摘要
实际工程中,结构系统的属性以及所受外载荷常常具有随机性和模糊性的特点。对于功能函数中含有模糊分布参数(FDP)的随机变量问题,如何准确且简便地评估其可靠性,是十分重要的。依据随机性和模糊性的基本概念,提出了当量概率密度函数的模糊可靠性分析方法。以FDP的隶属函数为基础,构造FDP的先验分布,应用Bayes理论,得到含有FDP随机变量的当量概率密度函数,并推导出具有常用隶属函数的FDP随机变量的数学期望和方差。这样就把含有FDP的随机变量处理成常规随机变量,进而可以应用传统的可靠性方法来分析结构的可靠性。本文所提方法解决了功能函数中含有多个FDP的随机变量时,模糊概率计算困难的问题。最后通过算例,与常用的模糊概率的可靠性分析方法进行比较,来验证本文算法的有效性。
The attributes of a structural system in engineering and the external loads acting on it are often char-acterized by randomness and fuzziness. For a problem with performance functions which include random varia-bles with fuzzy distribution parameters （FDP）, it is important to evaluate their reliability accurately and rapid- ly. Based on the concepts of randomness and fuzziness, a fuzzy reliability analysis method of probability density function equivalent is proposed in this article. Based on the membership function of an FDP, the prior distribution of the FDP is built. Then the probability density function equivalent of random variables with FDP can be obtained by using Bayes theory. Moreover, the mathematical expectation and variance of random variables are also deduced with FDP of traditional membership functions. In this way, random variables with FDP are turned to traditional random variables, and structural reliability can be analyzed by the traditional reliability analysis approaches. The method proposed in this article solves fuzzy probability problem of performance functions with many random variables whose FDP is hard to obtain. Finally, an example is given to prove the valid- ity of the proposed method by comparing it with the traditional reliability analysis method of fuzzy probability.
出处
《航空学报》
EI
CAS
CSCD
北大核心
2009年第5期886-894,共9页
Acta Aeronautica et Astronautica Sinica
基金
国家"863"计划(2006AA04Z410)
关键词
小子样
隶属函数
模糊分布参数
当量概率密度函数
模糊概率
可靠性
small sample
membership functions
fuzzy distribution parameters
probability density function equivalent
fuzzy probability
reliability
