考虑节点重要度的反导体系效能评估方法

doi:10.12305/j.issn.1001-506X.2026.02.18

Abstract

Abstract:

The anti-missile system of systems serves as a crucial defense line against hostile threats, how to exactly describe the anti-missile system of systems and evaluate its combat effectiveness is a significant and complex task. Aimming at the issue of effectiveness evaluation of anti-missile systems, the characteristics of the anti-missile combat system of systems are analyzed. Combining with graphical evaluation and review technique （GERT）, anti-missile combat GERT network is firstly constructed to provide a modeling framework for effectiveness evaluation. Secondly, the node importance idea is introduced. The correction of equipment abilities involves evaluating the significance of both the equipment itself and its related equipment. Based on this, the challenge of determining the combat effectiveness for an anti-missile system of systems based on the node significance is resolved by utilizing the superior qualities of Mersenne’s formula and the mother-of-moments function. Finally, a case study illustrates the efficiency and effectiveness of the effectiveness evaluation model for anti-missile system of systems based on node importance. The results demonstrate that the effectiveness evaluation method based on node importance can effectively quantify the impacts of equipment heterogeneity and network structure on overall effectiveness. This method fully accounts for the influence of critical nodes on system effectiveness. It provides a more practical approach for the effectiveness evaluation and optimization of anti-missile system of systems.

Key words: node importance, effectiveness evaluation, graphical evaluation and review technique (GERT) network, anti-missile, combat system of systems

CLC Number:

N 945

Xueting HAO, Zhigeng FANG, Ankang JIANG, Jingru ZHANG, Yunke SUN. Method of effectiveness evaluation for anti-missile system of systems based on node importance[J]. Systems Engineering and Electronics, 2026, 48(2): 569-577.

