可靠性敏度分析方法及其在非线性蠕变疲劳失效模型中的应用  

Reliability sensitivity algorithm and its application in creep/fatigue failure

作　　者：袁修开[1] 吕震宙[1] 

机构地区：[1]西北工业大学航空学院,陕西西安710072

出　　处：《计算力学学报》2007年第1期69-73,共5页Chinese Journal of Computational Mechanics

基　　金：航空基金(00B53010);航空基金(2003CH0502);陕西省自然科学基金(2003CS0501)资助项目

摘　　要：针对非线性极限状态方程,发展了两种基本随机变量为非正态情况下的可靠性敏度分析方法:基于改进一次二阶矩的近似解析法和基于Monte-Carlo的数字模拟法。近似解析法中非正态变量首先被等价变换为正态变量,然后用正态变量的敏度分析法和隐函数求导法则来得到失效概率对非正态变量分布参数的灵敏度,求解敏度的数字模拟法是从计算失效概率的所有样本点中选取合适的抽样点,利用回归分析和隐函数求导法则来求取可靠性灵敏度的。所提方法被用于非线性蠕变疲劳失效模式的可靠性灵敏度分析,近似解析法和数字模拟法结果的一致说明了所提方法的合理可行。蠕变疲劳失效的可靠性灵敏度随参数的变化趋势分析为工程设计提供了有益指导。For non-linear limit state equation, two algorithms, i.e., approximate analytics based on first-order and second-moment and numerical simulation based on Monte-Carlo method, are presented for reliability sensitivity analysis with non-normal basic random variables. In the approximate analytic algorithm, the non-normal basic random variable is transformed to normal one equivalently. Then, the reliability sensitivity algorithm for the normal random variables and the chain derivative rule are employed to calculate the sensitivity of failure probability with respect to the distribution parameters (such as mean values and variances) of the non-normal random variables. In the numerical simulation algorithm, the appropriate sampling points are selected from those of Monte-Carlo method for the regression analysis around the vicinity of the design point, afterwards, the chain derivative rule is used to obtain the reliability sensitivity. The presented algorithms are applied to the non-linear creep/fatigue failure model. The feasibility and the rationality of the present algorithms are illustrated by the good agreement between the analytics and the simulation. The reliability sensitivity of the creep/fatigue failure model varying with the distribution parameters of the random variables supplies helpful guidance for the engineering design.

关 键 词：可靠性 概率分析 一次二阶矩法 蒙特卡罗法 参数灵敏度 蠕变疲劳 

分 类 号：TB114.3[理学—概率论与数理统计] TG111.8[理学—数学]