基于混合加点准则的LOLA-DIST序贯设计方法

doi:10.12305/j.issn.1001-506X.2025.11.16

摘要/Abstract

摘要：

高效的仿真实验设计方法是建立高保真响应面模型的基础，而现有序贯实验设计难以应对维数爆炸的困境且多依赖于单一模型特性，通用性较差。因此，提出一种基于局部近似非线性-点间投影距离(local nonlinear approximations-intersite and projected distance, LOLA-DIST)准则的序贯设计方法，在非线性高且分布密度低的区域自适应采样，较好地平衡了全局探索与局部开发策略，不依赖于响应模型的特性，具有较好的通用性。最后，基于7类函数验证所提方法的有效性。实验结果表明，与LOLA-Voronoi、拉丁超立方抽样设计和随机设计对比，基于LOLA-DIST准则的序贯设计计算效率最高，在保证模型预测精度的基础上，有效减少了样本量和实验次数，具有更好的全局寻优性能。

关键词: 序贯实验设计, 混合加点准则, 局部近似非线性, 点间投影距离

Abstract:

An efficient simulation experimental design method is the basis for establishing high-fidelity response surface models, but the existing sequential experimental design is difficult to cope with the dilemma of dimensional explosion and relies on a single model characteristic, which is less general. Therefore, a sequential design method based on the local nonlinear approximations-intersite and projected distance （LOLA-DIST） criterion is proposed, which adaptively samples in the region with high nonlinearity and low distribution density, and better balances the global exploration and local development strategies, and is not dependent on the characteristics of the response model with good generality. Finally, the effectiveness of the proposed method is verified based on 7 types of functions. Experiment results show that the sequential design based on LOLA-DIST criterion has the highest computational efficiency compared with LOLA-Voronoi, Latin hypercube sampling design and stochastic design, which effectively reduces the sample size and the number of trials on the basis of ensuring the model prediction accuracy with better global optimization performance.

Key words: sequential experimental design, hybrid sampling criterion, local nonlinear approximations （LOLA）, intersite and projected distance （INPD）

中图分类号:

O 212.6

钟健, 程志君, 潘正强, 范俊, 刘天宇. 基于混合加点准则的LOLA-DIST序贯设计方法[J]. 系统工程与电子技术, 2025, 47(11): 3672-3684.

Jian ZHONG, Zhijun CHENG, Zhengqiang PAN, Jun FAN, Tianyu LIU. LOLA-DIST sequential design method based on hybrid sampling criterion[J]. Systems Engineering and Electronics, 2025, 47(11): 3672-3684.