Figures/Tables 11

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Table 1

Table 2

Table 3

Fig.6

Fig.7

Fig.8

References 35

1	李森, 田海林, 王刚, 等. 美一体化防空反导作战指控系统（IBCS）研究[J]. 现代防御技术, 2022, 50 (4): 84- 100.
	LI S, TIAN H L, WANG G, et al. Research on IAMD battle command system （IBCS） of the US[J]. Modern Defence Technology, 2022, 50 (4): 84- 100.
2	陈雅萍, 刘杰, 董诗潮, 等. 2023年国外防空反导领域发展综述[J]. 战术导弹技术, 2024 (2): 27- 35.
	CHEN Y P, LIU J, DONG S C, et al. Summary on development of foreign air and missile defense field in 2023[J]. Tactical Missile Technology, 2024 (2): 27- 35.
3	刘成刚, 叶雄兵. 战区联合作战指挥信息流评价模型[J]. 军事运筹与系统工程, 2018, 32 (1): 31- 36.
	LIU C G, YE X B. Evaluation model of joint warfare command information flow in theater of operations[J]. Military Operations Research and Systems Engineering, 2018, 32 (1): 31- 36.
4	PRITSKER A A B. GERT networks[J]. Production Engineer, 1968, 47 (10): 499- 506. doi: 10.1049/tpe.1968.0085
5	YANG X Y, FANG Z G, TAO L Y. Grey GERT network model of equipment lifetime evaluation based on small samples[J]. The Journal of Grey System, 2018, 30 (1): 110- 122.
6	方志耕, 华晨晨, 陈顶, 等. 复杂体系可靠性结构分析与建模GERT网络技术[J]. 系统工程与电子技术, 2024, 46 (10): 3427- 3436.
	FANG Z G, HUA C C, CHEN D, et al. GERT network technology for reliability structure analysis and modeling of complex system-of-systems[J]. Systems Engineering and Electronics, 2024, 46 (10): 3427- 3436.
7	LI Z Y, NIE X T, WANG B, et al. Analysis of the transmission of project duration and cost impacts based on the GERT network technique[J]. Symmetry, 2019, 11 (3): 337. doi: 10.3390/sym11030337
8	LIU H Q, FANG Z G, YUAN C Q, et al. “Inverse problem” model of GERT network and its application in complex equipment development project schedule planning[C]//Proc. of the IEEE International Conference on Grey systems and Intelligent Services, 2013: 384−390.
9	FANG Z G, WU S, ZHANG X L, et al. ADC-GERT network parameter estimation model for mission effectiveness of joint operation system[J]. Journal of Systems Engineering and Electronics, 2021, 32 (6): 1394- 1406.
10	WANG Z, LIU S F, FANG Z G. Research on SoS-GERT network model for equipment system of systems contribution evaluation based on joint operation[J]. IEEE Systems Journal, 2019, 14 (3): 4188- 4196.
11	GENG S Y, LIU S F, FANG Z G, et al. An optimal delay routing algorithm considering delay variation in the LEO satellite communication network[J]. Computer Networks, 2020, 173, 107166. doi: 10.1016/j.comnet.2020.107166
12	GENG S Y, LIU S F, FANG Z G, et al. A reliable framework for satellite networks achieving energy requirements[J]. Reliability Engineering & System Safety, 2021, 216, 107939.
13	NIE Y Y, FANG Z G, GAO S. Q-GERT survivability assessment of LEO satellite constellation[J]. Wireless Networks, 2021, 27: 249−268.
14	SHAO R R, FANG Z G, GAO S, et al. PS-G-GERT effectiveness evaluation model of link-based GEO satellite communication constellation under poor information background[J]. China Communications, 2022, 19 (12): 176- 196. doi: 10.23919/JCC.2022.00.001
15	方志耕, 张靖如, 夏悦馨, 等. 基于A-GERT网络的武器装备体系效能动态优化模型[J]. 中国管理科学, 2025, 33 (5): 214- 224.
	FANG Z G, ZHANG J R, XAI Y X, et al. Effectiveness dynamic optimization model for weapon and equipment system of systems based on A-GERT network[J]. Chinese Journal of Management Science, 2025, 33 (5): 214- 224.
16	HAO X T, FANG Z G, ZHANG J R, et al. Reinforcement model for unmanned combat system of systems based multi-layer grey target [J]. Journal of Grey System, 2024, 36(2): 54.
17	TAO L Y, WU D, LIU S F, et al. Schedule risk analysis for new product development: the GERT method extended by a characteristic function[J]. Reliability Engineering & System Safety, 2017, 167: 464−473.
18	LU H H, UDDIN S. A parameterised model for link prediction using node centrality and similarity measure based on graph embedding[J]. Neurocomputing, 2024, 593, 127820. doi: 10.1016/j.neucom.2024.127820
