基于通用生成函数的混合不确定性结构可靠性分析  

Reliability analysis on structure with hybrid uncertainties based on universal generating function

作　　者：李界 周金宇 LI Jie;ZHOU Jinyu(School of Mechanical Engineering,Jiangsu University of Technology,Changzhou 213001;School of Mechanical and Electrical Engineering,Jinling Institute of Science and Technology,Nanjing 211169)

机构地区：[1]江苏理工学院机械工程学院,江苏常州213001 [2]金陵科技学院机电工程学院,江苏南京211169

出　　处：《机械设计》2025年第2期141-147,共7页Journal of Machine Design

基　　金：国家自然科学基金面上项目(52075232);江苏省自然科学基金项目(BK20201112);江苏理工学院研究生实践创新计划(XSJCX21_31)。

摘　　要：针对同时存在随机、模糊和区间3种混合不确定性变量的结构可靠性分析问题,文中提出一种基于通用生成函数(UGF)的统一可靠性分析方法。采用广义密度函数法,将模糊变量转换为等效随机变量,结构几何参数采用区间变量描述时,基于熵最大原则,将区间变量视为在定义区间内服从均匀分布的随机变量,从而将混合不确定性问题转换为单一随机不确定性问题。对统一转化后的随机变量进行非均匀离散化,并采用求解精度高且不受随机变量非正态、功能函数非线性影响的UGF建立结构各分量UGF模型,通过复合运算得到整个结构UGF模型,求解功能函数获得结构的可靠度值。算例分析表明:采用文中方法与Monte Carlo法计算精度的相对误差小于1%,且计算效率提高近18倍。In this article,a unified reliability-analysis method based on the universal generating function(UGF)is proposed to deal with the reliability analysis on structure with hybrid uncertainties of the random,fuzzy and interval variables.The generalized density function is used to convert the fuzzy variable into the equivalent random variable.When the structure’s geometric parameters are described by the interval variable,based on the maximum entropy principle,the interval variable is considered to be an evenly-distributed random variable within the defined interval,which transforms the hybrid uncertainties into a single random uncertainty.The random variable which is transformed in a unified manner is discretized unevenly.Since UGF is characterized by high solution accuracy and is not affected by the random variable’s non-normal status and the function’s non-linearity,efforts are made to set up the UGF models of the structure’s each component.The whole structure’s UGF model is worked out through compound operation.The structure’s reliability value is calculated by solving the function.The examples indicate that the relative error of the calculation accuracy between the new method and the Monte Carlo method is less than 1%,and the calculation efficiency improves by 18 times.

关 键 词：可靠性 通用生成函数 广义密度函数 熵最大原则 非均匀离散化 

分 类 号：TB114.3[理学—概率论与数理统计]