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总览 评价 杜娟 ， 李海滨 * ， 贺云 （ 内蒙古工业大学理学院,呼和浩特 010051； ） 摘要： 在结构可靠性分析中，由于考虑变量间的相关性更能准确的反映出结构物可靠度的水平，对工程实践更具有参考价值，因此越来越受到相关学者和工业界的关注。本文给出了
杜娟， 李海滨*， 贺云
（
内蒙古工业大学理学院,呼和浩特 010051； ）
摘要：
在结构可靠性分析中，由于考虑变量间的相关性更能准确的反映出结构物可靠度的水平，对工程实践更具有参考价值，因此越来越受到相关学者和工业界的关注。本文给出了采用Copula函数构建变量间的联合概率密度函数的方法，该方法关键之处在于变量间相关性的描述，其中包括Copula函数相关参数的求解以及选择变量间相关结构的类型。文中基于Pearson线性相关系数和Kendall秩相关系数进行Copula函数相关参数的求解；基于AIC准则和BIC准则进行了最优Copula函数的选取，进而确定了变量间的相关结构。其次，结合基于Nataf逆变换的Monte Carlo法，建立了求解相关变量可靠度的Monte Carlo法。最后，通过建立原函数和被积函数的对偶神经网络，给出了基于对偶神经网络直接积分的可靠度计算方法。通过与Monte Carlo法进行对比分析，表明了本文方法是一种可用于求解含多个相关随机变量的结构可靠度的高效、高精度计算方法。
关键词：
应用力学；Copula函数；Nataf逆变换；对偶神经网络；直接积分法；可靠度
DU Juan， LI Haibin*， HE Yun
（
College of Science,Inner mongolia University,Hohhot 010051； ）
Abstract：
In structural reliability analysis, considering correlation among variables can more accurately reflect the level of structure reliability. The problem has more referential value to the engineering practice. It has attracted more and more attention by relevant scholars and industry. This paper used Copula function to build the joint probability density function among all variables. The description of correlation among variables was key, including solved correlated parameter of Copula function and chosen type of correlation structure among variableThe method of solving structural reliability with multiparameter correlation problems. Based on the Pearson linear correlation coefficient and the Kendall rank correlation coefficient, the correlated parameter of Copula function was solved. Based on the AIC and BIC criteria, the optimal Copula function was selected, and then correlation structure among variables was determined. In addition, Monte Carlo method that based on the Nataf inverse transformation was given. The Monte Carlo method solved correlated variable reliability. Finally, through establishing the dual neural network of original function and integrand function, this paper proposed the reliability calculation method based on the dual neural network and direct integration. By contrasted analysis with the Monte Carlo method, it shown that the proposed method can be used to calculate structure reliability of multiple correlated random variables and had high efficiency, high precision.
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