19	GUO H M, WANG S L, YAN X F, et al. Node importance evaluation method of complex network based on the fusion gravity model[J]. Chaos Solitons & Fractals, 2024, 183, 114924.
20	DUI H Y, ZHU Y W, TAO J Y. Multi-phased resilience methodology of urban sewage treatment network based on the phase and node recovery importance in IoT[J]. Reliability Engineering & System Safety, 2024, 247, 110130.
21	LIU Y H, CHEN S F, WANG L F. A node importance assessment method for complex networks based on the neighborhood influence [C]//Proc. of the IEEE 3rd International Conference on Software Engineering and Artificial Intelligence, 2023: 224−228.
22	WANG L, ZHANG S, SZUCS G, et al. Identifying the critical nodes in multi-modal transportation network with a traffic demand-based computational method[J]. Reliability Engineering and System Safety, 2024, 244, 109956. doi: 10.1016/j.ress.2024.109956
23	YANG C, SUN H Y, LI T, et al. Coupled model and node importance evaluation of electric power cyber-physical systems considering carbon power flow[J]. Energies, 2022, 15 (21): 8223. doi: 10.3390/en15218223
24	GUO S Y, MIAO S H, YIN H R, et al. Construction of coupling model and evaluation of node importance for electric sensor communication network [C]//Proc. of the IEEE 1st China International Youth Conference on Electrical Engineering, 2020.
25	XU M, WU J P, LIU M Q, et al. Discovery of critical nodes in road networks through mining from vehicle trajectories[J]. IEEE Trans. on Intelligent Transportation Systems, 2019, 20 (2): 583- 593. doi: 10.1109/TITS.2018.2817282
26	ZHAO J, RONG W Y, LIU D. Urban agglomeration high-speed railway backbone network planning: a case study of Beijing-Tianjin-Hebei region, China[J]. Sustainability, 2023, 15 (8): 6450. doi: 10.3390/su15086450
27	LI J L, LI J, CUI T, et al. Node importance evaluation method of satellite information network based on heterogeneous virtual subnet[J]. Journal of Physics: Conference Series, 2023, 2480 (1): 012017. doi: 10.1088/1742-6596/2480/1/012017
28	LIU F Y, XIE G, ZHAO Z P. Importance evaluation of power network nodes based on community division and characteristics of coupled network[J]. Electric Power Systems Research, 2022, 209, 108015. doi: 10.1016/j.jpgr.2022.108015
29	YANG Z F, LI Y G, LIU J Y. A method of node importance measurement base on community structure in heterogeneous combat networks [C]//Proc. of the Communications and Networking: 15th EAI International Conference, 2021: 766−775.
30	LIU C, WANG J Y, XIA R. Node importance evaluation in multi-platform avionics architecture based on TOPSIS and PageRank[J]. EURASIP Journal on Advances in Signal Processing, 2023, 27.
31	俞锦涛, 肖兵, 崔玉竹. 基于节点重要性和改进效能环的防空反导预警体系能力评估[J]. 兵工学报, 2024, 45 (1): 328- 338.
	YU J T, XIAO B, CUI Y Z. 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.
32	GUO J, LI T W, LI C X, et al. Construction of shipborne navigation equipment’s comprehensive effectiveness evaluation index system based on improved ADC model[C]// Proc. of the IEEE Chinese Guidance, Navigation and Control Conference, 2014: 822−826.
33	GJB 1364-1992. 装备费用-效能分析[S]. 北京: 国防科学技术工业委员会, 1992.
	GJB 1364-1992. Cost-effectiveness analysis for materiel[S]. Beijing: Commission of Science, Technology and Industry for National Defense, 1992.
34	GJB 451B-2021. 装备通用质量特性术语[S]. 北京: 中央军委装备发展部, 2021.
	GJB 451B-2021. General quality characteristics terms for materiel[S]. Beijing: Equipment Development Department of People’s Republic, 2021.
35	ZHANG J R, FANG Z G, DONG W J, et al. A mission success probability assessment framework for phased-mission-systems using extended graphical evaluation and review technique[J]. Reliability Engineering & System Safety, 2024, 249: 110248.

