改进熵权和灰关联模型的装备能力评估

doi:10.12305/j.issn.1001-506X.2026.02.14

Abstract

Abstract:

Addressing the issue that traditional information entropy method and grey correlation model have excessively high requirements for the quantity and quality of equipment test data, making it difficult to ensure accurate evaluation of equipment performance, an improved entropy weight method and grey correlational model are proposed. This method uses Bayes Bootstrap method to estimate the parameters of small sample experimental data, calculates the point estimation values of equipment indicator parameters, and constructs a judgment comparison matrix. the information entropy method is combined with parameter estimation values of equipment evaluation indicators to determine the objective weights of indicators. By examining the positional relationship between the estimated values of equipment indicator parameter points and the positive and negative ideal solutions, the positive and negative correlation coefficients of each estimated value of equipment indicator points are solved and aggregated to obtain the evaluation results. The use of this method to evaluate the detection capability of satellite systems and compare it with traditional information entropy method and grey correlation model proves the scientific and effective nature of the improved entropy weight and grey correlation model, providing reference for their application in evaluation methods.

Key words: information entropy, parameter estimation, judgment comparison matrix, ideal solution, grey correlation

CLC Number:

E 92

Bo WANG, Wenya ZHOU, Zhaojie KE, Fei ZONG, Jun LIU. Improved entropy weight and grey correlation model for equipment capability evaluation[J]. Systems Engineering and Electronics, 2026, 48(2): 524-534.

