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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