复杂多方向威胁下的导弹预警雷达优化部署方法

刘伟; 刘昌云; 郭相科; 樊良优; 何晟; 兰昊

doi:10.13700/j.bh.1001-5965.2022.0486

复杂多方向威胁下的导弹预警雷达优化部署方法

doi: 10.13700/j.bh.1001-5965.2022.0486

刘伟^{1, 2},
刘昌云³,
郭相科^3, ,,
樊良优¹,
何晟¹,
兰昊²

1.
空军工程大学研究生院，西安 710000
2.
中国人民解放军 63768部队，西安 710000
3.
空军工程大学防空反导学院，西安 710000

基金项目: 国家自然科学基金(62106283)

详细信息

通讯作者:
E-mail：guosyanyu@163.com

中图分类号: TN959.1
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- 被引次数: 0
出版历程
- 收稿日期: 2022-06-12
- 录用日期: 2022-08-10
- 网络出版日期: 2022-09-08
- 整期出版日期: 2024-04-29

Deployment optimization method for missile early warning radar under complex and multi-directional missile threats

LIU Wei^{1, 2},
LIU Changyun³,
GUO Xiangke^{3
, ,},
FAN Liangyou¹,
HE Sheng¹,
LAN Hao²

1.
Graduate School，Air Force Engineering University，Xi’ an 710000，China
2.
Unit 63768 of the PLA，Xi’an 710000，China
3.
Air and Missile Defense College，Air Force Engineering University，Xi’an 710000，China

Funds: National Natural Science Foundation of China (62106283)

More Information

Corresponding author: E-mail：guosyanyu@163.com

摘要

摘要:
针对现有导弹预警雷达部署相对独立、协同困难，难以满足大规模对抗场景的现状，从远程预警雷达、跟踪识别雷达、机动式预警雷达不同的任务特点出发，建立应对复杂多方向威胁的多型导弹预警雷达优化部署模型，在满足最优覆盖、协同交接、目标识别等任务约束下，解决雷达协同部署问题。针对所提模型设计了一种基于云自适应的分区优化离散粒子群(CPBPSO)算法，通过设计分区编码策略缩减算法求解空间、加入云自适应变异算子提高算法全局寻优和局部跳出能力，使算法更适用于导弹预警雷达部署问题的处理。实例验证了所提模型在求解单方向、多方向威胁场景部署问题的可行性，对比分析了CPBPSO算法的有效性，基本满足导弹预警雷达最优化协同部署的需求。
- 导弹预警雷达 /
- 协同预警 /
- 优化部署模型 /
- 云自适应变异 /
- 粒子群算法
Abstract:
An optimized deployment model of multiple missile early warning radars is established based on the distinct mission characteristics of early warning radar, tracking and identification radar, and transportable early warning radar in order to address the situation where the deployment of existing missile early warning radars is relatively independent, difficult to cooperate with, and difficult to meet the large-scale operation scenario. Under the constraints of optimal coverage, cooperative handover, and target identification, the cooperative deployment of early warning radars is solved. A cloud adaptive partition optimization binary particle swarm optimization (CPBPSO) algorithm is designed. In order to make the algorithm more suited for solving early warning radar deployment problems, the partition coding strategy is used to shrink the algorithm’s solution space. The cloud adaptive mutation operator is then added to enhance the algorithm’s global optimization and local jumping capability.The example verifies the feasibility of the model in solving the deployment problem of single-direction and multi-direction threat scenarios and analyzes the effectiveness of the CPBPSO algorithm, which basically meets the needs of the optimal cooperative deployment of missile early warning radar.
- missile early warning radar /
- collaborative early warning /
- deployment optimization model /
- cloud adaptive mutation /
- particle swarm optimization algorithm

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图 1 导弹预警雷达能力仿真

Figure 1. Simulation of missile early warning radar capability

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图 2 导弹预警系统协同预警示意图

Figure 2. Schematic diagram of missile early warning system coordinated early warning

