Capability Evaluation of Air Defense and Anti-missile Early Warning System-of-systems Based on Node Importance and Improved Effectiveness Loop

doi:10.12382/bgxb.2022.0488

Abstract

Abstract:

A capability evaluation method of air defense and anti-missile early warning system-of-systems (SOS) based on the node importance and improved effectiveness loop (EL) is proposed to address the problems in the capability evaluation of air defense and anti-missile SOS, such as weak realism, less consideration of heterogeneous characteristics and incomplete calculation of capabilities. The structure of the SOS is abstractly modeled based on the super-network model, and a more realistic EL model is proposed. The importance of nodes is calculated from the global and local aspects of the network. Then the effectiveness edges are analyzed according to the mutual influence relations among nodes. In addition, the capability expectation of the SOS is presented to improve the evaluation method by combining the node importance and reliability with the capability of the edge. Finally, the feasibility and rationality of the method are verified through the simulation analysis of anti-missile early warning combat example. The proposed method fully takes the realistic characteristics of the air defense and anti-missile early warning SOS and the heterogeneous features of the equipment into account, and can assess the capability of SOS in a more comprehensive manner, which provides theoretical support for the capability evaluation and structural optimization of SOS.

Key words: air defense and anti-missile early warning system-of-systems, effectiveness loop, node importance, capability evaluation

CLC Number:

E917

YU Jintao, XIAO Bing, CUI Yuzhu. Capability Evaluation of Air Defense and Anti-missile Early Warning System-of-systems Based on Node Importance and Improved Effectiveness Loop[J]. Acta Armamentarii, 2024, 45(1): 328-338.

Figures/Tables 10

Fig.1 Basic combat process of air defense and anti-missile

Fig.2 General ELs

Table 1 Types and meanings of ELs in combat SOS

效能环	含义
T-O-P-D-A-T	标准的效能环
T-O-O-P-D-A-T	具有协同探测的效能环
T-O-P-P-D-A-T	具有信息交互的效能环
T-O-P-D-D-A-T	具有协同指控的效能环
T-O-O-P-P-D-A-T	具有协同探测和信息交互的效能环
T-O-O-P-D-D-A-T	具有协同探测和指控的效能环
T-O-O-P-P-D-D-A-T	具有协同探测、指控和信息交互的效能环

Fig.3 Capability indexes of air defense and anti-missile early warning SOS

Fig.4 Combat capability evaluation process of air defense and anti-missile early warning SOS

Fig.5 Combat network structure diagram of anti-missile early warning SOS

Table 2 Importance and reliability of nodes in SOS network

节点	节点重要性	归一化节点重要性	节点可靠性
$T o u t (1)$	4.1984		1
$T o u t (2)$	4.1984		1
O⁽¹⁾	5.5105	0.1050	1
O⁽²⁾	6.1077	0.1164	0.98
O⁽³⁾	5.1870	0.0989	0.98
P⁽¹⁾	6.4870	0.1236	1
P⁽²⁾	7.0945	0.1352	1
D⁽¹⁾	6.4502	0.1229	1
D⁽²⁾	6.4605	0.1231	1
A⁽¹⁾	4.1490	0.0791	0.99
A⁽²⁾	5.0225	0.0957	0.99
$T i n (1)$	3.1394
$T i n (2)$	2.3291

Table 2 Importance and reliability of nodes in SOS network

节点	节点重要性	归一化节点重要性	节点可靠性
$T o u t (1)$	4.1984		1
$T o u t (2)$	4.1984		1
O⁽¹⁾	5.5105	0.1050	1
O⁽²⁾	6.1077	0.1164	0.98
O⁽³⁾	5.1870	0.0989	0.98
P⁽¹⁾	6.4870	0.1236	1
P⁽²⁾	7.0945	0.1352	1
D⁽¹⁾	6.4502	0.1229	1
D⁽²⁾	6.4605	0.1231	1
A⁽¹⁾	4.1490	0.0791	0.99
A⁽²⁾	5.0225	0.0957	0.99
$T i n (1)$	3.1394
$T i n (2)$	2.3291

