可靠性分析改进元模型重要抽样算法
收稿日期: 2024-05-27
修回日期: 2024-07-31
录用日期: 2024-11-13
网络出版日期: 2024-11-25
基金资助
重庆市自然科学基金(CSTB2022NSCQ-MSX0861);航空科学基金(20220009053001);陕西省科学技术协会青年人才托举计划(20230446);广东省基础与应用基础研究基金(2022A1515011515);国家自然科学基金(12002237)
Enhanced metamodel-based importance sampling method for reliability analysis
Received date: 2024-05-27
Revised date: 2024-07-31
Accepted date: 2024-11-13
Online published: 2024-11-25
Supported by
Natural Science Foundation of Chongqing(CSTB2022NSCQ-MSX0861);Aeronautical Science Foundation of China(20220009053001);Young Talent Fund of Association for Science and Technology in Shaanxi of China(20230446);Guangdong Basic and Applied Basic Research Foundation(2022A1515011515);National Natural Science Foundation of China(12002237)
为了高效地开展结构可靠性分析，通过引入代理模型更新的误差停止准则，提出了改进的元模型重要抽样算法。首先，建立了元模型重要抽样算法中失效概率预测值与真实值之间相对误差的解析关系；其次，推导了失效概率预测值与真实值之间相对误差上限与Kriging代理模型预测精度之间的近似关系，通过失效概率预测值与真实值之间相对误差不大于预设精度，建立了基于失效概率预测误差指导的Kriging代理模型更新准则，提高了Kriging代理模型在元模型重要抽样算法中的更新效率；最后，将所提的改进元模型重要抽样算法应用至数值算例及涡轮轴疲劳寿命可靠性分析的工程算例中，计算结果验证了所提算法的高效性和准确性。
关键词： 可靠性分析; 元模型; 重要抽样算法; Kriging代理模型; 误差停止准则
员婉莹 , 李逢源 , 黄博 , 王思予 , 焦韵菲 , 白馨雨 , 黄雪琪 . 可靠性分析改进元模型重要抽样算法[J]. 航空学报, 2025 , 46(7) : 230738 -230738 . DOI: 10.7527/S1000-6893.2024.30738
To give an efficient analysis of structural reliability， an enhanced metamodel-based importance sampling method is proposed in this paper by introducing an error-based stopping criterion for updating the Kriging model. Firstly， an analytical relationship of the relative error between the estimate of failure probability by the metamodel-based importance sampling method and the true value obtained by the actual limit state function is established. Secondly， an approximate relationship between the upper bound of the relative error between the estimate of failure probability and the true value and the prediction accuracy of the Kriging model is derived. By ensuring that the relative error between the estimate of failure probability by the metamodel-based importance sampling method and the true value obtained by the actual limit state function does not exceed a predefined accuracy， an error-based stopping criterion for updating the Kriging model is established to improve the efficiency of the existing metamodel-based importance sampling method. Finally， the proposed method is applied to numerical examples and engineering examples of reliability analysis of turbine shaft fatigue life. The results verify the efficiency and accuracy of the proposed method.
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