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

A Copula Function Based Evidence Theory Model For Correlation Analysis and Corresponding Structural Reliability Method

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。

A Copula function based evidence theory model for correlation analysis and corresponding structural reliability method is proposed to deal with reliability design problems with dependent evidence variables. The Copula function is used to describe the correlation between evidence variables, and to identify the best copula, a Bayesian method which is usually used in probabilistic problem is expanded to evidence theory, the empirical distribution is used to convert the evidence variables to standard uniform variables, and the weight is calculated from the samples to identify the best copula function. The joint basic probability assignment（BPA） is gained by making the difference between the marginal BPAs using copula function. Then the reliability interval is gained by calculating the cumulative BPA of the focal elements in the reliable domain. Three examples are investigated to verify the effectiveness of the proposed method, the results show that the correlation between evidence variables may influence the reliability results significantly, and the commonly used independence assumption may lead to big error of the reliability result.