结构体系可靠度分析中二维标准正态分布函数的近似计算

An approximation to bi-normal probability distribution function in reliability analysis of structural system

二维标准正态分布函数在结构体系可靠度分析中经常被用到,但它的计算一般涉及数值积分,工程不便应用。本文根据概率乘法定理,利用以条件数学期望和方差为参数的一维正态分布近似代替原来的条件分布,从而得出计算二维标准正态分布函数值的近似公式。通过数值积分结果比较表明,近似公式计算简单,应用方便,精度较好。

Bi-normal probability distribution function is often used in reliability analysis of the structural system.Numerical integration of bi-normal distributions is uneasy to evaluate in practice.Based on multiplication theorem of probability,an effective approximation is presented to the bi-normal distribution with substituting the original conditional distribution by the standard normal distribution of the same expectation and variance.The comparative studies with the exact integration and the examples considered in the paper show that the proposed approximation of calculation formula is simple and has a good accuracy.