基于耦合约束满足的雷达抗干扰试验样本空间特征分析

doi:10.12305/j.issn.1001-506X.2025.07.07

摘要/Abstract

摘要：

针对雷达抗干扰试验中试验因子多、样本空间大、全面试验成本高等问题, 引入约束满足的方法对雷达抗干扰试验样本空间进行特征分析, 实现对有限样本空间的约简。提出一种雷达抗干扰试验样本空间的分析框架, 将对样本空间的分析从电磁领域映射到数学领域, 建立一种耦合约束满足模型。结合图论和基于孪生变量法的耦合约束求解算法以及弧相容算法对试验样本空间中的耦合约束进行求解。结果表明, 经过求解后的空间比初始试验样本空间压缩了约76 760.76倍, 可较好地解决后续试验设计中样本集选取困难的问题, 为雷达抗干扰试验的设计与评估提供支撑。

关键词: 抗干扰试验, 样本空间, 耦合约束满足问题, 孪生变量法, 弧相容

Abstract:

In order to address the challenges posed by multiple test factors, a large sample space, and high overall test cost in radar anti-jamming testing, the constraint satisfaction method is introduced to analyze the characteristics of the radar anti-jamming test sample space and reduce its limited size. A framework for analyzing the sample space of radar anti-interference tests is proposed. The analysis of the sample space is translated from electromagnetic field to mathematical field, and a coupling constraint satisfaction model is established. The graph theory coupled constraint solving algorithm based on the twin variable method and the arc compatibility algorithm are combined to solve the coupling constraints in the test sample space. The results indicate that the reduced space is approximately 76 760.76 times more compact than the original test sample space, addressing the challenging issue of sample set selection in subsequent test design and offering support for radar anti-jamming test design and evaluation.

Key words: anti-interference test, sample space, coupling constraint satisfaction problem, twin variable method, arc consistent

中图分类号:

TN974

龙志涛, 程志君, 封琛. 基于耦合约束满足的雷达抗干扰试验样本空间特征分析[J]. 系统工程与电子技术, 2025, 47(7): 2136-2145.

Zhitao LONG, Zhijun CHENG, Chen FENG. Spatial characteristics analysis of radar anti-jamming test samples based on coupling constraint satisfaction[J]. Systems Engineering and Electronics, 2025, 47(7): 2136-2145.

