Efficient metamodel-based importance sampling coupled with single-loop estimation method for parameter global reliability sensitivity analysis基于高效元模型重要性抽样与单循环估计耦合的参数全局可靠性灵敏度分析方法
![]()
Yun WY, Li FY, Chen XM, Wang Z, 2024. Efficient metamodel-based importance sampling coupled with single-loop estimation method for parameter global reliability sensitivity analysis. Probabilistic Engineering Mechanics, 76: 103597.DOI: 10.1016/j.probengmech.2024.103597
摘要 | Abstract
为高效估计不确定性分布参数对失效概率不确定性的主效应和总效应，本文通过引入辅助变量并使用等概率变换构建了单循环估计格式。这种方法避免了原本嵌套的三重循环过程。对生成单循环估计格式中使用的样本，可以直接采用蒙特卡罗模拟。为减少蒙特卡罗模拟的样本数量，可以将重要性抽样技术整合到所提的单循环估计格式中。此外，为提高识别所有样本状态 (失效或安全) 的效率，可引入自适应 Kriging 模型。最后将自适应 Kriging 模型结合蒙特卡罗法与自适应 Kriging 模型结合重要抽样法嵌入到所推导的单循环格式中，以同时高效估计不确定性分布参数的主效应和总效应。三个案例研究的结果验证了所提方法的精度和效率。关键词: 参数全局可靠性灵敏度指标, 参数化非精确概率模型, 重要性抽样, 单循环过程, 自适应 Kriging 模型To efficiently estimate the main effects and total effects of uncertain distribution parameters on the uncertainty of failure probability, we construct single-loop estimation formulas by introducing auxiliary variables through the equal probability transformation. This approach circumvents the original nested triple-loop process. For generating samples used in the derived single-loop estimation formulas, direct Monte Carlo simulation can be employed. To reduce the number of samples in Monte Carlo simulation, the important sampling technique can be integrated into the proposed single-loop estimation formulas. Additionally, to enhance the efficiency of identifying the states (failure or safety) of all used samples, an adaptive Kriging model can be introduced. Subsequently, the adaptive Kriging model coupled with Monte Carlo simulation, and the adaptive Kriging model coupled with the importance sampling technique, are integrated into the derived single-loop formulas to concurrently and efficiently estimate the main effects and total effects of uncertain distribution parameters. The results of three case studies validate the accuracy and efficiency of the proposed method.Keywords: Parameter global reliability sensitivity indices; Parameterized imprecise probability model; Importance sampling; Single-loop process; Adaptive kriging model
![]()
Fig. 1. Flowchart of the proposed method
图 2: 不同样本数下单循环元模型—重要性抽样—自适应 Kriging 方法与单循环主动学习 Kriging —蒙特卡罗模拟方法的主效应估计Fig. 2. Main effect S_θ_i estimated by the single-loop Meta-IS-AK method and single-loop AK-MCS method with different sizes of N (N^(IS)).
图 3: 不同样本数下单循环元模型—重要性抽样—自适应 Kriging 方法与单循环主动学习 Kriging —蒙特卡罗模拟方法的总效应估计Fig. 3. Total effect S_Tθ_i estimated by single-loop Meta–IS–AK method and the single-loop AK-MCS method with different sizes of N (N^(IS)).
Fig. 4. Schematic diagram of roof truss structure
图 5: 第一类非精确概率分析模型下屋架结构案例研究的主效应与总效应估计及其标准差Fig. 5. S^_θ_i, S^_Tθ_i and their standard deviations SD_S_θ_i and SD_S_Tθ_i for case study II with the first type of imprecise probability analysis model
图 6: 第二类非精确概率分析模型下屋架结构案例研究的主效应与总效应估计及其标准差Fig. 6. S^_θ_i, S^_Tθ_i and their standard deviations SD_S_θ_i and SD_S_Tθ_i for case study II with the second type of imprecise probability analysis model
Fig. 7. Missile wing structure
Fig. 8. FEM of the missile wing structure
图 9: 导弹弹翼结构案例研究的主效应与总效应估计及其标准差Fig. 9. S^_θ_i, S^_Tθ_i and their standard deviations SD_S_θ_i and SD_S_Tθ_i of case study III
作者信息 | Authors
员婉莹 Wan-Ying Yun, 通讯作者 (Corresp.) 西北工业大学 (Northwestern Polytechnical University) 航空学院Email: wanying_yun@nwpu.edu.cn
西北工业大学 (Northwestern Polytechnical University) 航空学院
中国飞机强度研究所 (Aircraft Strength Research Institute of China) 强度与结构完整性全国重点实验室
中国飞机强度研究所 (Aircraft Strength Research Institute of China) 强度与结构完整性全国重点实验室
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)