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参考文献 34

1	LUALDI P, STURM R, SIEFKES T. Exploration-oriented sampling strategies for global surrogate modeling: a comparison between one-stage and adaptive methods[J]. Journal of Computational Science, 2022, 60, 101603. doi: 10.1016/j.jocs.2022.101603
2	ZHAI G, MA Y F, SONG X, et al. A novel flexible experiment design method[C]//Proc. of the Asian Simulation Conference, 2015: 28−39.
3	LIN Y, MISTREE F, ALLEN J, et al. Sequential metamodeling in engineering design[C]//Proc. of the 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 2004: 4304.
4	LIN Y. An efficient robust concept exploration method and sequential exploratory experimental design[M]. Atlanta: Georgia Institute of Technology, 2004.
5	DESCHRIJVER D, CROMBECQ K, NGUYEN H M, et al. Adaptive sampling algorithm for macromodeling of parameterized S-Parameter responses[J]. IEEE Trans. on Microwave Theory and Techniques, 2010, 59 (1): 39- 45.
6	QAZI M D, LINSHU H, MATEEN P. Hammersley sampling and support-vector-regression-driven launch vehicle design[J]. Journal of Spacecraft and Rockets, 2007, 44 (5): 1094- 1106. doi: 10.2514/1.22200
7	刘新亮, 郭波. 基于改进ESE算法的多目标优化试验设计方法[J]. 系统工程与电子技术, 2010, 32 (2): 410- 414.
	LIU X L, GUO B. Multi-objective experimentation design optimization based on modified ESE algorithms[J]. Systems Engineering and Electronics, 2010, 32 (2): 410- 414.
8	PALAR P S, SHIMOYAMA K. On efficient global optimization via universal Kriging surrogate models[J]. Structural and Multidisciplinary Optimization, 2018, 57 (6): 2377- 2397. doi: 10.1007/s00158-017-1867-1
9	雷永林, 王言, 于芹章, 等. 面向复杂仿真元建模的序贯近邻探索试验设计方法[J]. 系统工程与电子技术, 2021, 43 (5): 1232- 1239.
	LEI Y L, WANG Y, YU Q Z, et al. Design method of sequential neighbor exploratory experimental for complex simulation metamodeling[J]. Systems Engineering and Electronics, 2021, 43 (5): 1232- 1239.
10	PANTULA P D, MIRIYALA S S, MITRA K. Simultaneous knowledge discovery and development of smart neuro-fuzzy surrogates for online optimization of computationally expensive models[C]//Proc. of the Indian Control Conference, 2017: 260−267.
11	BURKARDT J, GUNZBURGER M, PETERSON J, et al. User manual and supporting information for library of codes for centroidal voronoi point placement and associated zeroth, first, and second moment determination[J]. Office of Scientific & Technical Information Technical Reports, 2002, 15 (26): 399- 406.
12	GUNZBURGER M. Advances in studies and applications of centroidal voronoi tessellations[J]. Numerical Mathematics Theory Methods & Applications, 2010, 3 (2): 119- 142.
13	CROMBECQ K. Surrogate modeling of computer experiments with sequential experimental design[D]. Belgium: Ghent University, 2011.
14	KE F, YUCHEN Z, PING M A. An adaptive sequential experiment design method for model validation[J]. Chinese Journal of Aeronautics, 2020, 33 (6): 1661- 1672. doi: 10.1016/j.cja.2019.12.026
15	COHN H, KUMAR A. Universally optimal distribution of samples on spheres[J]. Journal of the American Mathematical Society, 2007, 20(1): 99−148.
16	JONES D R, SCHONLAU M, WELCH W J. Efficient global optimization of expensive black-box functions[J]. Journal of Global Optimization, 1998, 13 (4): 455- 492. doi: 10.1023/A:1008306431147
17	张建侠, 马义中, 欧阳林寒, 等. 基于Kriging模型的多点加点准则和并行代理优化算法[J]. 系统工程理论与实践, 2020, 40 (1): 251- 261.
	ZHANG J X, MA Y Z, OUYANG L H, et al. A multi-samples infill sampling criterion and parallel surrogate-based optimization algorithm based on Kriging model[J]. System Engineering Theory and Practice, 2020, 40 (1): 251- 261.
18	LAURENCEAU J, MEAUX M, MONTAGNAC M, et al. Comparison of gradient-based and gradient-enhanced response-surface-based optimizers[J]. AIAA Journal, 2010, 48 (5): 981- 994. doi: 10.2514/1.45331
19	MUTONKOLE N, VILLIERS D D. Multivariate adaptive sampling of parameterized antenna responses[J]. IEEE Trans. on Antennas and Propagation, 2017, 65 (3): 1073- 1080. doi: 10.1109/TAP.2017.2653761
20	HERVIS S Y, PLETS D, MARTINEZ A R, et al. Tool for recovering after meteorological events using a real-time REM and IoT management platform[J]. Wireless Communications and Mobile Computing, 2019, 2019, 1- 13.
21	ZHOU X J, JIANG T, ZHOU Z H, et al. Sequential-support vector regression based online robust parameter design[J]. Computers & Industrial Engineering, 2021, 158, 107391.
22	VIANA F, HAFTKA R. Surrogate-based optimization with parallel simulations using the probability of improvement[C]//Proc. of the13th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference, 2010: 9392.
23	李正良, 彭思思, 王涛. 基于混合加点准则的近似模型优化设计方法[J]. 工程力学, 2022, 39 (1): 27- 33.
	LI Z L, PENG S S, WANG T. A surrogate-based optimization design method based on hybrid infill sampling criterion[J]. Engineering Mechanics, 2022, 39 (1): 27- 33.
24	LIU H T, SHEN L X, MENG J G, et al. A multi-response adaptive sampling approach for global metamodeling[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2018, 232 (1): 3- 16. doi: 10.1177/0954406216672250
25	BHATTACHARYYA, BISWARUP. A critical appraisal of design of experiments for uncertainty quantification[J]. Archives of Computational Methods in Engineering: State of the Art Reviews, 2018, 25 (3): 727- 751. doi: 10.1007/s11831-017-9211-x
26	缪继华. 基于支持向量回归模型的序列采样方法研究[D]. 武汉: 华中科技大学, 2017.
	MIAO J H. A sequential sampling method based on support vector regression[D]. Wuhan:Hua zhong University of Science and Technology, 2017.
27	季泽. 基于最小二乘支持向量回归的序贯设计与建模方法研究[D]. 郑州: 郑州大学, 2019.
	JI Z. Sequential design and modeling methods based on the LS-SVR[D]. Zhengzhou: Zhengzhou University, 2019.
28	WANG W Y, DOU F, XUAN Y, et al. Load forecasting method based on SVR under electricity market reform[C]//Proc. of the Conference Series: Earth and Environmental Science, 2020, 467(1): 012201.
29	尤杨, 金光, 潘正强, 等. 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.
	YOU Y, JING G, PAN Z Q, et al. Nearly-orthogonal space-filling experimental design method for constrained spaces[J]. Systems Engineering and Electronics, 2021, 43 (7): 1831- 1837.
30	姜维, 余义志, 蔡伯根, 等. LSSVM增强的受限环境列车定位精度优化方法[J]. 铁道学报, 2022, 44 (1): 65- 70.
	JIANG W, YU Y Z, CAI B G, et al. Optimization method for integrated positioning accuracy of trains in restricted environment based on LSSVM[J]. Journal of the China Railway Society, 2022, 44 (1): 65- 70.
31	CHICK S E, BRANKE J, SCHMIDT C. Sequential sampling to myopically maximize the expected value of information[J]. Informs Journal on Computing, 2010, 22 (1): 71- 80. doi: 10.1287/ijoc.1090.0327
32	段文睿, 田凌, 韩文彬. 刻蚀机装备设计中的序贯试验设计方法研究[J]. 真空科学与技术学报, 2015, 35 (5): 625- 633.
	DUAN W R, TIAN L, HAN W B. Analysis of sequential design strategy of etching reactor of 18 inch silicon wafer[J]. Chinese Journal of Vacuum Science and Technology, 2015, 35 (5): 625- 633.
33	孟祥争. 基于K折叠SVR近似模型的晶格结构设计优化方法研究[D]. 武汉: 华中科技大学, 2018.
	MENG X Z. Research on optimization method of lattice structure design based on K-fold SVR metamodel[D]. Wuhan: Huazhong University of Science and Technology, 2018.
34	LIU H T, CAI J F, ONG Y S. An adaptive sampling approach for Kriging metamodeling by maximizing expected prediction error[J]. Computers & Chemical Engineering, 2017, 106, 171- 182.

