针对多失效相关的动态机械系统,利用Copula函数描述各单元之间失效模式的相关性,提出了一种具有多失效相关的动态机械系统可靠性模型,采用R-Vine Copula函数将复杂系统的可靠性问题转化为多个二维Pair Copula函数进行分析,利用最大生成树算法(MST)选定最优R-Vine结构,通过非参数核密度估计(KDE)对模型中的时变参数进行描述,并重点对机械系统中常见的串-并联系统(混联系统)进行建模分析,最后通过航天器开闭轴系的算例,验证该模型的有效性。
Abstract
Aiming at the dynamic mechanical system with multiple failure correlation, the copula function is used to describe the correlation of failure modes among units, and a reliability model of dynamic mechanical system with multiple failure correlations is proposed. The reliability problem of complex system is transformed into multiple two-dimensional pair copula functions by using R-Vine copula function. The optimal R-Vine structure is selected by using MST algorithm. The time-varying parameters in the model are described by nonparametric kernel density estimation(KDE). The common series parallel system(hybrid system) in mechanical system is modeled and analyzed. Finally, the effectiveness of the model is verified by an example of spacecraft open and close shafting.
关键词
R-VineCopula函数 /
串-并联系统 /
非参数核密度估计(KDE) /
可靠性
{{custom_keyword}} /
Key words
R-Vine Copula function /
Series-parallel system /
Nonparametric kernel density estimation(KDE) /
Reliability
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] 刘惟信.机械可靠性设计[M].北京:清华大学出版社,1996:288-302.LIU WeiXin.Mechanical reliability design[M].Beijing:Tsinghua University Press,1966:288-302(In Chinese).
[2] 袁涛.机械结构参数相关性与串并联体系可靠性灵敏度设计与应用[D].长春:吉林大学,2007:10-16.YUAN Tao.Reliability sensitivity design and application of mechanical structure parameters correlation and series parallel system[D].Changchun:Jilin University,2007:10-16(In Chinese).
[3] 吴帅兵,张坤,李典庆.相关非正态变量变换时相关性变化对可靠度的影响[J].武汉大学学报(工学版),2011,44(2):151-155.WU ShuaiBing,ZHANG Kun,LI DianQing.The influence of correlationchange on reliability in the transformation of correlated non normal variables[J].Journal of Wuhan University (Engineering Edition),2011,44(2):151-155(In Chinese).
[4] 喻天翔,孙玉秋,张祖明.多模式失效的机械零件可靠度计算新理论[J].机械工程学报,2009,39(3):134-138.YU TianXiang,SUN YuQiu,ZHANG ZuMing.New theory of reliability calculation for mechanical parts with multi mode failure[J].Journal of Mechanical Engineering,2009,39(3):134-138(In Chinese).
[5] MOSLEH A.Common cause failures:An analysis methodology and examples[J].Reliability Engineering and System Safety,1991,34(3):249-292.
[6] 唐家银,何平,陈崇双.相关性失效机械系统的可靠性分析方法[M].北京:国防工业出版社,2014:22-47.TANG JiaYin,HE Ping,CHEN ChongShuang.Reliability analysis method of mechanical system with dependent failure[M].Beijing:National Defense Industry Press,2014:22-47(In Chinese).
[7] 唐家银,赵永祥,何平,等.零件失效相关表决系统Copula可靠性模型[J].机械设计,2010,27(7):24-29.TANG JiaYin,ZHAO YongXiang,HE Ping,et al.Copula reliability model of component failure related voting system[J]Machine Design,2010,27(7):24-29(In Chinese).
[8] YI Wen De,WEI Gui Wu.Study on the reliability of dependenceparts vote system based on Copula functions[J].Journal of Southwest China Normal University (Natural Science Edition),2007,32(6):52-55.
[9] 胡启国,周松.Vine Copula模型的失效动态相关机械系统可靠性分析[J].机械科学与技术,2018,37(8):1149-1155.HU QiGuo,ZHOU Song.Reliability analysis of failure dynamic dependent mechanical system based on Vine Copula model[J].Mechanical Science and Technology,2018,37(8):1149-1155(In Chinese).
[10] NELSEN R B.An introduction to copulas[M].2nd ed.New York:Springer,2006:7-35.
[11] 李霞.Copula方法及其应用[M].北京:经济管理出版社,2014:28-60.LI Xia.Copula method and its application[M].Beijing:Economic Management Press,2014:28-60(In Chinese).
[12] JOE H.Families of m-variate distributions with given margins and m(m-1)/2 bivariate dependence parameters[J].Lecture Notes-Monograph Series,1996:120-141.
[13] BEDFORD T,COOKE R M.Vines:A new graphical model for dependent random variables[J].Annals of Statistics,2002,30(4):1031-1068.
[14] 裴宏杰,陈钰荧,李公安,等.基于Copula函数的铣削力、振动与表面粗糙度的相关性分析[J].航空制造技术,2019,62(9):59-67.PEI HongJie,CHEN YuYing,LI GongAn,et al.Cor-relation analysis of milling force,vibration and surface roughness based on Copula function[J].Aviation Manufacturing Technology,2019,62(9):59-67(In Chinese).
[15] 张乔微,李艳婷.基于R-Vine Copula的多维混合型数据控制图设计[J].工业工程,2019,22(5):126-132.ZHANG QiaoWei,LI YanTing.Design of multidimensional mixed data control chart based on R-Vine Copula[J].Industrial Engineering,2019,22(5):126-132(In Chinese).
[16] Li Dian Qing,Tang Xiao Song,Zhou Chuang Bing,et al.Uncertainty analysis of correlated non-normal geotechnical parameters using Gaussian copula[J].Science China Technological Sciences,2012,55(11):3081-3089.
[17] Cherubini U,Gobbi F,Mulinacci S,et al.Dynamic copula methods in finance[M].Hoboken,NJ:Wiley,2012:175-227.
[18] 栾世杰,于佳伟,郑松林,等.基于非参数核密度估计法的商用车服役载荷环境研究与应用[J].机械强度,2020,42(2):443-452.LUAN ShiJie,YU JiaWie,ZHENG SongLin,et al.Research and application of commercial vehicle service load environme-nt based on nonparametric kernel density estimation met-hod[J].Journal of Mechanical Strength,2020,42(2):443-452(In Chinese).
[19] 吴吉林,孟纹羽.时变混合Copula模型的非参数估计及应用研究[J].数量经济技术经济研究,2013,30(8):124-136.WU JiLin,MENG WenYu.Nonparametric estimation in time varying mixture copula and its application in stock markets[J].The Journal of Quantitative&Technical Economics,2013,30(8):124-136(In Chinese).
[20] Cornell C A.Bounds on the reliability of structural system-s[J].J.Struct.Meth,1967,93(1):171-200.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
基金
国家自然科学基金项目(61627819)资助。
{{custom_fund}}
PDF(856 KB)