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图 3 威胁空域模型

Figure 3. Threat airspace model

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图 4 弹道覆盖示意图

Figure 4. Schematic of ballistic coverage

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图 5 地形遮蔽影响探测能力

Figure 5. Terrain masking affects detection capability

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图 6 弹头目标运动模型

Figure 6. Warhead target motion model

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图 7 协同预警预测交接

Figure 7. Coordinated early warning prediction handover

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图 8 粒子映射关系

Figure 8. Particle mapping relationships

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图 9 粒子分区编码示意

Figure 9. Schematic of particle partition encoding

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图 10 云模型示意图

Figure 10. Cloud model diagram

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图 11 威胁空域示意

Figure 11. Schematic diagram of threat airspace

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图 12 单方向威胁优化部署方案

Figure 12. Optimal radar deployment in single direction threat

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图 13 跟踪识别雷达地形遮蔽示意图

Figure 13. Schematic of tracking and identifying radar terrain shadowing

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图 14 多方向威胁优化部署方案

Figure 14. Optimal radar deployment in multi-direction threat

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图 15 算法对比实验分析

Figure 15. Comparison analysis of algorithms

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表 1 单方向威胁空域的典型弹道信息

Table 1. Typical ballistic information of single direction threat airspace

弹道序号	发点位置/（°）	落点位置/（°）	弹道弧长/km	关机点速度/ （km·s⁻¹）	飞行时间/s
1	(27.4,133.1)	(41.0,80.3)	7036.7	6.534	1934.7
2	(19.2,127.8)	(41.0,80.3)	7072.5	6.498	1928.3
3	(27.2,129.0)	(41.0,80.3)	5140.5	5.865	1186.9
4	(23.7,127.1)	(41.0,80.3)	5258.1	5.904	1203.4

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表 2 雷达基本参数

Table 2. Basic parameter of radar

雷达类型	最大探测距离/km	方位范围/（°）	俯仰范围/（°）
远程预警雷达	3 000	±60	0～85
跟踪识别雷达	500	0～360	10～90
前置预警雷达	1 500	±53	10～85

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表 3 雷达优化部署参数

Table 3. Optimal radar deployment parameter

雷达类型	部署点位	海拔/km	法向/（°）
前置预警雷达	(24.83°N 114.83°E)	0.0293	353.5
远程预警雷达	(45.62°N 116.82°E)	0.8979	148.6
跟踪识别雷达	(43.27°N 85.23°E)	3.7204

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表 4 单方向威胁预警能力分析

Table 4. Analysis of single direction threat early warning capability

弹道名称	首点告警时间/s	持续跟踪时长/s	弹道覆盖率/%	高识别时长/s
BM1	T₀+56.18	1831.58	94.67	71.41
BM2	T₀+39.21	1601.45	83.05	56.10
BM3	T₀+50.36	1117.22	94.13	113.88
BM4	T₀+40.29	1106.76	92.07	100.85
注：T₀为导弹发射时刻。

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表 5 多方向威胁空域的典型弹道信息

Table 5. Typical ballistic information of multi-direction threat airspace

弹道序号	发点位置/（°）	落点位置/（°）	弹道弧长/km	关机点速度/ （km·s⁻¹）	飞行时间/s
1	(56.3,123.5)	(41.0,80.3)	6003.7	5.236	984.5
2	(37.0,127.0)	(41.0,80.3)	4839.7	5.550	1078.9
3	(23.7,130.0)	(41.0,80.3)	6083.4	5.993	1234.8
4	(13.7,105.0)	(41.0,80.3)	4167.3	5.904	1607.3
5	(7.5,91.5)	(41.0,80.3)	4601.5	5.392	1053.3
6	(1.6,60.0)	(41.0,80.3)	5699.9	5.747	1216.6
注：为便于表示，每个空域仅选填1条典型最优能量弹道。

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表 6 雷达部署及任务分配

Table 6. Radar deployment and task assignment

雷达类型	名称	部署点位/（°）	高程/ km	法向/ （°）	E₁	E₂	E₃	E₄	E₅	E₆
前置预警雷达	FBR1	(44.8,113.3)	1.278	7.2	√	√
	FBR2	(25.7,119.1)	0.568	4.8		√	√
	FBR3	(27.9,88.1)	4.758	88.4				√	√
远程预警雷达	PBR1	(29.6,109.4)	0.569	304.7	√	√	√
远程预警雷达	PBR2	(38.6,90.2)	3.138	147.9				√	√	√
跟踪识别雷达	XBR1	(42.4,81.4)	3.951		√	√	√	√	√	√
跟踪识别雷达	XBR2	(41.7,77.6)	5.199		√	√	√	√	√	√

