Kriging与Breitung融合的可靠性分析方法  

Reliability analysis method based on Kriging and Breitung

作　　者：陈振中 黄冬宇 田娇 李晓科 CHEN Zhenzhong;HUANG Dongyu;TIAN Jiao;LI Xiaoke(College of Mechanical Engineering,Donghua University,Shanghai,China;College of Mechanical and Electronical Engineering,Zhengzhou University of Light Industry,Zhengzhou,Henan,China)

机构地区：[1]东华大学机械工程学院,上海 [2]郑州轻工业大学机电工程学院,河南郑州

出　　处：《东华大学学报（自然科学版）》2024年第6期86-93,共8页Journal of Donghua University(Natural Science)

基　　金：中央高校基本科研业务费专项资金(23D110316);国家自然科学基金(52375236,51905492)。

摘　　要：针对一阶可靠性方法在处理非线性极限状态函数时精度不足,以及Breitung方法在随机变量维度较高时计算效率低的问题,提出融合Kriging模型与Breitung方法的可靠性分析策略。采用一阶可靠性方法求解极限状态函数的最大可能失效点,并基于迭代过程中产生的样本点训练Kriging模型。通过Breitung方法计算Kriging模型在最大可能失效点各方向上的曲率,并据此构建近似抛物面。为避免Breitung方法概率公式中的奇异解问题,引入鞍点近似来计算近似抛物面的失效概率。通过3个数值算例和一个复合材料压力容器的工程实例对比一阶可靠性方法、Breitung方法以及融合Kriging与Breitung的可靠性分析方法的效率与精度。结果显示,融合Kriging与Breitung的可靠性分析方法不仅提高了计算效率,并且求解过程稳定,具有较高的求解精度。Addressing the issues of insufficient accuracy of first-order reliability method and low computational efficiency of Breitung method,a reliability analysis method based on Kriging model and Breitung is proposed.The first-order reliability analysis method was used to solve the most probable point of the limit state function,and the Kriging model is trained according to the sample points generated during the iteration process and additional sample points.The Breitung method is used to calculate the curvature of the Kriging model in each direction of the most probable point,and the approximate parabolic surface is constructed by using the curvature.To circumvent the issue of singular solutions in the probability formula associated with Breitung’s method,the saddle point approximation is employed to determine the failure probability for the approximate parabolic surface.The efficiency and accuracy of the first-order reliability method,the Breitung method and the reliability analysis method based on Kriging and Breitung are compared by three numerical examples and engineering example of composite pressure vessel.The results demonstrate that Kriging-Breitung-bossed reliability analysis method significantly enhances computation efficiency while maintaining higher stability and precision.

关 键 词：可靠性分析 KRIGING模型 Breitung方法 鞍点近似 复合材料压力容器 

分 类 号：TB114.3[理学—概率论与数理统计]