基于图论与PageRank的要地反导己方目标重要性排序

doi:10.12305/j.issn.1001-506X.2021.03.14

摘要/Abstract

摘要：

针对要地反导作战己方目标重要性排序问题, 创新性地提出一种基于图论与网页排名(PageRank, PR)算法的排序方法。首先, 采用图论方法将各目标之间各种静态、动态关系网络抽象成二维拓扑结构图, 确立在不同关系下各目标之间的相互联系。其次, 根据要地反导作战实际情况，结合专家意见对静态、动态关系网络的重要程度进行打分。基于PR算法思想, 根据构建的目标关系模型, 计算己方目标关系矩阵及重要度值, 给出目标排序。最后, 结合要地反导作战案例进行验证分析。结果表明，该方法能够综合目标排序时的多方面因素, 给出科学、合理的重要性排序, 具有一定的可推广性和应用前景。

关键词: 要地反导作战, 目标重要性, 图论, 网页排名

Abstract:

Aiming at the problem of the importance ranking of own targets for the anti-missile operations in important places, an innovative ranking method based on graph theory and PageRank (PR) algorithm is proposed. Firstly, the static and dynamic relationship network among the targets is abstracted into a two-dimensional topological structure diagram by using the graph theory method, and the relationship among the targets under different relationships is established. Secondly, according to the actual situation of anti-missile operations in important places, the importance of static and dynamic relationship network is scored combined with expert opinions. Based on the idea of PR algorithm, according to the constructed target relation model, the objective relation matrix and importance value of own targets are calculated, and the target ranking is given. Finally, combining with the case of anti-missile operations in important places, the verification analysis is carried out. The results show that the method can synthesize many factors in the target ranking, and give a scientific and reasonable importance ranking, which has certain popularization and application prospects.

Key words: anti-missile operations in important place, importance of target, graph theory, PageRank (PR)

中图分类号:

TP303
E074

王䶮, 滕克难, 程业, 陈健. 基于图论与PageRank的要地反导己方目标重要性排序[J]. 系统工程与电子技术, 2021, 43(3): 709-715.

Yan WANG, Kenan TENG, Ye CHENG, Jian CHEN. Importance ranking of anti-missile targets in important places based on graph theory and PageRank[J]. Systems Engineering and Electronics, 2021, 43(3): 709-715.

