相关非正态变量变换时相关性变化对可靠度的影响

Effect of correlation change from transformation of correlated abnormal variables on structural reliability

为了系统定量地分析相关非正态变量变换到相关标准正态变量时相关性变化对结构可靠度的影响,首先通过结构可靠度计算中常用的正交变换和Nataf变换来定量地考虑这种相关性的差别.然后,给出了通用的基于正交变换和Nataf变换的FORM方法可靠度计算步骤.最后,以相关对数正态分布变量为例,系统地比较了Nataf变换后的相关标准正态空间中等效相关系数和原相关系数间差别,分析了相关系数变化对可靠指标的影响程度,并探讨了可靠指标变化程度随相关系数变化程度的变化规律.算例结果表明,当相关非正态变量的变异系数较小时,采用正交变换的FORM方法计算精度很高,尤其是变量间正相关情况.但是当相关非正态变量的变异系数较大而且是高度负相关时,正交变换的结果与蒙特卡罗模拟结果差别非常大,而Nataf变换的结果始终与蒙特卡罗模拟保持了较好的一致性.因此,含相关非正态变量的结构可靠度计算应该考虑映射变换时相关性的变化,建议优先采用Nataf变换方法.

This paper aims to investigate the correlation change from transformation of correlated abnormal variables on structural reliability in a systematical and quantitative way.Firstly,two often used transformation methods for reliability analysis,namely,orthogonal transformation and Nataf transformation,are selected to account for the change in correlation.Secondly,the procedure for reliability calculation using FORM involving the orthogonal transformation is proposed.Finally,an example with two correlated lognormal variables is used to systematically compare the difference between the original correlation coefficient and the equivalent correlation coefficient in the correlated standard normal space.Furthermore,the effect of such difference on reliability index is demonstrated quantitatively.The variation of reliability index difference on correlation coefficient difference is revealed.The results indicate that when the correlated abnormal variables have a small coefficient of variation,the FORM with the orthogonal transformation will result in significant error in reliability results,especially for the positively correlated abnormal variables.While the reliability results obtained from the FORM with the Nataf transformation agree well with those obtained from Monte Carlo simulation for all the cases.Therefore,the correlation change from transformation of correlated abnormal variables should be taken into consideration.It is recommended that the Nataf transformation to be used for reliability analysis involving correlated abnormal variables due to its high accuracy.