结构可靠性分析的通用生成函数法

Analysis of the Structural Reliability Based on Method of Universal Generating Function

提出一种基于通用生成函数(μ函数)结构可靠性分析新方法,其基本思路是以离散信号处理的z变换为理论基础,将随机变量转换成描述其不确定性分布的μ函数模型,利用μ函数的良好特性和μ函数结构逻辑关系算法,将输入不确定性传递到输出不确定性,根据μ函数可靠性指标,完成可靠性分析,为改进设计提供依据。文中着重解决了随机变量μ函数模型建立以及功能函数的代数运算在μ函数中如何计算问题。与Monte-Carlo方法相比,基于z变换的思想将离散实数域中的问题转换到类似离散复数域中进行求解,然后在类似离散复数域进行可靠性分析。文中算例对所提方法的高效性和可行性进行了验证。

A new analysis method of structural reliability based on universal generating function（μ function） isproduced, its basic thinking is based on the z transform of discrete signal processing, it transforms random variable intoμ function model which describes its uncertainty. And it utilizes favorable properties and logical relation algorithm ofμ function to pass the input uncertainty to the output uncertainty. According to the reliability indexes of μ of μ functionmodel is established in order to solve the computing problem of functional algebraic operation of μ function. Comparedto Monte-Carol method, the idea based on z transform transforms the problems of discrete real domain into the problemsof discrete complex domain, and conducts reliability analysis in domain which is similar to discrete complex domain.The calculating examples verify high efficiency and feasibility of the proposed method.