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表 7 多方向威胁预警能力分析

Table 7. Analysis of mutli-direction threat early warning capability

威胁区域	首点告警时间/s	持续跟踪时长/s	弹道覆盖率/%	高识别时长/s
E₁	T₀+56.68	905.28	92.12	76.11
E₂	T₀+50.39	1049.44	97.27	111.26
E₃	T₀+42.07	1022.90	82.84	93.425
E₄	T₀+59.97	1507.16	93.77	76.96
E₅	T₀+51.88	980.93	93.13	77.16
E₆	T₀+608.46	563.16	46.29	62.55

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参考文献(29)

[1]	CHRISTIAN A. US missile defence efforts and Chinese reservation in East Asia[J]. Asian Affairs, 2020(2): 605-620.
[2]	WEI P, ZHENG L, HUANG F, et al. Optimal deployment of radar network based on chaos genetic algorithm[C]//Proceedings of the Chinese Control and Decision Conference. Piscataway: IEEE Press, 2019: 6018- 6023.
[3]	LI J, DAI W, HU L. Research on intelligent station layout optimization of air defense radar network[C]//Proceedings of the 4th International Conference on Robot Systems and Applications. Piscataway: IEEE Press, 2021: 39-43.
[4]	YANG Y, ZHANG T, YI W. Deployment of multistatic radar system using multi objective particle swarm optimization[J]. IET Radar, Sonar & Navigation, 2018, 12(5): 485-493.
[5]	Ma Y, JIN H B, LI H, et al. Adaptive opposition-based particle swarm optimization algorithm and application research[C]//Proceedings of the IEEE 4th International Conference on Signal and Image Processing. Piscataway: IEEE Press, 2019: 518-523.
[6]	RAO D V, RAVISHANKAR M. A methodology for optimal deployment and effectiveness evaluation of air defence resources using game theory[J]. Sādhanā, 2020, 45(1): 1-15.
[7]	YU Z, SHAN G, XU G, et al. Method of multi-sensor optimal deployment for area coverage[C]//Proceedings of the International Conference on Electronics Technology. Piscataway: IEEE Press, 2018: 116-119.
[8]	付鑫, 张峰, 冯占林. 基于并行计算的混沌遗传算法对反导预警雷达部署优化研究[J]. 中国电子科学研究院学报, 2016, 11(3): 276-282. FU X, ZHANG F, FENG Z L. Research of chaos genetic algorithm based on parallel computing for anti-missile warning radar disposition[J]. Journal of CAEIT, 2016, 11(3): 276-282(in Chinese).
[9]	TIAN M, CHEN S, ZHENG X, et al. Sensors deployment optimization in multi-dimensional space based on improved particle swarm optimization algorithm[J]. Journal of Systems Engineering and Electronics, 2018, 29(5): 969-982. doi: 10.21629/JSEE.2018.05.09
[10]	田桂林, 刘昌云, 高嘉乐, 等. 基于烟花算法的多传感器优化模型部署[J]. 系统工程与电子技术, 2019, 41(8): 1742-1748. TIAN G L, LIU C Y, GAO J L, et al. Multi-sensor optimal disposition model based on fireworks algorithm[J]. Systems Engineering and Electronics, 2019, 41(8): 1742-1748(in Chinese).
[11]	刘伟, 刘昌云, 陈晨, 等. 反导预警装备部署方法综述[J]. 探测与控制学报, 2022, 44(3): 27-33. LIU W, LIU C Y, CHEN C, et al. Review on deployment methods of anti-missile early waring equipment[J]. Journal of Detection & Control, 2022, 44(3): 27-33(in Chinese).
[12]	KORDA M, KRISTENSEN H M. US ballistic missile defenses[J]. Bulletin of the Atomic Scientists, 2019, 75(6): 295-306.
[13]	ZHENG Y, YAN S, QU S, et al. Research on design and evaluation method of anti-missile early warning and detection plan[C]//Proceedings of the IEEE 5th Information Technology, Networking, Electronic and Automation Control Conference. Piscataway: IEEE Press, 2021: 864-867.
[14]	FLORES R, ALMEIDA G F, TEJERINA G R, et al. Radar coverage over irregular terrain: A practical algorithm for multipath propagation[C]//Proceedings of the IEEE Radar Conference. Piscataway: IEEE Press, 2018: 1383-1388.