作战活动(i，j)	活动概率p_ij	活动效果E_ij	执行装备i	装备能力
$({\mathrm{Start}},{O_1})$	0.33	0	−	−
$({\mathrm{Start}},{O_2})$	0.33	0
$({\mathrm{Start}},{O_3})$	0.33	0
$({O_1},{O_2})$	0.5	0.7924	${O_1}$	0.8452
$({O_1},{P_2})$	0.5	0.8979	${O_1}$	0.8452
$({O_2},{P_1})$	0.49	0.8268	${O_2}$	0.8204
$({O_2},{P_2})$	0.49	0.8474	${O_2}$	0.8204
$({O_3},{P_1})$	0.49	0.8077	${O_3}$	0.8002
$({O_3},{P_2})$	0.49	0.8253	${O_3}$	0.8002
$ ({P_1},{P_2}) $	0.33	0.8777	$ {P_1} $	0.8657
$ ({P_1},{D_1}) $	0.33	0.8678
$ ({P_1},{D_2}) $	0.33	0.8778
$ ({P_2},{D_1}) $	0.5	0.9505	$ {P_2} $	0.9559
$ ({P_2},{D_2}) $	0.5	0.9613	$ {P_2} $	0.9559

节点$i$	位置重要度	关联节点		关联重要度	节点重要度	归一化节点重要度
节点$i$	位置重要度	入节点	出节点	关联重要度	节点重要度	归一化节点重要度
$ {T_1} $	0.5	$ {A_1} $,$ {A_2} $	${O_1}$,${O_2}$,${O_3}$	0.8316	0.4158	0.0903
$ {T_2} $	0.4	$ {A_2} $	${O_1}$,${O_2}$,${O_3}$	0.6965	0.2786	0.0605
${O_1}$	0.4	$ {T_1} $,$ {T_2} $	${O_2}$,$ {P_2} $	0.8391	0.3356	0.0728
${O_2}$	0.5	$ {T_1} $,$ {T_2} $,${O_1}$	$ {P_1} $,$ {P_2} $	1.0194	0.5097	0.1106
${O_3}$	0.4	$ {T_1} $,$ {T_2} $	$ {P_1} $,$ {P_2} $	0.8504	0.3402	0.0738
$ {P_1} $	0.5	${O_2}$,${O_3}$	$ {P_2} $,$ {D_1} $,$ {D_2} $	1.0646	0.5323	0.1155
$ {P_2} $	0.6	${O_1}$,${O_2}$,${O_3}$,$ {P_1} $	$ {D_1} $,$ {D_2} $	1.1632	0.6979	0.1515
$ {D_1} $	0.5	$ {P_1} $,$ {P_2} $	$ {D_2} $,$ {A_1} $,$ {A_2} $	1.0092	0.5046	0.1095
$ {D_2} $	0.5	$ {P_1} $,$ {P_2} $,$ {D_1} $	$ {A_1} $,$ {A_2} $	1.0048	0.5024	0.1090
$ {A_1} $	0.3	$ {D_1} $,$ {D_2} $	$ {T_1} $	0.8253	0.1862	0.0404
$ {A_2} $	0.4	$ {D_1} $,$ {D_2} $	$ {T_1} $,$ {T_2} $	0.8253	0.3039	0.066 0

作战活动$(i,j)$	活动概率${p_{ij}}$	活动效果$E_{ij}^{'}$	等价传递函数${W_{ij}}$
$({\mathrm{Start}},{O_1})$	0.33	0	0.33
$({\mathrm{Start}},{O_2})$	0.33	0	0.33
$({\mathrm{Start}},{O_3})$	0.33	0	0.33
$({O_1},{O_2})$	0.5	0.7632	$0.5{\mathrm{Exp}}(0.763\;2s)$
$({O_1},{P_2})$	0.5	0.8648	$0.5{\mathrm{Exp}}(0.864\;8s)$
$({O_2},{P_1})$	0.49	0.8270	$0.49{\mathrm{Exp}}(0.827s)$
$({O_2},{P_2})$	0.49	0.8476	$0.49{\mathrm{Exp}}(0.847\;6s)$
$({O_3},{P_1})$	0.49	0.7787	$0.49{\mathrm{Exp}}(0.778\;7s)$
$({O_3},{P_2})$	0.49	0.7957	$0.49{\mathrm{Exp}}(0.795\;7s)$
$ ({P_1},{P_2}) $	0.33	0.8821	$0.33{\mathrm{Exp}}(0.882\;1s)$
$ ({P_1},{D_1}) $	0.33	0.8721	$0.33{\mathrm{Exp}}(0.872\;1s)$

