混料试验设计中置换阵的性质及其应用  

Applications and Properties of Permutation Matrix for Mixture Experimental Designs

作　　者：李俊鹏 李光辉[2] 张崇岐 LI Junpeng;LI Guanghui;ZHANG Chongqi(School of Economics and Statistics,Guangzhou University,Guangzhou 510006;School of Science,Kaili University,Kaili)

机构地区：[1]广州大学经济与统计学院,广州510006 [2]凯里学院理学院,凯里556011

出　　处：《工程数学学报》2023年第1期123-134,共12页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11901260,12071096);贵州省科学技术基金([2020]1Y010)。

摘　　要：为解决由于高维混料试验的设计阵的形式复杂且计算难度大的问题,使用高阶混料格点作为支撑集,提出了置换阵的定义。首先讨论了由置换阵构造出设计阵的方法;进而由此推导出信息矩阵与相关矩阵的显示表达;然后探索了置换阵的行列式、迹和特征值等方面的性质;最后通过实例验证置换阵用于设计分析的有效性,并进一步分析了利用置换阵构造高阶混料格点集和最优设计的必要性和可行性。In order to solve the problem of the complex form and complicated calculation of the design matrix for high-dimensional mixture experiments,the definition of the permutation matrix is proposed by using high-order mixture lattice points as the support set.Firstly,the method to construct the design matrix from the permutation matrix is discussed,and the representation of the information matrix and the correlation matrix are derived.Then,the properties of the determinant,trace,and eigenvalue of the permutation matrix are studied.Finally,the effectiveness of the permutation matrix for the analysis of mixture design is verified,and the necessity and feasibility of using the permutation matrix to construct a high-order lattice point set and an optimal design are further analyzed.

关 键 词：置换阵 信息矩阵 混料试验设计 D-最优设计 

分 类 号：O212.6[理学—概率论与数理统计]