结构失效概率分析的球层抽样方法  

Spherical Layer Sampling Method for Probability Evaluation on Structural Failure

作　　者：白冰 BAI Bing(Research Institute of Highway Ministry of Transport,Beijing 100088,China)

机构地区：[1]交通运输部公路科学研究所,北京100088

出　　处：《西南交通大学学报》2024年第3期691-699,共9页Journal of Southwest Jiaotong University

基　　金：中央级公益性科研院所基本科研业务费专项资金资助(2021-9012a)。

摘　　要：传统Monte Carlo抽样方法应用于小失效概率等复杂可靠度问题时,存在效率低下、精度有限等不足,针对这一问题提出一种球层抽样分析方法.首先,通过分离距离与方向参量,对标准正态随机向量进行重构,并验证其标准正态性与相互独立性;然后,采用分层抽样策略,将半径大于一阶可靠度指标外的正态空间划分为多个球层,进而利用所重构的向量逐层进行抽样,并结合全概率公式,形成估计结构失效概率的球层抽样算法;最后,通过对3个典型算例进行对比分析,验证算法性能.分析表明:所提出算法具有较高的抽样效率与收敛性能,算例计算结果误差在3%以内;与其他算法相比,其估计方差更小,且可有效解决多设计验算点等复杂可靠度问题;算法在抽样效率、适用范围以及稳定性等方面具有优势,更适用于实际复杂结构可靠度的求解分析.When the traditional Monte Carlo sampling method is applied to complex reliability problems such as small failure probability,there are some shortcomings such as low efficiency and limited accuracy.To solve this problem,a spherical layer sampling analysis method is developed.Firstly,by dividing the distance and direction parameters,the standard normal random vector is reconstructed,and its standard normality and mutual independence are verified.Thereafter,based on a layered sampling strategy,the standard normal space with the radius beyond first order reliability index is divided into multiple spherical layers,which are then sampled by the reconstructed vector layer by layer.Combined with the full probability formula,a spherical layer sampling algorithm is developed to estimate the structural failure probability.Finally,three typical examples are taken as objects of interest,and the performance of the algorithm is verified through comparative analysis.The results show that,the proposed algorithm has high sampling efficiency and convergence performance,and the error of calculation results is within 3%.Compared with other algorithms,its estimation variance is smaller,and it can effectively solve complex reliability problems such as multiple design check points.The algorithm has advantages in sampling efficiency,scope of application,and stability,and is more suitable for solving and analyzing the reliability of actual complex structures.

关 键 词：结构失效概率 抽样方法 变量构造 球层子区域 条件概率抽样 

分 类 号：O213.2[理学—概率论与数理统计] TU311.2[理学—数学]