[1]	Wen SUN, Juan CHENG, Yihao WANG, Kaichen CAO, Mengmeng GE, Liu HUANG, Geng ZHANG. Effectiveness analysis and modeling of ship target detection utilizing hyperspectral remote sensing satellites [J]. Systems Engineering and Electronics, 2025, 47(5): 1432-1442.
[2]	Ding CHEN, Zhigeng FANG, Baohua YANG, Feng YE, Na ZHANG, Jingru ZHANG. Grey principal component analysis model of effectiveness evaluation for joint operation system-of-systems considering indicator synergism reconstruction [J]. Systems Engineering and Electronics, 2025, 47(5): 1561-1574.
[3]	Zhangqiu YUAN, Zhaoxu YANG, Haijun RONG. Lightweight effectiveness evaluation method for high altitude airships for both qualitative and quantitative indicators [J]. Systems Engineering and Electronics, 2025, 47(3): 817-826.
[4]	Wei HAN, Fang GUO, Yujie LIU, Xichao SU, Jie LIU. Evaluation method of operational effectiveness for aircraft carrier formation based on triangular fuzzy number and operation loop [J]. Systems Engineering and Electronics, 2025, 47(3): 893-903.
[5]	Zhiguo SUN, Chuanling LIU, Zhenduo WANG. Interference efficiency evaluation method based on hybrid double chain quantum genetic algorithm [J]. Systems Engineering and Electronics, 2025, 47(12): 4186-4195.
[6]	Ziqiang ZHU, Songtao LIU, Ruihui PENG. Operational effectiveness evaluation of radar reconnaissance system based on Vague topology fusion and improved game theory [J]. Systems Engineering and Electronics, 2025, 47(11): 3699-3707.
[7]	Dijiu YUE, Jianhua LI, Zhe WANG. Node importance measurement method of command information system for resilience [J]. Systems Engineering and Electronics, 2024, 46(4): 1320-1329.
[8]	Lisha ZHENG, Dongliang YIN, Xuan WANG. Operational effectiveness evaluation of phased array radar based on improved D-S evidence theory [J]. Systems Engineering and Electronics, 2024, 46(4): 1330-1336.
[9]	Li MA, Peng SHI, Yu CHEN, Wenlong LI. Discrete event simulation and effectiveness evaluation of space-based information support system [J]. Systems Engineering and Electronics, 2024, 46(3): 906-913.
[10]	Tao HU, Liqun SHEN, Jingda ZHU, Chenghui SUN, Weifeng DONG. Sensitivity analysis of radar system effectiveness based on FAST and Sobol index method [J]. Systems Engineering and Electronics, 2024, 46(2): 561-569.
[11]	Yu CHEN, Peng SHI, Li MA, Wenlong LI. Modeling and effectiveness evaluation method of space-based information support system [J]. Systems Engineering and Electronics, 2024, 46(10): 3407-3415.
[12]	Rui LI, Mengtao ZHU, Yunjie LI. Online evaluation method of radar jamming effect based on inverse filtering processing [J]. Systems Engineering and Electronics, 2023, 45(9): 2706-2717.
[13]	Jiaping CAO, Mengxin OU, Yishan LI, Jiang JIANG, Jichao LI. Island air defense electronic countermeasure equipment system construction and effectiveness evaluation [J]. Systems Engineering and Electronics, 2023, 45(9): 2784-2792.
[14]	Changjiang QIN, Keyu WU, Qing CHENG, Jincai HUANG. Node importance evaluation in dynamic system based on kill-web contribution rate [J]. Systems Engineering and Electronics, 2023, 45(6): 1732-1742.
[15]	Xiaowen ZHU, Chengli FAN, Yingqi LU, Wenzheng ZHU, Xuan WU. Anti-missile weapon target allocation modeling and implementation based on improved BBO algorithm and fuzzy expectation effect [J]. Systems Engineering and Electronics, 2023, 45(11): 3544-3554.

Method of effectiveness evaluation for anti-missile system of systems based on node importance

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 11

References 35

Related Articles 15

Recommended Articles

Metrics

Comments