基于概率论和证据理论的小概率问题可靠性分析

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英文篇名：Reliability Analysis of Small Probability Problem Based on Probality and Evidence Theory 作者：曹亮 ; 陈国强 ; 董丽君 ; 黄中华 英文作者：CAO Liang;CHEN Guo-qiang;DONG Li-jun;HUANG Zhong-hua;College of Mechanical Engineering, Hunan Institute of Engineering;Hunan Province Cooperative Innovation Center for Wind Power Equipment and Energy Conversion,Hunan Institute of Engineering; 关键词：可靠性分析 ; 概率论 ; 证据理论 ; 贝叶斯转换 ; MCMC子集模拟 英文关键词：reliability analysis;;probability theory;;evidence theory;;Bayes conversion method;;MCMC subset simulation 中文刊名：GCHZ 英文刊名：Journal of Hunan Institute of Engineering(Natural Science Edition) 机构：湖南工程学院机械工程学院;风电装备与电能变换协同创新中心; 出版日期：2019-05-29 出版单位：湖南工程学院学报(自然科学版) 年：2019 期：v.29;No.92 基金：湖南省自然科学基金资助项目(2019JJ60035);; 湖南省科技计划资助项目(2017WK205);; 湘潭市产业技术协同创新资助项目(湘财教发[2018]23号) 语种：中文; 页：GCHZ201902007 页数：6 CN：02 ISSN：43-1356/N 分类号：33-38

摘要

在复杂结构可靠性分析研究中,往往因信息缺乏无法利用经典概率理论去定义结构系统中所有不确定参数.可利用概率论结合证据理论(描述认知不确定性)分析方法,提出一种新颖的基于概率论和证据理论分析结构可靠性的方法.先以贝叶斯转换方法用作证据体精确化,再通过反射变换方法将认知不确定性变量转换为正常随机变量,以MCMC子集模拟法引入合理中间失效事件来分析小概率问题的可靠性.给出了一个算例和工程实例验证了该方法的性能.结果表明,该方法的精度和计算效率很高,为混合不确定性的可靠性优化提供了依据.
        In reliability analysis of complex structures, it is not always to obtain sufficient information to model all uncertain parameters of structures system by the classical probability theory. Probability theory combined with evidence theory(model epistemic uncertainty) may be utilized in safety analysis of structures. This paper proposes a novel method for safety analysis of structures based on probability and evidence theory. Firstly, Bayes conversion method is used as the way for precision of evidence body. Then epistemic uncertainty variables are transformed to normal random variables by reflection transformation method, and MCMC subset simulation is used to solve reliability problem of small probability by introducing intermediate failure events. A numerical example and a engineering examples are given to demonstrate the performance of the proposed method. The results show both precision and computational efficiency of the method is high. Moreover, the proposed method provides referrence for reliability-based optimization with the hybrid uncertainties.

引文

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