Figures/Tables 18

Fig.1

Fig.2

Fig.3

Table 1

Table 2

Table 3

Table 4

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Table 6

Table 5

Fig.11

Fig.12

References 38

1	胡磊, 张岐龙, 张树才, 等. 以色列侦察卫星体系发展情况与特点分析[J]. 舰船电子对抗, 2021, 44 (4): 12- 16，20. doi: 10.16426/j.cnki.jcdzdk.2021.04.003
	HU L, ZHANG Q L, ZHANG S C, et al. Development state and characteristics analysis of Israel reconnaissance satellite system[J]. Shipboard Electronic Countermeasure, 2021, 44 (4): 12- 16，20. doi: 10.16426/j.cnki.jcdzdk.2021.04.003
2	唐雪梅, 周伯昭, 李荣. 武器装备小子样综合试验设计与鉴定技术[J]. 战术导弹技术, 2007 (2): 51- 56，79. doi: 10.3969/j.issn.1009-1300.2007.02.010
	TANG X M, ZHOU B Z, LI R. Integrated test design and evaluation technology of weapon system in small sample situation[J]. Tactical Missile Technology, 2007 (2): 51- 56，79. doi: 10.3969/j.issn.1009-1300.2007.02.010
3	徐榕, 吴茂林, 胡平. 电子装备系统效能评估方法现状与展望[J]. 舰船电子工程, 2022, 42 (3): 1- 6. doi: 10.3969/j.issn.1672-9730.2022.03.001
	XU R, WU M L, HU P. Current situation and prospect of effectiveness evaluation methods for electronic equipment system[J]. Ship Electronic Engineering, 2022, 42 (3): 1- 6. doi: 10.3969/j.issn.1672-9730.2022.03.001
4	LI H L, CHEN Y Y, QIU B Y. Network effectiveness evaluation method of tactical internet based on QoS performance[C]//Proc. of the International Symposium on Communication Engineering & Computer Science, 2018: 50−54.
5	陈浩, 王佳佳. 装备试验评估的应用与发展[J]. 中国设备工程, 2020, 22, 250- 251. doi: 10.3969/j.issn.1671-0711.2020.22.145
	CHEN H, WANG J J. Application and development of equipment test evaluation[J]. China Plant Engineering, 2020, 22, 250- 251. doi: 10.3969/j.issn.1671-0711.2020.22.145
6	HOFER E, MOHRENSCHILDT M. Model-free data mining of families of rotating machinery[J]. Applied Sciences, 2022, 12 (6): 3178. doi: 10.3390/app12063178
7	WANG C, GENG H J, SUN R, et al. Technological potential analysis and vacant technology forecasting in the graphene field based on the patent data mining[J]. Resources Policy, 2022, 77, 102661. doi: 10.1016/j.resourpol.2022.102636
8	LI J. Design of enterprise human resources decision support system based on data mining[J]. Soft Computing, 2022, 26 (20): 10823- 10832. doi: 10.21203/rs.3.rs-805084/v1
9	张家宾. 小样本条件下装备作战效能评估问题研究[J]. 计算机与数字工程, 2021, 49 (8): 1516- 1519，1565. doi: 10.3969/j.issn.1672-9722.2021.08.003
	ZHANG J B. Research on evaluation of equipment's combat effectiveness under the condition of small sample[J]. Computer & Digital Engineering, 2021, 49 (8): 1516- 1519，1565. doi: 10.3969/j.issn.1672-9722.2021.08.003
10	王博, 周文雅, 汪涛, 等. 多阶段任务装备体系作战能力评估[J]. 系统工程与电子技术, 2023, 45 (11): 3498- 3506. doi: 10.12305/j.issn.1001-506X.2023.11.16
	WANG B, ZHOU W Y, WANG T, et al. Operational capability evaluation of multi-phase mission equipment system[J]. Systems Engineering and Electronics, 2023, 45 (11): 3498- 3506. doi: 10.12305/j.issn.1001-506X.2023.11.16
11	李一哲, 卞贵学, 黄海亮, 等. 基于小样本参数估计的飞机异种金属连接结构加速环境谱[J]. 材料保护, 2023, 56 (12): 1- 6，111. doi: 10.16577/j.issn.1001-1560.2023.0281
	LI Y Z, BIAN G X, HUANG H L, et al. Accelerated corrosion environment spectrum for aircraft dissimilar metal joint structure based on small sample parameter estimation method[J]. Materials Protection, 2023, 56 (12): 1- 6，111. doi: 10.16577/j.issn.1001-1560.2023.0281
12	ANASTASIYA B, DIANA K. Applying fuzzy inference and machine learning methods for prediction with a small dataset: a case study for predicting the consequences of oil spills on a ground environment[J]. Applied Sciences, 2022, 12 (16): 8252. doi: 10.3390/app12168252
