基于旋转法的四水平空间填充设计的构造与性质

数学物理学报 ›› 2025, Vol. 45 ›› Issue (5): 1652-1670.

基于旋转法的四水平空间填充设计的构造与性质

康佐航(),欧祖军^*()

吉首大学数学与统计学院湖南吉首 416000

收稿日期:2024-10-18 修回日期:2025-02-10 出版日期:2025-10-26 发布日期:2025-10-14
通讯作者: * 欧祖军, E-mail:ozj9325@mail.ccnu.edu.cn
作者简介:康佐航, E-mail:kzh1022@stu.jsu.edu.cn
基金资助:
国家自然科学基金(12361053);国家自然科学基金(12161040);国家自然科学基金(11961027);湖南省自然科学基金(2023JJ30486);湖南省教育厅科研计划(22A0355)

Construction and Properties of Four-Level Space-Filling Designs Based on Rotation Methods

Zuohang Kang(),Zujun Ou^*()

College of Mathematics and Statistics, Jishou University, Hunan Jishou 416000

Received:2024-10-18 Revised:2025-02-10 Online:2025-10-26 Published:2025-10-14
Supported by:
NSFC(12361053);NSFC(12161040);NSFC(11961027);Natural Science Foundation of Hunan Province(2023JJ30486);Scientific Research Plan Item of Hunan Provincial Department of Education(22A0355)

摘要/Abstract

摘要：

空间填充设计因其具有良好的性质在计算机试验中广泛应用, 随着试验场景中对试验次数和因子数越来越多的现实需求, 大规模空间填充设计的构造日益重要. 该文提出了两种基于旋转法由两水平设计构造四水平空间填充设计的方法, 在字长计数器和分层型计数器下分别研究了所构造的四水平空间填充设计与两水平初始设计的联系, 建立了其字长计数器和分层型计数器与初始两水平设计的距离分布的联系, 给出了所构造的四水平空间填充设计的广义字长型和空间填充模式与两水平初始设计的广义字长型的解析关系, 并获得了所构造的四水平空间填充设计的字长计数器和分层型计数器下界. 数值例子表明: 该文所构造的四水平空间填充设计具有很好的空间填充性质和分层性质, 且其构造方法简便, 可应用于大规模试验场景并推广至多水平和混水平空间填充设计的构造.

关键词: 空间填充设计, 旋转法, 字长计数器, 分层型计数器

Abstract:

Space-filling designs are widely used in computer experiments due to their favorable properties, and the construction of large-scale space-filling designs is becoming increasingly important with the realistic demand for an increasing number of runs and factors in experimental scenarios. In this paper, two methods are proposed to construct four-level space-filling designs from two-level designs based on rotation methods, and the connections between the constructed four-level space-filling designs and initial two-level designs are investigated under the wordlength enumerator and stratification pattern enumerator, respectively. The connection between their wordlength enumerator and stratification pattern enumerator and the distance distribution of initial two-level designs is established. Analytical relationships between the generalized wordlength pattern and space-filling pattern of the constructed four-level space-filling design and the ones of its initial two-level design are given. The lower bounds of wordlength enumerator and stratification pattern enumerator of the constructed four-level space-filling design are obtained. Numerical examples show that the constructed four-level space-filling designs in this paper have good space-filling and stratification properties, the construction methods are simple and can be applied to large scale experimental scenarios and generalized to the construction of multi-level and mixed-level space-filling designs.

Key words: space-filling designs, rotation method, wordlength enumerator, stratification pattern enumerator

中图分类号:

O212.6

康佐航, 欧祖军. 基于旋转法的四水平空间填充设计的构造与性质[J]. 数学物理学报, 2025, 45(5): 1652-1670.

Zuohang Kang, Zujun Ou. Construction and Properties of Four-Level Space-Filling Designs Based on Rotation Methods[J]. Acta mathematica scientia,Series A, 2025, 45(5): 1652-1670.

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