基于vine copula函数的结构不确定性传播分析
发布时间：2018-07-27 12:02
【摘要】：现有的不确定性传播分析方法大都假设各输入变量相互独立,然而实际工程中,很多变量间具有相关性,特别是多维相关性问题广泛存在实际工程中.为此,本文提出了一种基于vine copula函数的结构不确定性传播分析方法,为复杂多维相关问题的不确定性传播分析提供了一种有效工具.首先,根据随机变量的样本由vine copula构造输入变量的联合概率密度函数;其次,先由Rosenblatt变换将相关变量转换成独立变量,再由降维积分法计算响应的前四阶原点矩;最后,由最大熵原理计算响应的概率密度函数.算例分析表明,本文方法在计算精度和计算效率方面具有较好的综合性能,能够用于变量间具有相关性的复杂工程问题的不确定性传播分析.
[Abstract]:Most of the existing methods of uncertainty propagation analysis assume that the input variables are independent of each other. However, in practical engineering, many variables have correlation, especially the multi-dimensional correlation problem exists widely in practical engineering. Therefore, this paper presents a structural uncertainty propagation analysis method based on vine copula function, which provides an effective tool for the uncertainty propagation analysis of complex multi-dimension related problems. Firstly, the joint probability density function of input variable is constructed by vine copula according to the sample of random variable. Secondly, the correlation variable is transformed into independent variable by Rosenblatt transform, and then the first four order origin moments of response are calculated by dimension reduction integration method. The probability density function of the response is calculated by the maximum entropy principle. The numerical examples show that the proposed method has better comprehensive performance in terms of computational accuracy and efficiency, and can be used to analyze the uncertainty propagation of complex engineering problems with correlation among variables.
【作者单位】： 湖南大学机械与运载工程学院汽车车身先进设计制造国家重点实验室;中航工业贵阳万江航空机电有限公司;
【基金】：国家自然科学基金重大项目(批准号:51490662);国家自然科学基金重点项目(批准号:11232004)资助 国家重点研发计划项目(批准号:2016YFD0701105)
【分类号】：O211
，
本文编号：2147762
[Abstract]:Most of the existing methods of uncertainty propagation analysis assume that the input variables are independent of each other. However, in practical engineering, many variables have correlation, especially the multi-dimensional correlation problem exists widely in practical engineering. Therefore, this paper presents a structural uncertainty propagation analysis method based on vine copula function, which provides an effective tool for the uncertainty propagation analysis of complex multi-dimension related problems. Firstly, the joint probability density function of input variable is constructed by vine copula according to the sample of random variable. Secondly, the correlation variable is transformed into independent variable by Rosenblatt transform, and then the first four order origin moments of response are calculated by dimension reduction integration method. The probability density function of the response is calculated by the maximum entropy principle. The numerical examples show that the proposed method has better comprehensive performance in terms of computational accuracy and efficiency, and can be used to analyze the uncertainty propagation of complex engineering problems with correlation among variables.
【作者单位】： 湖南大学机械与运载工程学院汽车车身先进设计制造国家重点实验室;中航工业贵阳万江航空机电有限公司;
【基金】：国家自然科学基金重大项目(批准号:51490662);国家自然科学基金重点项目(批准号:11232004)资助 国家重点研发计划项目(批准号:2016YFD0701105)
【分类号】：O211
，
本文编号：2147762
本文链接：https://www.wllwen.com/kejilunwen/yysx/2147762.html