函数序号	函数名	取值范围	维度
F1	MATYAS	[−10, 10]	2
F2	PEAKS	[−5, 5]	2
F3	SIX-HUMP CAMEL	[−2, 2]	2
F4	ACKLEYS	[−32, 32]	2，10
F5	ROSENBROCK	[−5, 10]	4
F6	BRATLEY ET AL	[0, 1]	4~6
F7	DETTE&PEPELYSHEV	[0, 1]	8

函数序号	函数名	维度	样本数	LOLA-DIST	LOLA-Vorinoi	随机设计	LHS
F1	MATYAS	2	22	0.0001	0.0001	0.1736	0.0569
F2	PEAKS	2	214	0.0181	0.0435	1.1085	0.4825
F3	SIX-HUMP CAMEL	2	86	0.0027	0.0473	0.0267	0.0678
F4	ACKLEYS	2	40	0.0458	0.0760	0.0856	0.0962
F4	ACKLEYS	10	406	0.0485	0.0534	0.1309	0.0715
F5	ROSENBROCK	4	102	0.0382	0.0437	0.0916	0.0653
F6	BRATLEY ET AL.	4	46	0.0410	0.0267	0.2210	0.0855
		5	65	0.0482	0.0469	0.0662	0.0732
		6	178	0.0425	0.0497	0.0649	0.0571
F7	DETTE&PEPELYSHEV	8	190	0.0499	0.0543	0.0699	0.0593