[15]	徐志明, 艾小锋, 刘晓斌, 等. 基于散射中心滑动特性的双基地雷达锥体目标微动特征提取方法[J]. 电子学报, 2021, 49(3): 461-469. XU Z M, AI X F, LIU X B, et al. Micro-motion feature extraction of bistatic radar cone-shaped targets based on characteristic analysis of sliding scattering centers[J]. Acta Electonica Sinica, 2021, 49(3): 461-469(in Chinese).
[16]	马梁. 弹道中段目标微动特性及综合识别方法[D]. 长沙: 国防科学技术大学, 2011: 49-68. MA L. The micro-motion characteristic and combining classification of ballistic target[D]. Changsha: National University of Defense Technology, 2011: 49-68(in Chinese).
[17]	KIM J, CHO D H, LEE W C, et al. Optimal target assignment with seamless handovers for networked radars[J]. Sensors, 2019, 19(20): 4555. doi: 10.3390/s19204555
[18]	郑玉军, 田康生, 刘俊凯, 等. 早期预警雷达和多功能相控阵雷达的目标指示交接方法[J]. 兵工学报, 2017, 38(1): 106-113. ZHENG Y J, TIAN K S, LIU J K, et al. The target designation and handover method of early-warning radar and multifunction phased array radar[J]. Acta Armamentarii, 2017, 38(1): 106-113(in Chinese).
[19]	FREITAS D, LOPES L G, MORGADO F. Particle swarm optimization: A historical review up to the current developments[J]. Entropy, 2020, 22(3): 362. doi: 10.3390/e22030362
[20]	WANG D S, TAN D P, LIU L. Particle swarm optimization algorithm: An overview[J]. Soft Computing, 2018, 22(2): 387-408. doi: 10.1007/s00500-016-2474-6
[21]	GUO G Y, LV Y S, YANG X R, et al. Ballistic missile defense system deployment simulation based particle swarm optimization[C]//Proceedings of the IEEE CSAA Guidance, Navigation and Control Conference. Piscataway: IEEE Press, 2018: 1-4.
[22]	魏法, 杨明磊, 何小静, 等. 基于改进粒子群算法的平面阵同时多波束赋形方法[J]. 系统工程与电子技术, 2022, 44(6): 1789-1797. WEI F, YANG M L, HE X J, et al. Simultaneous multi-beam forming method for planar array based on improved particle swarm algorithm[J]. Systems Engineering and Electronics, 2022, 44(6): 1789-1797(in Chinese).
[23]	LIU S, HUANG F, YAN B. Optimal design of multi-missile formation based on an adaptive SA-PSO algorithm[J]. Aerospace, 2022, 9(1): 21.
[24]	练青坡, 王宏健, 袁建亚, 等. 基于粒子群优化算法的USV集群协同避碰方法[J]. 系统工程与电子技术, 2019, 41(9): 2034-2040. LIAN Q P, WANG H J, YUAN J Y, et al. Collaborative collision avoidance method of USV cluster based on particle swarm optimization algorithm[J]. Systems Engineering and Electronics, 2019, 41(9): 2034-2040(in Chinese).
[25]	黄飞腾, 翁国庆, 南余荣, 等. 基于改进云自适应粒子群的多DG配电网EV充电站优化配置[J]. 中国电机工程学报, 2018, 38(2): 514-525. HUANG F T, WENG G Q, NAN Y R, et al. Optimization of electric vehicle charging stations based on improved cloud adaptive particle swarm in distribution network with multiple DG[J]. Proceedings of the CSEE, 2018, 38(2): 514-525(in Chinese).
[26]	XIANG L I, CHEN J. A modified PSO algorithm based on cloud theory for optimizing the fuzzy PID controller[J]. Journal of Physics: Conference Series, 2022, 2183(1): 012014. doi: 10.1088/1742-6596/2183/1/012014
[27]	陈国龙, 郭文忠, 陈羽中. 无线传感器网络任务分配动态联盟模型与算法研究[J]. 通信学报, 2009, 30(11): 48-55. CHEN G L, GUO W Z, CHEN Y Z. Research on dynamic alliance of task allocation and its algorithm in wireless sensor network[J]. Journal on Communications, 2009, 30(11): 48-55(in Chinese).
[28]	韩晋山, 邢建平, 张浩, 等. 美国导弹预警系统的发展现状与趋势分析[J]. 科技导报, 2019, 37(4): 91-95. HAN J S, XING J P, ZHANG H, et al. Development of American missile early warning system[J]. Science Technology Review, 2019, 37(4): 91-95(in Chinese).
[29]	唐嘉诚. 多功能雷达组网资源调度方法研究[D]. 成都: 电子科技大学, 2021: 33-51. TANG J C. Research on resource scheduling method of multifunctional radar network[D]. Chengdu: University of Electronic Science and Technology of China, 2021: 33-51(in Chinese).