基于Copula函数的证据理论相关性分析模型及结构可靠性计算方法

发布时间：2018-11-02 17:22

【摘要】：提出一种基于Copula函数的证据理论相关性分析模型及结构可靠性计算方法,可处理证据变量间具有相关性的可靠性分析问题。该方法引入Copula函数描述证据变量间的相关性,将贝叶斯方法拓展至证据理论,利用经验分布公式将证据变量转换为标准均匀变量,计算证据变量样本的权重获得结构输入变量间的最优Copula函数。通过最优Copula函数对证据变量边缘基本可信度分配(marginal-BPA)函数差分获得联合可信度分配(joint-BPA)函数,并对每个焦元进行极值分析,计算可靠域内焦元的累积联合BPA值获得结构的可靠性区间。通过三个数值算例验证了本方法的有效性,计算结果表明证据变量间的相关性可能对可靠性计算结果产生较大影响,常用的独立性假设可能对可靠性分析结果造成较大误差。
[Abstract]:This paper presents a correlation analysis model of evidence theory based on Copula function and a structural reliability calculation method, which can deal with reliability analysis problems with correlation between evidence variables. In this method, Copula function is introduced to describe the correlation between evidence variables, Bayesian method is extended to evidence theory, and empirical distribution formula is used to transform evidence variables into standard uniform variables. The optimal Copula function between structural input variables is obtained by calculating the weight of the sample of evidence variables. The joint confidence distribution (joint-BPA) function is obtained by the difference of the edge basic confidence distribution (marginal-BPA) function of the evidence variable by the optimal Copula function, and the extreme value of each focal element is analyzed. The cumulative joint BPA values of focal elements in reliable domain are calculated to obtain the reliability interval of the structure. The validity of the method is verified by three numerical examples. The results show that the correlation between the evidence variables may have a great impact on the reliability calculation results, and the commonly used independence assumptions may cause greater errors to the reliability analysis results.
【作者单位】：湖南大学汽车车身先进设计制造国家重点实验室;湖南大学机械与运载工程学院;
【分类号】：TB114.3

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