图/表 13

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表5

图8

参考文献 30

1	程志君,潘正强,刘天宇,等.复杂约束条件下导引头抗干扰试验样本空间分析[J].国防科技,2023,44(4):103-110.
	CHENGZ J,PANZ Q,LIUT Y,et al.Sample space analysis of anti-jamming tests for seekers under complex constraints[J].National Defense Technology,2023,44(4):103-110.
2	李岩松,王超,戎建刚,等.复杂电磁环境量化表征方法研究综述[J].航天电子对抗,2020,36(6):23-27.
	LIY S,WANGC,RONGJ G,et al.A review of quantitative characterization methods of complex electromagnetic environment[J].Aerospace Electronic Warfare,2020,36(6):23-27.
3	刘蛟,唐莽,王鑫,等.对海作战场景复杂电磁环境仿真技术研究[J].现代雷达,2021,43(8):28-35.
	LIUJ,TANGM,WANGX,et al.A study on simulation techno-logy of complex electromagnetic environment in sea battlefield[J].Modern Radar,2021,43(8):28-35.
4	王宇,贺英杰,赵海.雷达抗干扰能力指标测试环境设计[J].航天电子对抗,2014,30(4):61-64.
	WANGY,HEY J,ZHAOH.Design of test environment of radar anti-jamming ability index[J].Aerospace Electronic Warfare,2014,30(4):61-64.
5	邹钊,李娅,李培林.电磁环境复杂度量化及展现方法[J].电子信息对抗技术,2018,33(6):63-66, 75.
	ZOUZ,LIY,LIP L.Comprehensive research on the quantitative methods of electromagnetic environment complexity[J].Electronic Information Warfare Technology,2018,33(6):63-66, 75.
6	龚卓, 刘家伟, 段晓君, 等. 基于贝叶斯优化的导引头抗干扰性能试验序贯设计方法[C]//第5届体系工程学术会议论, 2023: 701-706.
	GONG Z, LIU J W, DUAN X J, et al. A Bayesian optimization based sequential design method for anti-jamming performance experiment of seeker[C]//Proc. of the 5th Academic Conference on SoS Engineering, 2023: 701-706.
7	潘正强, 刘天宇, 程志君. 导引头抗干扰性能试验空间构设方法研究[C]//第3届体系工程学术会, 2021: 214-219.
	PAN Z Q, LIU T Y, CHENG Z J. Research on construction method of seeker anti-jamming performance test space[C]//Proc. of the 3rd Academic Conference on SoS Engineering, 2021: 214-219.
8	周伟江,柳立志,王鑫,等.基于通用型半实物仿真平台的导引头复杂电磁环境构建及试验方法[J].航天电子对抗,2020,36(4):46-50, 64.
	ZHOUW J,LIUL Z,WANGX,et al.The construction of complex electromagnetic environment and the test method of seeker based on universal semi-physical test platform[J].Aerospace Electronic Warfare,2020,36(4):46-50, 64.
9	杨镜宇,司光亚,胡晓峰.信息化战争体系对抗探索性仿真分析方法研究[J].系统仿真学报,2005,17(6):1469-1472, 1496.
	YANGJ Y,SIG Y,HUX F.Study on simulation-based exploratory analysis method of information warfare system of system(SoS) encounter[J].Journal of System Simulation,2005,17(6):1469-1472, 1496.
10	BINGG,RONGX L,QIANM L,et al.Construction of orthogonal general sliced Latin hypercube designs[J].Statistical Papers,2022,64(3):987-1014.
11	刘根,王治华,屈怀远,等.基于多变量优化的恒定应力加速退化试验设计[J].系统工程与电子技术,2021,43(1):267-271. doi: 10.3969/j.issn.1001-506X.2021.01.33
	LIUG,WANGZ H,QUH Y,et al.Constant stress acceler ated degradation test design based on multivariate optimization[J].Systems Engineering and Electronics,2021,43(1):267-271. doi: 10.3969/j.issn.1001-506X.2021.01.33
12	尤杨. 复杂试验空间下试验设计方法及应用研究[D]. 长沙: 国防科技大学, 2022.
	YOU Y. Method and application of experimental design in complex test space[D]. Changsha: National University of Defense Technology, 2022.
13	张路路,潘正强,刘天宇,等.基于高斯过程模型的定性定量因子混合补充试验设计方法[J].系统工程与电子技术,2023,45(7):2078-2085. doi: 10.12305/j.issn.1001-506X.2023.07.18
	ZHANGL L,PANGZ Q,LIUT Y,et al.Supplemental experimental design method of qualitative-quantitative hybrid factor based on Gaussian process model[J].Systems Engineering and Electronics,2023,45(7):2078-2085. doi: 10.12305/j.issn.1001-506X.2023.07.18
14	NEMPONTO,ATIFJ,BLOCHI.A constraint propagation approach to structural model based image segmentation and re-cognition[J].Information Sciences,2013,246,1-27.
15	VANEGASM C,BLOCHI,INGLADAJ.Fuzzy constraint satisfaction problem for model-based image interpretation[J].Fuzzy Sets and Systems,2016,286,1-29.
16	LUGERG F.Artificial intelligence: structures and strategies for complex problem solving[M].New Jersey:Pearson Education,2005:10-38.
17	SIOUTIS M, WOLTER D. Dynamic branching in qualitative constraint networks via counting local models[C]//Proc. of the 27th International Symposium on Temporal Representation and Reasoning, 2020.
18	MOUHOUB M, AL-MARRI H, ALANAZI E. Learning qualitative constraint networks[C]//Proc. of the 25th International Symposium on Temporal Representation and Reasoning, 2018.
19	魏毅寅,杨文华.海战场典型干扰对抗场景及反舰导弹应对策略研究[J].战术导弹技术,2020(5):1-8.
	WEIY Y,YANGW H.Study on typical jamming scenes in naval battle field and countermeasures of anti-ship missile[J].Tactical Missile Technology,2020(5):1-8.
20	夏雄志,金嘉旺,胡生亮.舰艇编队箔条冲淡干扰效果研究建模与仿真[J].舰船电子工程,2007,27(4):42-44.
	XIAX Z,JINGJ W,HUS L.Modeling and simulation of re search on the effect of ship formation chaff dilution interference[J].Ship Electronic Engineering,2007,27(4):42-44.
21	李健辉. 对反舰导弹箔条干扰方法研究[D]. 西安: 西安电子科技大学, 2021.
	LI J H. Research on chaff-jamming method foranti-ship missile[D]. Xi'an: Xidian University, 2021.
22	冯兴如,李水清,尹宝树.海气动量通量研究综述[J].海洋科学,2018,42(10):103-109.
	FENGX R,LIS Q,YINB S.Review of research on momentum flux through air-sea interface[J].Marine Sciences,2018,42(10):103-109.
23	佟玉华,朱文凭,崔树双,等.多路径效应对低空箔条云RCS影响分析[J].光电对抗与无源干扰,1997(4):33-37.
	TONGY H,ZHUW P,CUIS S,et al.Analysis of the influence of multipath effect on low-level chaff cloud RCS[J].Electro-Optic Technology Application,1997(4):33-37.
24	何国宝,宋广.箔条云雷达截面积(RCS值)的预计方法[J].水雷战与舰船防护,2009,17(4):60-63, 68.
	HEG B,SONGG.Estimation method for radar cross section of chaff cloud[J].Mine Warfare & Ship Self-Defence,2009,17(4):60-63, 68.
25	郭勇,朱晓川,董金海.影响海上箔条云RCS的因素分析[J].电子对抗技术,2004(3):43-46.
	GUOY,ZHUX C,DONGJ H.A research on the factors affecting the chaff's RCS[J].Electronic Information Warfare Technology,2004(3):43-46.
26	曾茂生,修继信.多路径效应对低空箔条云RCS的影响[J].航天电子对抗,2008(6):54-55, 58.
	ZENGM S,XIUJ X.Multi-path effect on the RCS of the low altitude chaff[J].Aerospace Electronic Warfare,2008(6):54-55, 58.
27	管有林,孟庆良,闫鹏武,等.箔条扩散特性与风速研究[J].制导与引信,2022,43(1):12-16.
	GUANY L,MENGQ L,YANP W,et al.Study on chaff diffusion characteristics and wind velocity[J].Guidance & Fuze,2022,43(1):12-16.
28	司雪圆. 基于约束可满足的航天器自主任务规划方法研究[D]. 北京: 北京理工大学, 2015.
	SI X Y. Autonomous mission planning method of space craft based on the constraint satisfaction[D]. Beijing: Beijing Institute of Technology, 2015.
29	陈永府,黄正东,陈立平.数值与符号的耦合约束求解模型[J].计算机工程与设计,2008,29(11):2806-2808, 2837.
	CHENY F,HUANGZ D,CHENL P.Model for solving numerical and symbolic coupling constraints[J].Computer Engineering and Design,2008,29(11):2806-2808, 2837.
30	陈永府. 基于三维几何模型的计算机辅助工艺规划技术[D]. 武汉: 华中科技大学, 2006.
	CHEN Y F. Research on computer aided process planning based on three dimensional geometric models[D]. Wuhan: Huazhong University of Science & Technology, 2006.

