非正态概率分布对一次可靠度方法精度影响

一次可靠度方法(FORM)基本原理是将非正态分布基本变量变换为独立标准正态分布，并将功能函数在基本变量的验算点坐标位置线性化，因此功能函数在独立标准正态分布空间的非线性程度将直接影响一次可靠度方法(FORM)的计算精度。功能函数非线性的另一个来源是非正态变量的概率变换。本文通过研究9种非正态分布类型的正态概率变换函数的曲率值，得出了不同非正态分布类型对一次可靠度方法计算精度的影响规律。

Errors in FORM's failure probability induced by non-Gaussian variables

The basic ideas behind the first order reliability method (FORM) are first to transform non-Gaussian variables into independent standard Gaussian ones, and then to linearize performance functions at the design point. The errors in the failure probability given by FORM come from nonlinear properties of performance functions at the design point. This paper shows that errors in the failure probability also come from curvatures in transformation functions from nine non-Gaussian distributions ,and that senses and values of these errors in the failure probability given by FORM depend on which distribution function the concerned variable has and whether resistance or load the variable is.