Table 3 Capability value of SOS effectiveness edge

效能边	能力值	效能边	能力值
T⁽¹⁾-O⁽¹⁾	0.7489	P⁽¹⁾-D⁽¹⁾	0.8678
T⁽¹⁾-O⁽²⁾	0.7113	P⁽¹⁾-D⁽²⁾	0.8778
T⁽¹⁾-O⁽³⁾	0.8618	P⁽²⁾-D⁽¹⁾	0.9505
T⁽²⁾-O⁽¹⁾	0.7489	P⁽²⁾-D⁽²⁾	0.9613
T⁽²⁾-O⁽²⁾	0.7113	D⁽¹⁾-D⁽²⁾	0.8328
T⁽²⁾-O⁽³⁾	0.8618	D⁽¹⁾-A⁽¹⁾	0.8132
O⁽¹⁾-O⁽²⁾	0.8457	D⁽¹⁾-A⁽²⁾	0.8284
O⁽¹⁾-P⁽²⁾	0.9583	D⁽²⁾-A⁽¹⁾	0.8256
O⁽²⁾-P⁽¹⁾	0.9020	D⁽²⁾-A⁽²⁾	0.8426
O⁽²⁾-P⁽²⁾	0.9244	A⁽¹⁾-T⁽¹⁾	0.9099
O⁽³⁾-P⁽¹⁾	0.8234	A⁽²⁾-T⁽¹⁾	0.9096
O⁽³⁾-P⁽²⁾	0.8414	A⁽²⁾-T⁽²⁾	0.7300
P⁽¹⁾-P⁽²⁾	0.8777

Table 4 Effectiveness loop and corresponding capability value for Target 1

序号	效能环路径	能力值
1	T⁽¹⁾-O⁽¹⁾-O⁽²⁾-P⁽¹⁾-P⁽²⁾-D⁽¹⁾-D⁽²⁾-A⁽¹⁾-T⁽¹⁾	0.2892
2	T⁽¹⁾-O⁽¹⁾-O⁽²⁾-P⁽¹⁾-P⁽²⁾-D⁽¹⁾-D⁽²⁾-A⁽²⁾-T⁽¹⁾	0.2951
3	T⁽¹⁾-O⁽¹⁾-O⁽²⁾-P⁽¹⁾-P⁽²⁾-D⁽¹⁾-A⁽¹⁾-T⁽¹⁾	0.3421
4	T⁽¹⁾-O⁽¹⁾-O⁽²⁾-P⁽¹⁾-P⁽²⁾-D⁽¹⁾-A⁽²⁾-T⁽¹⁾	0.3483
︙	︙	︙
59	T⁽¹⁾-O⁽³⁾-P⁽²⁾-D⁽²⁾-A⁽¹⁾-T⁽¹⁾	0.5080
60	T⁽¹⁾-O⁽³⁾-P⁽²⁾-D⁽²⁾-A⁽²⁾-T⁽¹⁾	0.5183
	平均值	0.4052

Table 5 Effectiveness loop and corresponding capability value for Target 2

序号	效能环路径	能力值
1	T⁽²⁾-O⁽¹⁾-O⁽²⁾-P⁽¹⁾-P⁽²⁾-D⁽¹⁾-D⁽²⁾-A⁽²⁾-T⁽²⁾	0.2368
2	T⁽²⁾-O⁽¹⁾-O⁽²⁾-P⁽¹⁾-P⁽²⁾-D⁽¹⁾-A⁽²⁾-T⁽²⁾	0.2796
3	T⁽²⁾-O⁽¹⁾-O⁽²⁾-P⁽¹⁾-P⁽²⁾-D⁽²⁾-A⁽²⁾-T⁽²⁾	0.2876
4	T⁽²⁾-O⁽¹⁾-O⁽²⁾-P⁽¹⁾-D⁽¹⁾-D⁽²⁾-A⁽²⁾-T⁽²⁾	0.2463
︙	︙	︙
29	T⁽²⁾-O⁽³⁾-P⁽²⁾-D⁽¹⁾-A⁽²⁾-T⁽²⁾	0.4043
30	T⁽²⁾-O⁽³⁾-P⁽²⁾-D⁽²⁾-A⁽²⁾-T⁽²⁾	0.4160
	平均值	0.3284