因子名称	符号	取值范围	设计水平
无人机搜索方向/(°)	α	[0, 45], [315,360]	19
雷达开机距离/km	R_k	[10,20]	11
方位探测角度/(°)	γ	[10,90]	10
距离探测范围/km	L	[1.5, 5]	9
舰船运动方向/(°)	C_w	[60,360]	31
舰船速度/kn	V_w	[10,30]	31
箔条布放策略	s	1, 2, 3, 4, 5	5
箔条间距/m	D	[20,100]	20
箔条舵角/(°)	θ	[-35, 35]	71
箔条发射时机/s	t_fs	[-5, 5]	11
箔条飞行时长/s	T_f	[1,3]	3
箔条形成时长/s	T_d	[2,3]	10
箔条云发射距离/km	R₀	[1,3]	3
箔条的RCS/m²	RCS_c	[20,40]	21
风速/kn	V_f	[0, 10]	100
风向/(°)	θ_f	[60,360]	31
海流强度/(m/s)	c	[0.05, 3]	61
海浪高度/ft	h	[1,8]	80

序号	风速/kn	浪高/ft
1	< 7	1
2	7~12	1~3
3	12~16	3~5
4	16~19	5~8
5	-	-

因子名称	符号	取值范围
无人机导弹飞行速度/(m/s)	v_m	300
系统反应时间/s	t_yf	30
舰艇高度/m	H_w	0
重叠系数	J	1.2~1.4
雷达搜索角速度/(°/s)	ω_m	20
距离波门的搜索速度/kn	v	30
波浪周期/s	T	6~10
参数	a	2
参数	b	10
阻力系数	k	0.5
参数	k₁	60
参数	k₂	0.01
参数	k₃	0.03
反射系数	ρ₀	0.04
雷达信号的波长/m	λ	0.03
箔条在自由空间的RCS/m²	σ	20
舰船RCS/m²	RCS_boat	20
箔条理想状态RCS/m²	RCS_max	40

约束符号	公式	约束符号	公式
C0	(4)	C6	(6)
C1	(2)	C7	(11)
C2	(3)	C8	(5)
C3	(10)	C9	(12)(14)
C4	(9)	C10	(12)(13)
C5	(7)	K	表 2

模块	部分解	模块	部分解
1	[60, 110, 315]	3	[1, 1]
1	[60, 200, 335]	3	[1, 2,]
1	[70, 140, 335]	3	[-2, 3]
1	[340, 160, 20]	3	[-3, 4]
2	[2.2, 8, 1.3, 2.9]	4	[1, 10, 1.5, -5, 2, 10]
2	[2.6, -1, 1.4, 2.9]	4	[1, 17, 2.5, 0, 2, 90]
2	[2.8, 28, 0.7, 2.5]	4	[2, 16, 4.0, -5, 2, 30]
2	[3.0, 30, 0.8, 2.4]	4	[3, 18, 4.0, 5, 3, 60]