13	KROTULSKI A J, JANSEN S V, BARRY K L. Sample mining and data mining: combined real-time and retrospective approaches for the identification of emerging novel psychoactive substances[J]. Journal of Forensic Sciences, 2020, 65 (2): 550- 562. doi: 10.1111/1556-4029.14184
14	肖支才, 高华明, 丁通, 等. 自助法在小样本数据均值估计中的应用[J]. 海军航空工程学院学报, 2009, 24 (5): 563- 567，572. doi: 10.3969/j.issn.1673-1522.2009.05.020
	XIAO Z C, GAO H M, DING T, et al. Research on data analysis of small sample based on bootstrap method[J]. Journal of Naval Aeronautical and Astronautical University, 2009, 24 (5): 563- 567，572. doi: 10.3969/j.issn.1673-1522.2009.05.020
15	周凯锐, 刘鑫, 景丽萍, 等. 概念驱动的小样本判别特征学习方法[J]. 智能系统学报, 2023, 18 (1): 162- 172. doi: 10.11992/tis.202203061
	ZHOU K R, LIU X, JING L P, et al. Concept-driven discriminative feature learning for few-shot learning[J]. CAAI Transactions on Intelligent Systems, 2023, 18 (1): 162- 172. doi: 10.11992/tis.202203061
16	TSOUMPLEKAS G, ATHANASIADIS C, DOUKAS I D, et al. Few-shot load forecasting under data scarcity in smart grids: a meta-learning approach[J]. Energies, 2025, 18 (3): 742. doi: 10.3390/en18030742
17	崔一博, 赵林海, 吕向东. 基于股票分析与灰关联的JTC轨面设备故障诊断方法[J]. 铁道学报, 2021, 43 (5): 112- 120. doi: 10.3969/j.issn.1001-8360.2021.05.013
	CUI Y B, ZHAO L H, LV X D. Fault diagnosis method for JTC rail surface equipment based on stock analysis and grey correlation analysis[J]. Journal of the China Railway Society, 2021, 43 (5): 112- 120. doi: 10.3969/j.issn.1001-8360.2021.05.013
18	傅惠民, 李子昂, 付越帅. 机械产品小样本可靠性评估与更新方法[J]. 机电产品开发与创新, 2021, 34 (5): 9- 21. doi: 10.3969/j.issn.1002-6673.2021.05.001
	FU H M, LI Z A, FU Y S. Reliability assessment and updating methods of mechanical products based on small sample[J]. Development & Innovation of Machinery & Electrical Products, 2021, 34 (5): 9- 21. doi: 10.3969/j.issn.1002-6673.2021.05.001
19	于江, 柳洋. 一种采用自定义参量实现小样本评估可靠性的方法[J]. 火工品, 2022 (5): 13- 16. doi: 10.3969/j.issn.1003-1480.2022.05.004
	YU J, LIU Y. A method for assessing reliability in small samples using custom parametrics[J]. Initiators and Pyrotechnics, 2022 (5): 13- 16. doi: 10.3969/j.issn.1003-1480.2022.05.004
20	赵燕, 朱景伟, 任萍. 基于数据预处理的小样本开关磁阻电机智能方法建模[J]. 电机与控制学报, 2025, 29 (2): 85- 95. doi: 10.15938/j.emc.2025.02.009
	ZHAO Y, ZHU J W, REN P. Modeling of switched reluctance motor by intelligent method with small samples and data pretreatment[J]. Electric Machines and Control, 2025, 29 (2): 85- 95. doi: 10.15938/j.emc.2025.02.009
21	HUU-THO N, SITI Z M D, YUSOFF N, et al. An integrated MCDM model for conveyor equipment evaluation and selection in an FMC based on a fuzzy AHP and fuzzy ARAS in the presence of vagueness[J]. PLoS ONE, 2017, 11 (4): e0153222. doi: 10.1371/journal.pone.0153222
22	BUETTI D, ISABELLE B, MAZIAR J. Examining the competencies required by evaluation capacity builders in community-based organizations[J]. Evaluation and Program Planning, 2023, 97, 102242. doi: 10.1016/j.evalprogplan.2023.102242
23	关爱杰, 徐博奥, 李聪. 一种基于仿真的导弹部队作战方案评估方法[J]. 军事运筹与系统工程, 2022, 36 (1): 70- 74. doi: 10.19949/j.ams.mora.20210917.01
	GUAN A J, XU B A, LI C. A simulation based evaluation method for missile troops' operational plans[J]. Military Operations Research and Systems Engineering, 2022, 36 (1): 70- 74. doi: 10.19949/j.ams.mora.20210917.01
24	BROWN S A T, MCNAMARA J A, CHOI H J, et al. Assessment of a marksmanship simulator as a tool for clothing and individual equipment evaluation[J]. Proceedings of the Human Factors and Ergonomics Society Annual Meeting, 2016, 60 (1): 1424- 1428. doi: 10.1177/1541931213601327
