含有正态相关变量的多设计点/多失效模式情况下的方向抽样可靠性灵敏度分析

针对含有正态相关变量的多设计点/多失效模式系统的可靠性问题,提出了两种有效的基于方向抽样的可靠性灵敏度分析方法。可靠性灵敏度分析方法的基本思路是首先将正态相关变量进行等价独立标准正态变换,利用改进的方向抽样可靠性灵敏度分析方法得到独立标准正态空间的可靠性及灵敏度结果;通过复合求导法则,将独立标准正态空间的可靠性及灵敏度结果转化到正态相关空间,得到失效概率对相关正态变量分布参数(均值、标准差和相关系数)的偏导数,并对所推导的可靠性及灵敏度估计值进行了方差分析。与经典的MonteCarlo数字模拟法相比较,文中所列的数值算例和简单工程算例的分析结果验证了所提方法的可行性与有效性。

Reliability Sensitivity Analysis Based on Directional Simulation for Systems of Multiple Design Points/Failure Modes with Normal Correlated Variables

For the reliability problem of systems of multiple design points or multiple failure modes with normal correlated variables, two reliability sensitivity analysis methods based on directional simulation are presented. First, the normal correlated variables are transformed into equivalent independent standard normal variables. Second, two reliability sensitivity methods based on directional simulation are employed for multiple design point or multiple failure mode systems with independent standard normal variables. Third, the reliability sensitivity of independent standard normal variables, the partial derivatives of the distribution parameters of independent standard normal variables, can be transformed into those of normal correlated variables by means of equivalent transformation. The variances of reliability estimators and sensitivity estimators are analyzed to realize convergence. Compared with the classical Monte Carlo numerical simulation, the results of numerical examples and engineering examples can validate the feasibility and validity of the proposed methods.