图/表 9

图1

图2

图3

图4

图5

图6

表1

表2

表3

参考文献 30

1	邱学军. 城市防空中需掩护目标的重要性层次分析[J]. 现代防御技术, 2002, 30 (1): 6- 10. doi: 10.3969/j.issn.1009-086X.2002.01.002
	QIU X J . Hierarchical analysis of importance of defence aim needed in city air defence[J]. Modern Defence Tecbologys, 2002, 30 (1): 6- 10. doi: 10.3969/j.issn.1009-086X.2002.01.002
2	卢盈齐, 王颖龙, 祝长英. TOPSIS法用于区域防空重点保卫目标排序计算[J]. 火力与指挥控制, 2006, 30 (2): 20- 21, 28. doi: 10.3969/j.issn.1002-0640.2006.02.007
	LU Y Q , WANG Y L , ZHU C Y . Application of TOPSIS to sequencing computation of protected important targets in area air defence[J]. Fire Control and Command Control, 2006, 31 (2): 20- 21, 28. doi: 10.3969/j.issn.1002-0640.2006.02.007
3	汪鑫, 龙光正, 汪志宏, 等. 基于灰色聚类和序关系的防空保卫目标排序研究[J]. 弹箭与制导学报, 2018, 38 (2): 25- 29.
	WANG X , LONG G Z , WANG Z H , et al. Based on the grey clustering method to resolve the defend target[J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2018, 38 (2): 25- 29.
4	EMMA C , MARIE G , BENEDICTE D , et al. Dynamic functional connectivity and graph theory metrics in a rat model of temporal lobe epilepsy reveal a preference for brain states with a lower functional connectivity, segregation and integration[J]. Neurobiology of Disease, 2020, 139, 104808. doi: 10.1016/j.nbd.2020.104808
5	周翔翔, 姚佩阳, 王欣, 等. 基于图论的作战指挥决策群组划分算法[J]. 系统工程与电子技术, 2011, 33 (3): 575- 580. doi: 10.3969/j.issn.1001-506X.2011.03.21
	ZHOU X X , YAO P Y , WANG X , et al. Algorithm of combat command decision group partition based on graph theory[J]. Systems Engineering and Electronics, 2011, 33 (3): 575- 580. doi: 10.3969/j.issn.1001-506X.2011.03.21
6	刘志成, 严建钢, 陈榕, 等. 基于图论的防空节点攻击价值研究[J]. 火力与指挥控制, 2012, 37 (8): 188- 190. doi: 10.3969/j.issn.1002-0640.2012.08.049
	LIU Z C , YAN J G , CHEN R , et al. Rearch on attack value of the aerial defense node based on graph theory[J]. Fire Control and Command Control, 2012, 37 (8): 188- 190. doi: 10.3969/j.issn.1002-0640.2012.08.049
7	EMILY J P , JASON R T , SIMON S K , et al. Interictal structural and functional connectivity in idiopathic generalized epilepsy: a systematic review of graph theoretical studies[J]. Epilepsy & Behavior, 2020, 106, 107013.
8	BEHNAZ A , ABBAS E . A framework for seizure detection using effective connectivity, graph theory, and multi-level modular network[J]. Biomedical Signal Processing and Control, 2020, 59, 101878. doi: 10.1016/j.bspc.2020.101878
9	BENITO-LEON J , SANZ-MORALES E , MELERO H , et al. Graph theory analysis of resting-state functional magnetic resonance imaging in essential tremor[J]. Human Brain Mapping, 2019, 41 (16): 4686- 4702.
10	YAN C , NOOR Q , CHAD V M . Bayesian network and game theory risk assessment model for third-party damage to oil and gas pipelines[J]. Process Safety and Environmental Protection, 2020, 134, 178- 188. doi: 10.1016/j.psep.2019.11.038
11	刘敬蜀, 姜文志, 刘涛, 等. 动态火力接入下要地防空作战系统研究[J]. 指挥控制与仿真, 2015, 37 (5): 25- 28.
	LIU J S , JIANG W Z , LIU T , et al. Research on operation system of key position air-defense under dynamic fire access[J]. Command Control & Simulation, 2015, 37 (5): 25- 28.
12	刘敬蜀, 姜文志, 代进进, 等. 动态火力接入下要地防空制导决策方法[J]. 海军航空工程学院学报, 2015, 30 (6): 537- 542.
	LIU J S , JIANG W Z , DAI J J , et al. Guidance-making method of essential air-defense under dynamic fire access[J]. Journal of Naval Aeronautical and Astronautical University, 2015, 30 (6): 537- 542.
13	刘敬蜀, 姜文志, 雷宇曜, 等. 动态火力接入下要地防空导弹杀伤区远界研究[J]. 现代防御技术, 2016, 44 (1): 34- 41. doi: 10.3969/j.issn.1009-086x.2016.01.007
	LIU J S , JIANG W Z , LEI Y Y , et al. Far boundary of kill zone for air-defense missile protecting key points under dynamic fire access[J]. Modern Defence Technology, 2016, 44 (1): 34- 41. doi: 10.3969/j.issn.1009-086x.2016.01.007
14	程绍成, 刘敬蜀, 张广法, 等. 基于发射时间序列的反舰导弹联合突防方法[J]. 海军航空工程学院学报, 2013, 28 (3): 289- 291.
	CHENG S C , LIU J S , ZHANG G F , et al. An anti-ship missile joint penetrate method based on launch time series model[J]. Journal of Naval Aeronautical and Astronautical University, 2013, 28 (3): 289- 291.
15	李彪, 刘敬蜀, 刘丹. 熵损失下无失效数据的Bayes估计[J]. 海军航空工程学院学报, 2013, 28 (5): 577- 580.
	LI B , LIU J S , LIU D . Bayes estimation of zero-failure data under entropy loss[J]. Journal of Naval Aeronautical and Astronautical University, 2013, 28 (5): 577- 580.
16	雷宇曜, 姜文志, 刘敬蜀. 要地防空弹炮结合武器系统射击时机分析[J]. 现代防御技术, 2014, 42 (3): 96- 100. doi: 10.3969/j.issn.1009-086x.2014.03.018
	LEI Y Y , JIANG W Z , LIU J S . Shooting opportunity analysis of antiaircraft gun missile system in point air defense[J]. Modern Defence Technology, 2014, 42 (3): 96- 100. doi: 10.3969/j.issn.1009-086x.2014.03.018
17	程贲, 谭跃进, 黄魏, 等. 基于能力需求视角的武器装备体系评估[J]. 系统工程与电子技术, 2011, 33 (2): 320- 323. doi: 10.3969/j.issn.1001-506X.2011.02.18
	CHENG B , TAN Y J , HUANG W , et al. Weapon system-of-systems evaluation based on capability requirement perspective[J]. Systems Engineering and Electronics, 2011, 33 (2): 320- 323. doi: 10.3969/j.issn.1001-506X.2011.02.18
18	马其东, 方立恭, 江言林, 等. 基于直觉模糊多属性决策的作战效能综合评估方法[J]. 指挥控制与仿真, 2011, 33 (2): 45- 48. doi: 10.3969/j.issn.1673-3819.2011.02.013
	MA Q D , FANG L G , JIANG Y L , et al. Method of comprehensive evaluation of operational effectiveness based on intuitionistic fuzzy sets multi-attributes decision making[J]. Command Control & Simulation, 2011, 33 (2): 45- 48. doi: 10.3969/j.issn.1673-3819.2011.02.013
19	雷宇曜, 杨历彪, 高健. 外部预警支援下地空导弹要地反导作战建模与仿真[J]. 指挥控制与仿真, 2019, 41 (1): 95- 98.
	LEI Y Y , YANG L B , GAO J . Modeling and simulation of ground-to-air missile anti-missile operation in reef area supported by external early warning[J]. Command Control & Simulation, 2019, 41 (1): 95- 98.
20	马新星, 滕克难, 侯学隆. 岛礁防空火力单元配置距离计算模型[J]. 兵工自动化, 2017, 36 (10): 38- 41, 79.
	MA X X , TENG K N , HOU X L . Models to calculate the deployment distance of reef air defense fire units[J]. Ordnance Industry Automation, 2017, 36 (10): 38- 41, 79.
21	GUANG F C , CHEN X , JING Y , et al. Nonnegative matrix factorization for link prediction in directed complex networks using PageRank and asymmetric link clustering information[J]. Expert Systems With Applications, 2020, 148, 113290. doi: 10.1016/j.eswa.2020.113290
22	JIUNG L , MARIANA O . PageRank on inhomogeneous random digraphs[J]. Stochastic Processes and their Applications, 2020, 130 (4): 2312- 2348. doi: 10.1016/j.spa.2019.07.002
23	FAN C , YINI Z , KARL R . Targeted sampling from massive block model graphs with personalized PageRank[J]. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2020, 82 (1): 99- 126. doi: 10.1111/rssb.12349
24	KIM E , JEON M . Proposal for implementation of a ranking model for Olympic Taekwondo competitions using PageRank[J]. International Journal of Performance Analysis in Sport, 2019, 19 (2): 227- 235. doi: 10.1080/24748668.2019.1586506
25	HENNI K , MEZGHANI N , GOUIN C . Unsupervised graph-based feature selection via subspace and pagerank centrality[J]. Expert Systems With Applications, 2018, 114, 46- 53. doi: 10.1016/j.eswa.2018.07.029
26	EKATERINA M , ANDREA L B , FAN C . A semi-supervised heat kernel pagerank MBO algorithm for data classification[J]. Communication in Mathematical Sciences, 2018, 16 (5): 1241- 1265. doi: 10.4310/CMS.2018.v16.n5.a4
27	CHUAN Q G , XIANG L J , CHEN C S , et al. A GMRES-power algorithm for computing PageRank problems[J]. Journal of Computational and Applied Mathematics, 2018, 343, 113- 123. doi: 10.1016/j.cam.2018.03.017
28	王永攀, 杨江平, 邓翔, 等. 基于贝叶斯网络的复杂装备维修质量评价模型[J]. 海军工程大学学报, 2017, 29 (1): 84- 90.
	WANG Y P , YANG J P , DENG X , et al. Assessment model of complex equipment maintenance quality based on Bayesian network[J]. Journal of Naval University of Engineering, 2017, 29 (1): 84- 90.
29	吴敏. 区间值直觉犹豫模糊多属性决策方法研究[J]. 陕西理工大学学报(自然科学版), 2018, 34 (2): 79- 85. doi: 10.3969/j.issn.1673-2944.2018.02.014
	WU M . Research on multiple-attribute decision making method with interval-valued intuitionistic hesitant fuzzy information[J]. Journal of Shanxi University of Technology (Natural Science Edition), 2018, 34 (2): 79- 85. doi: 10.3969/j.issn.1673-2944.2018.02.014
30	周存宝, 高明. 不完全信息的火力打击效能直觉模糊评估[J]. 兵工自动化, 2015, 34 (9): 7- 9.
	ZHOU C B , GAO M . The intuitionistic fuzzy evaluation of fire fighting efficiency with incomplete information[J]. Ordnance Industry Automation, 2015, 34 (9): 7- 9.