25	JIA G H, ZHOU J. Effectiveness evaluation method of application of mobile communication system based on factor analysis[J]. Sensors, 2021, 21 (16): 5414. doi: 10.3390/s21165414
26	QI Z Y, ZHANG Y Y, FANG L Q, et al. Research on effectiveness evaluation method of weapon system based on cloud model[J]. Journal of Physics: Conference Series, 2021, 1965, 012105. doi: 10.1088/1742-6596/1965/1/012005
27	YU C Y. Research on effectiveness evaluation method and application of quality management system of manufacturing enterprise based on interval-valued hesitation fuzzy set[J]. Vibroengineering PROCEDIA, 2017, 14, 294- 299. doi: 10.21595/vp.2017.18937
28	郑秋红, 丁全玉, 王应明. 考虑属性关联的区间灰熵决策模型[J]. 运筹与管理, 2024, 33 (5): 42- 47. doi: 10.12005/orms.2024.0145
	ZHENG Q H, DING Q Y, WANG Y M. Interval grey entropy decision model considering attribute association[J]. Operations Research and Management Science, 2024, 33 (5): 42- 47. doi: 10.12005/orms.2024.0145
29	BRYANT D J. Rethinking OODA: toward a modern cognitive framework of command decision making[J]. Military Psychology, 2006, 18 (3): 183- 206. doi: 10.1207/s15327876mp1803_1
30	HUANG G Q, XU S H, ZHAO W B. Study on the effectiveness evaluation method based on the combination of AHP and grey interval correlation[J]. Journal of Electrical and Electronic Engineering, 2015, 3 (5): 151- 155. doi: 10.11648/j.jeee.20150305.23
31	柯肇捷, 周文雅. 基于灰自助和未确知有理数的小样本试验数据估计[J]. 兵工学报, 2019, 40 (4): 874- 879. doi: 10.3969/j.issn.1000-1093.2019.04.023
	KE Z J, ZHOU W Y. Parameter estimation model of small test samples based on grey bootstrap method and unascertained rational number[J]. Acta Armamentarii, 2019, 40 (4): 874- 879. doi: 10.3969/j.issn.1000-1093.2019.04.023
32	孙慧玲, 胡伟文, 刘海涛. 小样本情况下参数区间估计的改进方法[J]. 哈尔滨理工大学学报, 2017, 22 (1): 109- 113. doi: 10.15938/j.jhust.2017.01.019
	SUN H L, HU W W, LIU H T. An improvement to interval estimation for small samples[J]. Journal of Harbin University of Science and Technology, 2017, 22 (1): 109- 113. doi: 10.15938/j.jhust.2017.01.019
33	SHANNON C E. A mathematical theory of communication[J]. The Bell System Technical Journal, 1948, 27 (4): 623- 656. doi: 10.1002/j.1538-7305.1948.tb00917.x
34	罗琴, 杨根, 刘智, 等. 结合主动学习的威胁情报IOC识别方法[J]. 电子科技大学学报, 2023, 52 (1): 108- 115. doi: 10.12178/1001-0548.2022090
	LUO Q, YANG G, LIU Z, et al. A threat intelligence IOC identification method combined with active learning[J]. Journal of University of Electronic Science and Technology of China, 2023, 52 (1): 108- 115. doi: 10.12178/1001-0548.2022090
35	WANG W C, LIU H L, LI F S, et al. Effects of unsaturated fatty acid methyl esters on the oxidation stability of biodiesel determined by gas chromatography-mass spectrometry and information entropy methods[J]. Renewable Energy, 2021, 175, 880- 889. doi: 10.1016/j.renene.2021.04.132
36	陈亭羲. 矿井煤与瓦斯突出灰关联评价[D]. 成都: 四川师范大学, 2022.
	CHEN T X. Grey relational evaluation of coal and gas outburst in mines[D]. Chengdu: Sichuan Normal University, 2022.
37	郭国强, 牛智奇, 李亚超, 等. 综合最优赋权和云模型的导引头方案优选方法[J]. 系统工程与电子技术, 2025, 47(9): 3011−3021.
	GUO G Q, NIU Z Q, LI Y C, et al. An optimization method for seeker scheme integrating optimal weighting and cloud model[J]. Systems Engineering and Electronics, 2025, 47(9): 3011−3021.
38	申卯兴, 薛西锋, 张小水. 灰色关联分析中分辨系数的选取[J]. 空军工程大学学报（自然科学版）, 2003 (1): 68- 70. doi: 10.3969/j.issn.1009-3516.2003.01.019
	SHEN M X, XUE X F, ZHANG X S. Determination of discrimination coefficient in grey incidence analysis[J]. Journal of Air Force Engineering University （Natural Science Edition）, 2003 (1): 68- 70. doi: 10.3969/j.issn.1009-3516.2003.01.019

