大型的五水平空间填充设计的构造  

Construction of five-level space-filling designs with large run sizes

作　　者：薛慧丽 黄兴友 柏启明 李洪毅[1] Xue Huili;Huang Xingyou;Bai Qiming;Li Hongyi(College of Mathematics and Statistics,Jishou University,Jishou 416000,China)

机构地区：[1]吉首大学数学与统计学院,湖南吉首416000

出　　处：《河南师范大学学报（自然科学版）》2022年第5期36-41,共6页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(12161040;11701213;11961027;11871237);湖南省自然科学基金(2020JJ4497;2021JJ30550);湖南省研究生科研创新项目(CX20211054);吉首大学科研创新项目(Jdy20057;Jdy21009).

摘　　要：大型的五水平空间填充设计因其实际应用需要被广泛关注,其构造方法也成了亟须解决的问题.基于因子的水平置换和折叠反转,从较小规模的五水平设计出发,构造具有优良性质的大规模五倍设计.首先,基于离散偏差建立了五倍设计的离散偏差值与初始设计相遇数之间的关系,并获得五倍设计的一个紧的下界;其次,基于E(f_(NOD))准则建立初始设计与五倍设计之间的关系,并给出五倍设计关于E(f_(NOD))的一个下界;最后,通过数值例子进一步支撑所获得的理论结果.Five-level space filling design with large run sizes is widely concerned because of its practical application, and its construction has become an urgent problem to be solved. Based on code mapping and foldover of factors, a novel method called quintupling is proposed to construct a large scale Quintuple design with excellent properties from a small scale five-level design in this paper. Firstly, the relationship between the discrete discrepancy of the Quintuple design and the coincidence number of the initial design is established based on discrete discrepancy, and a tight lower bound of the discrete discrepancy of the Quintuple design is obtained. Secondly, the relationship between the initial design and the Quintuple design is established under E(f) criterion, and a tight lower bound of the E(f) value of the Quintuple design is given. Finally, these theoretical results are supported by numerical examples further.

关 键 词：E(f_(NOD)) 空间填充设计 离散偏差 五倍设计 

分 类 号：O212.6[理学—概率论与数理统计]