References 24

[1]	龚亮, 王庆权, 罗红吉. 防空导弹武器系统作战效能评估实战化改进模型[J]. 现代防御技术, 2021, 49(6): 9-15. doi: 10.3969/j.issn.1009-086x.2021.06.003
	GONG L, WANG Q Q, LUO H J. Real combat-like improved model of operational effectiveness evaluation of air defense missile weapon system[J]. Modern Defence Technology, 2021, 49(6): 9-15. (in Chinese)
[2]	汪慧阳, 刘松涛, 赵帅. 基于改进ADC模型的通信对抗系统作战效能评估[J]. 探测与控制学报, 2021, 43(5): 92-98.
	WANG H Y, LIU S T, ZHAO S. Communication countermeasure system operational effectiveness evaluation based on improved ADC model[J]. Journal of Detection & Control, 2021, 43(5): 92-98. (in Chinese)
[3]	KULIK T. The multi-criteria method for the evaluation of combat capabilities of anti-aircraft missile systems under the NAREW programme[J]. Safety & Defense, 2021, 7(2): 90-104.
[4]	SUN L F, CHANG J S, ZHANG J J, et al. Evaluation of unmanned aerial vehicles cooperative combat effectiveness based on conditional entropy combination weight method[J]. Journal of Aerospace Technology and Management, 2021, 13:238704439.
[5]	雷永林, 朱智, 甘斌, 等. 基于仿真的复杂武器系统作战效能评估框架研究[J]. 系统仿真学报, 2020, 32(9): 1654-1663. doi: 10.16182/j.issn1004731x.joss.20-0373
	LEI Y L, ZHU Z, GAN B, et al. Combat effectiveness simulation evaluation framework of complex weapon system[J]. Journal of System Simulation, 2020, 32(9): 1654-1663. (in Chinese) doi: 10.16182/j.issn1004731x.joss.20-0373
[6]	CARES J R. Distributed networked operations:the foundations of network centric warefare[M]. New York,NY,US: Alidade, 2005.
[7]	SATO H, KUBO M, NAMATAME A. Evaluation of combat simulation from network perspective[C]// Proceedings of the 6th International Conference on Soft Computing and Intelligent Systems. Kobe, Japan: IEEE, 2012: 941-944.
[8]	POLISHCHUK O. Models and methods of complex evaluation of complex network and hierarchically network systems: arXiv:2104.13852[R]. Ithaca,NY, US: Cornell University, 2021:2104.13852.
[9]	谭跃进, 张小可, 杨克巍. 武器装备体系网络化描述与建模方法[J]. 系统管理学报, 2012, 21(6): 781-786.
	TAN Y J, ZHANG X K, YANG K W. Research on networked description and modeling methods of armament system-of-systems[J]. Journal of Systems & Management, 2012, 21(6): 781-786. (in Chinese)
[10]	张国强, 刘小荷, 蒋方婷, 等. 基于“作战环”的区域反导装备体系效能评估[J]. 系统工程, 2016, 34(5):154-158.
	ZHANG G Q, LIU X H, JIANG F T, et al. Effectiveness evaluation for TBDES based on operation loop[J]. Systems Engineering, 2016, 34(5): 154-158. (in Chinese)
[11]	陈文钰, 李为民, 张涛, 等. 基于作战交互网络的体系作战能力计算[J]. 兵工学报, 2023, 44(10): 2885-2896. doi: 10.12382/bgxb.2022.1039
	CHEN W Y, LI W M, ZHANG T, et al. Calculation of system combat capability using an interactive network approach[J]. Acta Armamentarii, 2023, 44(10):2885-2896. (in Chinese) doi: 10.12382/bgxb.2022.1039
[12]	HUAT N, STEVENS C. Capabilities based testing of defense multi-intelligence systems[C]// Proceedings of the 2019 NDIA Ground Vehicle Systems Engineering and Technology Symposium.MI, US: NDIA, 2019:1-8.
