约束空间近似正交的空间填充试验设计方法

doi:10.12305/j.issn.1001-506X.2021.07.14

摘要/Abstract

摘要：

试验设计空间存在约束是一种广泛存在的实际工程问题, 针对现有的约束空间试验设计方法存在生成设计点数不灵活, 算法优化时间长、效率低, 适用约束类型有限, 设计准则单一等问题, 提出一种约束空间近似正交的空间填充试验设计方法。基于设计点之间的距离和相关系数值构造试验设计准则, 通过改进的随机坐标交换算法进行方案求解。所提算法适合凸约束、非凸约束、解析约束、非解析约束等多种类型的约束, 而且适用于多维度的不规则试验设计空间。示例分析表明, 与现有方法相比, 所提算法具有优良的空间填充特性和较好的正交性。

关键词: 正交性, 空间填充, 约束空间, 坐标交换

Abstract:

The existence of constraints in experimental design space is a widespread practical engineering problem. In view of the problems in the existing experimental design methods for constrained spaces, such as inflexibility in generating design points, long optimization time and low efficiency, limited applicability for different types of constraints, single design criteria, and so on, an experimental design method of nearly-orthogonal space-filling for constrained spaces is proposed. The experimental design criterion is constructed based on the distance between design points and the correlation coefficient, and the scheme is solved by the improved stochastic coordinate-exchange algorithm. The proposed algorithm is suitable for convex constraints, non-convex constraints, analytical constraints, non-analytical constraints and other types of constraints, and it is suitable for multi-dimensional irregular experimental design space. The analysis of the example shows that the algorithm proposed in this paper has better space-filling characteristics and orthogonality compared with the existing methods.

Key words: orthogonality, space-filling, constrained spaces, coordinate-exchange

中图分类号:

尤杨, 金光, 潘正强, 郭芮. 约束空间近似正交的空间填充试验设计方法[J]. 系统工程与电子技术, 2021, 43(7): 1831-1837.

Yang YOU, Guang JIN, Zhengqiang PAN, Rui GUO. Nearly-orthogonal space-filling experimental design method for constrained spaces[J]. Systems Engineering and Electronics, 2021, 43(7): 1831-1837.

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设计结果对比	设计方法
设计结果对比	MO-SCE		SF-SCE
实验设计矩阵	-0.118 085 4	0.388 962 66	0.684 245 17	-0.729 252 04
	-0.481 210 4	-0.088 931 35	0.780 969 88	0.624 568 69
	-0.986 807 1	0.161 900 34	-0.115 731 25	-0.453 720 89
	0.125 649 5	0.992 074 69	-0.995 879 04	-0.090 691 45
	0.088 457 5	-0.369 740 72	-0.443 171 48	-0.896 436 86
	-0.802 788 3	0.596 264 16	0.171 774 83	-0.985 136 24
	0.981 662 7	-0.190 626 06	0.408 751 58	-0.133 227 01
	0.411 611 0	-0.911 359 65	-0.777 281 80	-0.629 152 60
	-0.394 724 4	0.918 799 56	-0.562 111 53	0.827 061 44
	0.455 593 3	0.091 650 22	-0.890 377 84	0.455 222 26
	-0.561 403 0	-0.827 542 53	0.938 115 09	-0.346 323 66
	0.899 504 3	0.436 911 91	0.445 711 37	0.895 176 73
	0.608 468 6	0.793 577 95	0.989 691 68	0.143 214 47
	0.780 627 3	-0.624 996 86	0.141 466 27	0.392 416 61
	-0.143 843 8	-0.989 258 13	-0.383 351 87	0.132 873 13
	-0.851 157 8	-0.516 591 76	-0.043 186 79	0.999 067 02
相关性准则	2.9×10^-4		1.5×10^-2
空间填充准则ϕ₂	9.24		9.43

设计点数	MO-SCE		SF-SCE
设计点数	相关性准则	空间填充准则ϕ₁₀	相关性准则	空间填充准则ϕ₁₀
5	1.2×10^-4	0.83	1.6×10^-1	0.82
16	3.7×10^-6	1.98	1.4×10^-3	1.94
30	6.3×10^-6	3.14	2.1×10^-2	3.13
100	1.2×10^-3	8.44	3.2×10^-2	7.88

设计结果对比	设计方法
设计结果对比	MO-SCE		SF-SCE
试验设计矩阵	0.089 168 36	0.999 752 4	0.088 967 29	0.999 436 4
	0.088 971 11	0.999 400 0	0.088 947 07	0.999 725 4
	0.089 008 87	0.999 823 3	0.088 863 19	0.999 630 5
	0.088 740 56	0.999 664 1	0.088 802 91	0.999 765 1
	0.088 886 33	0.999 758 7	0.089 166 36	0.999 711 1
	0.088 904 22	0.999 997 0	0.088 761 26	0.999 891 7
	0.089 096 84	0.999 620 6	0.089 019 38	0.999 544 5
	0.088 666 74	0.999 756 1	0.089 103 33	0.999 806 6
	0.088 945 48	0.999 555 6	0.088 925 99	0.999 973 4
	0.089 111 61	0.999 872 6	0.089 061 94	0.999 663 8
	0.088 840 55	0.999 898 6	0.088 692 22	0.999 803 6
	0.088 837 72	0.999 604 0	0.088 872 64	0.999 846 2
	0.088 983 41	0.999 682 2	0.088 741 01	0.999 663 2
	0.088 735 77	0.999 848 4	0.089 002 55	0.999 858 1
相关性准则	0.09		0.21
空间填充准则ϕ₂₀	3.88		4.02