基于高阶矩最大熵方法的结构混合可靠性分析  

Hybrid Reliability Analysis for Structures Based on High-order Moments and Maximum Entropy Method

作　　者：郑宏伟 孟广伟 李锋 郭亚明 宣默涵 赵卫东 王宇 ZHENG Hongwei;MENG Guangwei;LI Feng;GUO Yaming;XUAN Mohan;ZHAO Weidong;WANG Yu(College of Mechanical and Aerospace Engineering,Jilin University,Changchun 130025;Changchun Equipment Technology Research Institute,Changchun 130012)

机构地区：[1]吉林大学机械与航空航天工程学院,长春130025 [2]长春设备工艺研究所,长春130012

出　　处：《机械工程学报》2021年第14期282-290,303,共10页Journal of Mechanical Engineering

基　　金：国防基础科研计划资助项目(JCKY2016208B003)。

摘　　要：针对随机-区间变量混合模型可靠性分析问题,提出一种基于高阶矩最大熵法的结构混合可靠性分析方法。对于区间变量采用区间Taylor展开方法得到功能函数的下界表达式,对于随机变量首先采用最大熵方法确定功能函数概率密度表达式,然后利用Taylor展开和Pearson曲线族方法确定功能函数标准化后的六阶矩,利用Matlab求解概率密度函数的参数,并拟合概率密度曲线,最后积分求解功能函数的最大失效概率。该方法应用于一个数值算例和一个工程结构算例,数值算例计算结果与区间蒙特卡洛方法对比,验证了该方法具有较好的精度和效率,工程结构算例以旋压设备旋轮座体在某典型产品旋压过程中的退让量为目标建立功能函数,结合有限元分析软件得到了最大失效概率,为工程结构可靠性分析提供了理论支持。A reliability analysis model is proposed for structures with mixed uncertainty based on high-order moments and maximum entropy method(MEM). For interval variables, Taylor expansion method is used to obtain the lower bounds of the function, for random variables, the MEM is used to determine the probability density expression at first, and then Taylor expansion and Pearson curves method are used to determine the normalized six order moments of the function. At the same time, Matlab is used to obtain the parameters required for the probabilistic density function, then the probability density curve is fitted, and the lower bound failure probabilities of the function are solved by integral solution. The method is applied to a numerical example and an engineering application example, while the comparison between the results with interval Monte Carlo shows that the method has better accuracy and efficiency.

关 键 词：随机-区间变量混合模型 可靠性分析 泰勒展开 高阶矩 最大熵法 

分 类 号：TB114[理学—概率论与数理统计]