编号	目标名称
1	指挥所
2	通信站
3	防空雷达
4	弹药装备库
5	水库
6	食品库
7	油料库
8	医院
9	机场
10	码头
11	电子战车
12	防空车1
13	防空车2
14	防空车3

编号	重要度数值(×10⁷)
1	1.939 6
2	1.146 5
3	0.727 7
4	1.453 3
5	0.437 6
6	0.437 6
7	1.147 5
8	0.220 5
9	0.540 2
10	0.419 0
11	0.463 1
12	0.308 7
13	0.308 7
14	0.308 7

编号	目标名称
1	指挥所
2	弹药装备库
3	油料库
4	通信站
5	防空雷达
6	机场
7	电子站车
8	水库
9	食品库
10	码头
11	防空车1
12	防空车2
13	防空车3
14	医院

[1]	刘同林, 杨芷柔, 张虎, 滕祥意, 刘静. 基于复杂网络的军事通信网络建模与性能分析[J]. 系统工程与电子技术, 2020, 42(12): 2892-2898.
[2]	周翔翔，姚佩阳，王欣，谢必昌. 基于图论的作战指挥决策群组划分算法[J]. Journal of Systems Engineering and Electronics, 2011, 33(3): 575-580.
[3]	李一兵, 杨蕊, 高振国. 基于着色理论的认知无线电频谱分配算法[J]. Journal of Systems Engineering and Electronics, 2010, 32(6): 1109-1112.