model based sequential importance sampling method for structural reliability analysis under high dimensional small failure probability基于元模型的顺序重要抽样方法用于高维小失效概率可靠性分析
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Zhang YM, Ma J, 2024. Meta-model based sequential importance sampling method for structural reliability analysis under high dimensional small failure probability. Probabilistic Engineering Mechanics, 76: 103620.DOI: 10.1016/j.probengmech.2024.103620
摘要 | Abstract
对具有严格可靠性要求的复杂结构，可靠性分析是一项重要挑战。虽然序列重要性抽样 (sequential importance sampling, SIS) 和子集模拟 (subset simulation, SUS) 已证明在处理高维小失效概率问题时非常有效，但由于数值模拟过程耗时长，力学模拟的计算成本仍然很大。因此，本文提出了一种新方法，即自适应 Kriging 序列重要性抽样，它将序列重要性抽样与 Kriging 元模型结合，专门针对小失效概率的计算挑战。该方法的基本原理是利用自适应 Kriging 蒙特卡罗模拟技术 (Echard et al. 2011) 作为序列重要性抽样方法的前置步骤来初步生成元模型。在后续步骤中，这些元模型代替功能函数使用，从而显著减少在直接应用序列重要性抽样技术模拟复杂工程问题时所需的函数调用次数。通过继承序列重要性抽样的优势，自适应 Kriging 序列重要性抽样已证明其适用于涉及高维空间和小失效概率的可靠性分析。此外，自适应 Kriging 序列重要性抽样不受失效域形状的限制，消除了求解设计点的需要，特别适合分析失效域不连续、多个失效域、复杂失效域以及罕遇事件的可靠性。通过涵盖非线性、高维算例和工程应用的严格评估证明了自适应 Kriging 序列重要性抽样的有效性。这些算例验证共同为具有严格可靠性要求的复杂结构的可靠性分析奠定了坚实的方法论框架。关键词: 结构可靠性分析, 小失效概率, 序列重要性抽样, 模拟, Kriging 模型Reliability analysis poses a significant challenge for complex structures with stringent reliability requirements. While Sequential Importance Sampling (SIS) and Subset Simulation (SUS) have proven highly effective in addressing high-dimensional problems with small failure probabilities, the computational burden of mechanical simulations remains substantial due to the time-consuming nature of numerical simulation processes. Consequently, this paper introduces a novel approach, denoted as AK-SIS, which combines SIS with Kriging metamodeling specifically designed to address computational challenges associated with small failure probabilities. The fundamental principle of this approach involves utilizing AK-MCS technology (Echard et al., 2011) as a precursor to the SIS approach to initially generate metamodels. These metamodels are then employed in lieu of performance functions in subsequent steps, significantly reducing the number of function calls required to simulate complex engineering problems when applying SIS techniques directly. By inheriting the advantages of SIS, AK-SIS has demonstrated its suitability for reliability analysis in scenarios involving high-dimensional spaces and small fault probabilities. Furthermore, AK-SIS is not limited by the shape of the failure domain, eliminates the need to solve the design point, and is particularly well-suited for analyzing reliability in cases of discontinuous failure domains, multiple failure domains, as well as complex failure domains and rare events. The efficacy of AK-SIS is substantiated through rigorous evaluation encompassing nonlinear, high-dimensional examples, and an engineering application. These empirical validations collectively contribute to a robust methodological framework for reliability analysis of intricate structures characterized by stringent reliability requirements.Keywords: Structural reliability analysis; Small failure probability; Sequential importance sampling; Simulation; Kriging![]()
Fig. 1. Transition from the target distribution to the proposed distribution
图 2: 二维非线性函数的验证结果图: (a) 自适应 Kriging 序列重要性抽样近似; (b) 概率收敛结果Fig. 2. Visual verification results of example 1: (a) Approximation by AK-SIS; (b) Probabilistic convergence results
Fig. 3. Probabilistic convergence results
Fig. 4. 10 structural diagram of rod truss
Fig. 5. Cantilever pipe structure schematic
作者信息 | Authors
西安电子科技大学 (Xidian University) 机电工程学院
马娟 Juan Ma, 通讯作者 (Corresp.) 西安电子科技大学 (Xidian University) 机电工程学院Email: juanma@stu.xidian.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)