指标	专家序号
指标	1	2	3	4	5
探测视场	0.96	0.98	0.93	0.95	0.96
探测距离	0.84	0.86	0.92	0.88	0.93
成像距离	0.73	0.78	0.80	0.81	0.76
可探测信号特征	0.88	0.92	0.86	0.90	0.87
探测概率	0.93	0.92	0.88	0.95	0.88
测距精度	0.86	0.82	0.88	0.84	0.80
定位精度	0.88	0.93	0.94	0.85	0.81
成像分辨率	0.66	0.67	0.76	0.72	0.78
探测频率	0.85	0.90	0.93	0.88	0.91
探测响应时间	0.92	0.88	0.90	0.88	0.89

指标	专家序号
指标	1	2	3	4	5
探测视场	0.88	0.90	0.86	0.92	0.83
探测距离	0.88	0.82	0.80	0.86	0.85
成像距离	0.82	0.76	0.83	0.81	0.83
可探测信号特征	0.85	0.82	0.86	0.81	0.83
探测概率	0.85	0.83	0.80	0.85	0.88
测距精度	0.90	0.93	0.92	0.86	0.90
定位精度	0.85	0.83	0.84	0.85	0.81
成像分辨率	0.82	0.87	0.86	0.82	0.88
探测频率	0.65	0.70	0.73	0.68	0.71
探测响应时间	0.82	0.78	0.80	0.78	0.79

指标	专家序号
指标	1	2	3	4	5
探测视场	0.82	0.88	0.83	0.85	0.86
探测距离	0.74	0.76	0.72	0.78	0.73
成像距离	0.83	0.88	0.80	0.88	0.86
可探测信号特征	0.85	0.82	0.76	0.80	0.83
探测概率	0.90	0.91	0.89	0.91	0.86
测距精度	0.76	0.72	0.78	0.74	0.70
定位精度	0.78	0.73	0.74	0.75	0.71
成像分辨率	0.86	0.87	0.86	0.82	0.88
探测频率	0.75	0.70	0.73	0.78	0.71
探测响应时间	0.82	0.66	0.80	0.68	0.79

指标	专家序号
指标	1	2	3	4	5
探测视场	0.90	0.92	0.96	0.94	0.91
探测距离	0.94	0.96	0.92	0.98	0.93
成像距离	0.83	0.88	0.80	0.81	0.86
可探测信号特征	0.78	0.82	0.76	0.80	0.77
探测概率	0.83	0.82	0.78	0.85	0.78
测距精度	0.86	0.82	0.88	0.84	0.80
定位精度	0.78	0.83	0.84	0.85	0.86
成像分辨率	0.86	0.87	0.76	0.82	0.88
探测频率	0.95	0.96	0.93	0.98	0.96
探测响应时间	0.92	0.98	0.93	0.96	0.92

方法	1号	2号	3号	4号
传统灰关联法	0.4907	0.5394	0.5186	0.4856
Bayes灰关联法	0.5075	0.6311	0.5476	0.5079

Improved entropy weight and grey correlation model for equipment capability evaluation

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 18

References 38

Related Articles 15

Recommended Articles

Metrics

Comments

指标	系统序号
指标	1	2	3	4
探测视场	0.9525	0.8796	0.8545	0.9258
探测距离	0.8867	0.8430	0.7456	0.9437
成像距离	0.7787	0.8169	0.8464	0.8268
可探测信号特征	0.8907	0.8348	0.8125	0.7779
探测概率	0.9225	0.8506	0.8928	0.8099
测距精度	0.8452	0.9026	0.7460	0.7376
定位精度	0.8675	0.8495	0.7376	0.8495
成像分辨率	0.7277	0.8557	0.8617	0.8511
探测频率	0.8938	0.6951	0.7460	0.9520
探测响应时间	0.8908	0.7969	0.8129	0.9523