函数序号	维度	加点准则	收敛点	MAPE	函数序号	维度	加点准则	收敛点	MAPE
F1	2	LOLA-DIST	12	0.0170	F5	4	LOLA-DIST	88	0.0628
		LOLA-Voronoi	15	0.0220			LOLA-Voronoi	89	0.0986
		随机设计	28	0.0788			随机设计	89	0.0944
		LHS	16	0.0826			LHS	91	0.0979
F2	2	LOLA-DIST	166	0.0867	F6	4	LOLA-DIST	24	0.0978
		LOLA-Voronoi	178	0.0860			LOLA-Voronoi	21	0.0778
		随机设计	238	0.6562			随机设计	82	0.0853
		LHS	358	0.0945			LHS	46	0.0855
F3	2	LOLA-DIST	43	0.0816		5	LOLA-DIST	45	0.0836
		LOLA-Voronoi	85	0.0728			LOLA-Voronoi	61	0.0566
		随机设计	64	0.0922			随机设计	36	0.0978
		LHS	82	0.0843			LHS	46	0.0971
F4	2	LOLA-DIST	25	0.0902		6	LOLA-DIST	106	0.0749
		LOLA-Voronoi	30	0.0918			LOLA-Voronoi	70	0.0944
		随机设计	40	0.0962			随机设计	70	0.0885
		LHS	35	0.0910			LHS	82	0.0917
	10	LOLA-DIST	226	0.0836	F7	8	LOLA-DIST	58	0.0889
		LOLA-Voronoi	190	0.0818			LOLA-Voronoi	94	0.0954
		随机设计	598	0.1000			随机设计	70	0.0873
		LHS	238	0.0889			LHS	58	0.0962

函数序号	维度	加点准则	收敛点	MAPE	函数序号	维度	加点准则	收敛点	MAPE
F1	2	LOLA-DIST	12	0.0170	F5	4	LOLA-DIST	93	0.0451
		LOLA-Voronoi	15	0.0220			LOLA-Voronoi	102	0.0437
		随机设计	39	0.0365			随机设计	106	0.0360
		LHS	19	0.0345			LHS	126	0.0443
F2	2	LOLA-DIST	178	0.0214	F6	4	LOLA-DIST	34	0.0454
		LOLA-Voronoi	214	0.0435			LOLA-Voronoi	46	0.0267
		随机设计	394	0.0385			随机设计	166	0.0423
		LHS	370	0.0459			LHS	70	0.0416
F3	2	LOLA-DIST	44	0.0289		5	LOLA-DIST	56	0.0487
		LOLA-Voronoi	86	0.0473			LOLA-Voronoi	65	0.0469
		随机设计	69	0.0496			随机设计	79	0.0489
		LHS	90	0.0395			LHS	71	0.0484
F4	2	LOLA-DIST	40	0.0458		6	LOLA-DIST	166	0.0491
		LOLA-Voronoi	56	0.0472			LOLA-Voronoi	178	0.0497
		随机设计	106	0.0468			随机设计	286	0.0481
		LHS	120	0.0498			LHS	298	0.0499
	10	LOLA-DIST	406	0.0485	F7	8	LOLA-DIST	238	0.0499
		LOLA-Voronoi	442	0.0490			LOLA-Voronoi	298	0.0496
		随机设计	>1210	—			随机设计	490	0.0500
		LHS	670	0.0467			LHS	502	0.0498

函数序号	维度	加点准则	收敛点	MAPE	函数序号	维度	加点准则	收敛点	MAPE
F1	2	LOLA-DIST	13	0.0045	F5	4	LOLA-DIST	173	0.0094
		LOLA-Voronoi	22	0.0001			LOLA-Voronoi	197	0.0093
		随机设计	54	0.0095			随机设计	193	0.0099
		LHS	39	0.0092			LHS	210	0.0095
F2	2	LOLA-DIST	238	0.0068	F6	4	LOLA-DIST	58	0.0077
		LOLA-Voronoi	346	0.0092			LOLA-Voronoi	82	0.0064
		随机设计	466	0.0075			随机设计	466	0.0097
		LHS	538	0.0067			LHS	178	0.0079
F3	2	LOLA-DIST	50	0.0098		5	LOLA-DIST	156	0.0098
		LOLA-Voronoi	125	0.0067			LOLA-Voronoi	167	0.0097
		随机设计	125	0.0074			随机设计	207	0.0097
		LHS	131	0.0080			LHS	201	0.0093
F4	2	LOLA-DIST	322	0.0091		6	LOLA-DIST	586	0.0099
		LOLA-Voronoi	430	0.0099			LOLA-Voronoi	610	0.0100
		随机设计	490	0.0096			随机设计	694	0.0096
		LHS	466	0.0095			LHS	658	0.0098
F4	10	LOLA-DIST	>1210	—	F7	8	LOLA-DIST	682	0.0096
		LOLA-Voronoi	>1210	—			LOLA-Voronoi	718	0.0093
		随机设计	>1210	—			随机设计	742	0.0099
		LHS	>1210	—			LHS	802	0.0094