摘要
针对工程中常见的多变量、小失效概率的隐式非线性极限状态方程的可靠性分析问题,提出马尔可夫链样本模拟与线抽样相结合的高效数字模拟法。所提方法采用马尔可夫链快速得到失效域中的样本,并依据这些样本获取线抽样的重要方向,然后再采用线抽样技术在重要方向上进行抽样,进而得到失效概率的高效估计。与传统的有限差分法相比,基于马尔可夫链的重要方向获取方法具有结果准确和稳定的优点。将文中方法用于分析多级循环载荷作用下某发动机涡轮盘的低周疲劳寿命的可靠性,结果表明所提方法对于高维、小失效概率的可靠性分析是有效可行的。
For reliability analysis of implicit non-linear limit state function with high dimensionality of basic variables and small failure probability in engineering, a novel numerical simulation is presented on the combination of Markov Chain simulation and line sampiing. In the presented method, Markov Chain simulation is used to draw samples in the failure domain rapidly, and important direction for the line sampling is determined by these samples. Then the line sampling technique is employed to take samples according to the important direction, and the failure probability can be evaluated by hne sampling with high efficiency. Comparing to the finite differential method for obtaining the important direction, higher accuracy and higher robustness of the important direction result are obtained by the presented method. These advantages brought to the line sampling result in precision improvement of the failure probability evaluation. The application of the presented method in the reliability analysis of low cycle fatigue life of an engine turbine disc structure, which is applied by multiple cyclic loads, demonstrates the efficiency and feasibility.
出处
《机械强度》
EI
CAS
CSCD
北大核心
2007年第6期952-955,共4页
Journal of Mechanical Strength
基金
国家自然科学基金(10572117)
新世纪优秀人才支持计划资助项目(NCET-05-0868)~~
关键词
失效概率
马尔可夫链
线抽样
低周疲劳寿命
Failure probability
Markov Chain simulation
Line sampling
Low cycle fatigue life