[1]	Ning GAO, Feng XU, Juan YANG. Parameter estimation algorithm of underwater moving small target in MIMO sonar based on FrFT [J]. Systems Engineering and Electronics, 2025, 47(9): 2797-2807.
[2]	Ziqing ZHEN, Dong HUANG, Song HAN, Haoming FENG. Construction of economic evaluating indicator system for service life of ships [J]. Systems Engineering and Electronics, 2025, 47(7): 2275-2282.
[3]	Xiaohui BA, Wenfei WEN, Baigen CAI, Jian WANG, Wei JIANG, Linguo CHAI. Linear frequency modulation interference suppression method for GNSS signal [J]. Systems Engineering and Electronics, 2025, 47(7): 2339-2348.
[4]	You ZHANG, Yonghui HUANG, Zhihao LI, Tianshu CUI, Zhugang WANG. Parameter estimation algorithm for time-frequency difference using Savitzky-Golay filtering and cross-ambiguity function [J]. Systems Engineering and Electronics, 2025, 47(5): 1395-1403.
[5]	Zhou XU, Lianzhao LIU, Kai ZHOU, Daoyou WANG, Hui MA. SMSP jamming analysis and cancellation methods based on parameter estimation [J]. Systems Engineering and Electronics, 2025, 47(12): 4048-4056.
[6]	Peng SUN, Xinping WEI, Heng WANG, Wei WANG, Kexian GONG. Satellite single-mixed signal identification method based on multi-feature fusion [J]. Systems Engineering and Electronics, 2025, 47(11): 3859-3867.
[7]	Weihong FU, Yufei ZHOU, Xinyu ZHANG, Naian LIU. Single-channel blind source separation algorithm based on parameter estimation and Kalman filter [J]. Systems Engineering and Electronics, 2024, 46(8): 2850-2856.
[8]	Shuo MENG, Chen MENG, Cheng WANG. Research on LFM signal parameter estimation method based on Z-transform and improved FRI [J]. Systems Engineering and Electronics, 2024, 46(7): 2228-2236.
[9]	Qianpeng XIE, Yihang DU, Bing SUN, Hua YAN, Xiaoyi PAN, Feng ZHAO. High resolution multidimensional parameter estimation for low complexity bistatic EMVS-MIMO radar based on reduced-dimensional transformation [J]. Systems Engineering and Electronics, 2024, 46(6): 1899-1907.
[10]	Haiying WANG, Qunying ZHANG, Wenhai CHENG, Jiaming DONG, Xiaojun LIU. Research progress on LPI radar signal modulation recognition and parameter estimation [J]. Systems Engineering and Electronics, 2024, 46(6): 1908-1924.
[11]	Wangxiang CHEN, He TIAN, Jier WANG, Dan TIAN. Geometric parameters estimation of spherical cone target based on scattering model [J]. Systems Engineering and Electronics, 2024, 46(3): 892-897.
[12]	Liyuan WANG, Huafeng HE, Xiaofei HAN, Yaomin HE, Zhen LI. Joint estimation method of DOA and polarization parameters based on broadband coherent signals [J]. Systems Engineering and Electronics, 2024, 46(3): 805-813.
[13]	Yunlong DONG, Yan ZHANG. ECEF-GLS estimation algorithm based on fading factor [J]. Systems Engineering and Electronics, 2024, 46(1): 137-142.
[14]	Ran LAI, Gang SUN, Wei ZHANG, Tao ZHANG. Space-time moving target parameter estimation algorithm based on non-convex relaxation of atomic norm [J]. Systems Engineering and Electronics, 2023, 45(9): 2761-2767.
[15]	Qian SU, Yuanfu ZHONG, Zhiqin CAO, Yingchao ZHANG. Target threat assessment model based on operational situation and improved CRITIC-TOPSIS [J]. Systems Engineering and Electronics, 2023, 45(8): 2343-2352.