[13]	FAN J R, LI D G, LI R P. Evaluation of MAV / UAV collaborative combat capability based on network structure[J]. International Journal of Aerospace Engineering, 2018: 5301752. DOI:10.1155/2018/5301752.
[14]	芦荻, 商慧琳. 基于反导作战环的装备作战网络能力评估[J]. 太赫兹科学与电子信息学报, 2016, 14(3):372-377.
	LU D, SHANG H L. Evaluation of equipment combat network capability based on antimissile combat ring[J]. Journal of Terahertz Science and Electronics, 2016, 14(3):372-377. (in Chinese)
[15]	梁家林, 熊伟. 基于作战环的武器装备体系能力评估方法[J]. 系统工程与电子技术, 2019, 41(8):1800-1819. (in Chinese)
	LIANG J L, XIONG W. Capabilities assessment of the weaponry system based on combat ring[J]. Systems Engineering and Electronics, 2019, 41(8): 1800-1819. (in Chinese)
[16]	赵丹玲. 基于异质网络的武器装备体系贡献率评估方法研究[D]. 长沙: 国防科技大学, 2019.
	ZHAO D L. Research on contribution rate of weapon and equipment system evaluation method basedon heterogeneous network[D]. Changsha: National University of Defense Technology, 2019. (in Chinese)
[17]	罗承昆, 陈云翔, 王莉莉, 等. 基于作战环和改进信息熵的体系效能评估方法[J]. 系统工程与电子技术, 2019, 41(1): 73-80.
	LUO C K, CHEN Y X, WANG L L, et al. Effectiveness evaluation method of system-of-systems based on operation loop and improved information entropy[J]. Systems Engineering and Electronics, 2019, 41(1): 73-80. (in Chinese) doi: 10.3969/j.issn.1001-506X.2019.01.11
[18]	LIU Q, FANG J Q, LI Y. Some characteristics of supernetworks based on unified hybrid network theory framework[J]. International Journal of Modern Physics C, 2017, 28(5):1750057. doi: 10.1142/S0129183117500577 URL
[19]	刘凤增, 肖兵, 金宏斌, 等. 预警情报体系超网络建模与分析[J]. 现代防御技术, 2019, 47(6):19-26.
	LIU F Z, XIAO B, JIN H B, et al. Super network modeling and analysis of early warning intelligence system-of-systems[J]. Modern Defence Technology, 2019, 47(6):19-26. (in Chinese)
[20]	BOYD J R. A discourse on winning and losing[M]. AL,US: Air University Press, 2018.
[21]	俞锦涛, 肖兵, 熊家军. 基于效能环的预警情报体系能力评估[J]. 火力与指挥控制, 2022, 47(2): 32-36,42.
	YU J T, XIAO B, XIONG J J. Capability evaluation of early warning intelligence system-of-systems based on intelligence effectiveness loop[J]. Fire Control & Command Control, 2022, 47(2):32-36,42. (in Chinese)
[22]	YU J T, XIAO B, XIONG J J, et al. Linguistic multi-attribute group decision-making method based on similarity measurement of cloud model[C]// Proceedings of the 33rd Chinese Control and Decision Conference, Kunming, China: IEEE, 2021: 3914-3919.
[23]	周琛, 尚柏林, 宋笔锋, 等. 基于作战环的航空武器装备体系贡献率评估[J]. 航空学报, 2022, 43(2):224958. doi: 10.7527/S1000-6893.2020.24958
	ZHOU C, SHANG B L, SONG B F, et al. Aviation armament system of systems contribution evaluation based on operation loop[J]. Acta Aeronautica et Astronautica Sinica, 2022, 43(2): 224958. (in Chinese) doi: 10.7527/S1000-6893.2020.24958
[24]	赵丹玲, 谭跃进, 李际超, 等. 基于作战环的武器装备体系贡献度评估[J]. 系统工程与电子技术, 2017, 39(10): 2239-2247.
	ZHAO D L, TAN Y J, LI J C, et al. Armament system of systems contribution evaluation based on operation loop[J]. Systems Engineering and Electronics, 2017, 39(10):2239-2247. (in Chinese) doi: 10.3969/j.issn.1001-506X.2017.10.13