Seismic reliability analysis using subset simulation enhanced with an explorative adaptive conditional sampling algorithm基于探索性自适应条件抽样算法改进子集模拟的抗震可靠性分析
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Sepúlveda JG, Glavind ST, Faber MH, 2024. Seismic reliability analysis using subset simulation enhanced with an explorative adaptive conditional sampling algorithm. Probabilistic Engineering Mechanics, 78: 103690.DOI: 10.1016/j.probengmech.2024.103690
地震作用下结构可靠性分析是一项重大工程挑战。由于需进行非线性动力数值分析，对于小失效概率计算成本很大，且生成地震模型表达要包含数千个随机变量。子集模拟是一类有效的可靠性分析技术，与直接蒙特卡罗模拟相比，它可以应对高维空间挑战，且能降低结构分析调用次数。在本文中，首先我们研究了有效进行子集模拟的条件。然后，我们提出了对现有子集模拟方法的改进，该方法表明，子集模拟在新一水平下进行改进 Markov 链蒙特卡罗模拟策略具有巨大潜力。最后，本研究从模拟中收集信息，以验证子集模拟是否从物理角度提供了有意义的结果。关键词: 自适应条件抽样, 子集模拟, OpenSEES, 可靠性分析, 结构可靠性, 抗震可靠性, 前沿模拟技术, 非线性结构分析, 蒙特卡罗模拟技术, Markov 链蒙特卡罗Reliability analysis of structures under earthquake loading represents a significant engineering challenge. This is due to the required and rather numerically involving non-linear dynamic analysis, the large computational burden when targeting small failure probabilities, and the synthetic earthquake model representation that may contain thousands of random variables. Subset Simulation is an efficient reliability analysis technique that can handle the challenge of a high-dimensional space with a reduced number of structural analysis calls compared to crude Monte Carlo Simulation. In this contribution, firstly, we investigate the conditions for which Subset Simulation performs efficiently. Thereafter we propose an enhancement to the existing Subset Simulation schemes that shows significant potentials for enhancing the strategy for the starting of the Markov Chain Monte Carlo simulations whenever a new level is reached in the Subset Simulation. Finally, the information gathered from the simulations is investigated to verify that Subset Simulation provides meaningful results from a physical point of view.
Keywords: Adaptive conditional sampling; Subset simulation; OpenSees; Reliability analysis; Structural reliability; Seismic reliability; Advanced simulation techniques; Non-linear structural analysis; Monte Carlo simulation techniques; Markov chain Monte Carlo.![]()
Fig. 1. Scheme of the generation of chains in batches of N_a chains
图 2: 计算失效概率随子集模拟独立运行阈值水平的变化Fig. 2. Failure probability computation as a function of the threshold level for independent runs of SuS
图 3: 失效概率估计量的变异系数与估计量的期望值Fig. 3. CoV of the failure probability estimator vs expected value of the estimator
Fig. 4. Scaling factors vs average acceptance rates for each SuS level
图 5: 失效概率估计量的变异系数随不同可靠性水平接受率的变化Fig. 5. CoV of the estimator of the probability of failure as a function of the acceptance rate for different levels of reliability
图 6: 完全抽样与自适应条件抽样格式的变异系数与失效概率水平Fig. 6. CoV vs failure probability level for the pS and the aCS scheme
图 7: 自适应条件抽样格式下子集模拟各水平的缩放因子期望值与平均接受率迭代演化Fig. 7. Expected values of the scaling factor and average acceptance rate iterations evolution for each level of SuS with the aCS scheme
图 8: 改进自适应条件抽样格式下子集模拟各水平的缩放因子期望值与平均接受率迭代演化Fig. 8. Expected values of the scaling factor and average acceptance rate iterations evolution for each level of SuS with the EaCS scheme
图 9: 不同子集模拟格式的变异系数与失效概率水平Fig. 9. CoV vs failure probability level for different SuS schemes
Fig. 10. Normalized efficiency for the three SuS schemes
图 11: 失效域独立标准正态空间中基准激励模型主要参数样本的概率密度函数Fig. 11. PDFs of the base excitation model main parameters samples in U-space laying in the failure domain F
Fig. 12. Failure probabilities conditional on values of the distance to the epicenter
Fig. 13. Failure probabilities conditional on values of the moment magnitude
Fig. 14. Structural model: Numbering of loads and design variables
图 15: 结构模型: 整体模型节点与模型单元编号Fig. 15. Structural model: Global model nodes and model elements numbering
Fig. 16. Structural model: Internal nodes element 4
Fig. 17. Black-box function system response Y (·)
作者信息 | Authors
Juan G. Sepúlveda, 通讯作者 (Corresp.)丹麦奥尔堡大学 (Aalborg University) 建筑环境系Email: jgsa@build.aau.dk
丹麦奥尔堡大学 (Aalborg University) 建筑环境系
丹麦奥尔堡大学 (Aalborg University) 建筑环境系
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)
