基于Hermite多项式的等效相关系数求解及可靠度分析

Solution of equivalent correlation coefficient and reliability analysis using Hermite polynomials

改进了相关非正态变量变换到相关标准正态空间时相关系数计算的Hermite多项式方法.介绍了Hermite多项式方法计算等效相关系数的基本原理.系统地比较了Hermite多项式方法与Nataf变换方法的计算精度、计算效率及适用范围.最后研究了变量变换时相关系数的变化对边坡可靠度的影响.结果表明:Hermite多项式方法具有与Nataf变换方法相同的精度,不受变量分布类型的影响,适用范围广,避免了无穷积分问题及非线性积分方程的求解问题,计算效率高,建议优先采用;忽略黏聚力和内摩擦角变换到相关标准正态空间时相关系数的变化将会严重高估边坡失效概率,使得边坡设计偏于保守.

This paper improves a Hermite polynomial method to determine the equivalent correlation coefficient in standard normal space when the correlated nonnormal variables are transformed into correlated standard normal variables. The Hermite polynomials are briefly introduced. The Hermite polynomial method and the Nataf transformation method are compared in three aspects, namely, accuracy, efficiency, and applicability. The reliability of rock slope stability is used as an example to demonstrate the capacity of the Hermite polynomial method. The resuits indicate that the Hermite polynomial method can produce the accurate results. Compared with the Nataf transformation method, the Hermite polynomial method is more applicable and efficient. It can circumvent the infinite integral problem and solving nonlinear equation, which should be recommended to calculate the equivalent correlation coefficient. Neglecting the negative correlation between the cohesion and friction angle will significantly overestimate the probability of failure for rock slope stability, which are conservative for design of rock slope.