多阶段攻防对抗体系效能评估MS-GERT模型

doi:10.12305/j.issn.1001-506X.2025.07.17

Abstract

Abstract:

Effectiveness is an important indicator for measuring the performance of multi-stage offensive and defensive adversarial system-of-systems (SoS), which represents the tasks completion degree. During the execution of tasks, the external environment constantly changes, and the effectiveness of the SoS shows time dependent relationship. To address this issue, an expanded graphical evaluation and review technique (GERT) is proposed to evaluate the effectiveness of multi-stage offensive and defensive adversarial SoS. Firstly, a GERT network is constructed based on the multi-stage characteristics of SoS task execution, and the transmission characteristics of the network are analyzed. Then, in the calculation of effectiveness results, a new task time effectiveness parameter considering time factor is designed to reflect the time-dependent characteristics of effectiveness, using the c and z tag method to obtain the relevant parameters for critical tasks execution by the critical component system. Finally, taking the a missile defense SoS' defensive combat mission as an example, the execution effect of the defense combat mission is evaluated, and indicator data such as SoS effectiveness, combat time, missile inventory, and the time of the missile's first hit on the target are obtained, which provides decision-making indicators that cover more information for optimizing the SoS configuration scheme.

Key words: offensive and defensive adversarial system-of-systems (SoS), effectiveness, graphical evaluation and review technique (GERT), task time effectiveness

CLC Number:

C935

Jingru ZHANG, Zhigeng FANG, Yunke SUN, Shuang WU, Ding CHEN. MS-GERT model for effectiveness evaluation of multi-stage offensive and defensive adversarial system-of-systems[J]. Systems Engineering and Electronics, 2025, 47(7): 2237-2245.

Figures/Tables 7

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References 37

1	SERVI L D , GARVEY P R . Deriving global criticality conditions from local dependencies using functional dependency network analysis (FDNA)[J]. Systems Engineering, 2017, 20 (4): 297- 306.
2	李智, 吕铁鑫, 潘艳辉. 联合全域作战智能博弈优化一体化决策问题[J]. 火力与指挥控制, 2023, 48 (3): 1- 8. doi: 10.3969/j.issn.1002-0640.2023.03.001
	LI Z , LYU T X , PAN Y H . Research on integrated decision-making problems of intelligent game optimization in JADO[J]. Fire Control & Command Control, 2023, 48 (3): 1- 8. doi: 10.3969/j.issn.1002-0640.2023.03.001
3	MAIERE M W . Architecting principles for systems-of-systems[J]. Systems Engineering: The Journal of the International Council on Systems Engineering, 1998, 1 (4): 267- 284.
4	张子伟, 郭齐胜, 董志明, 等. 体系作战效能评估与优化方法综述[J]. 系统仿真学报, 2022, 34 (2): 303- 313.
	ZHANG Z W , GUO Q S , DONG Z M , et al. Review of system of systems combat effectiveness evaluation and optimization methods[J]. Journal of System Simulation, 2022, 34 (2): 303- 313.
5	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.
6	GAO Y , CHENG J Y , TIAN Y L , et al. Machine learning-based evaluation of the contribution effectiveness in SoS missions[J]. IEEE Systems Journal, 2023, 17 (4): 5877- 5888.
7	钟季龙, 郭基联. 空中远程作战体系效能评估的组合分析方法[J]. 系统工程, 2015, 33 (11): 140- 145.
	ZHONG J L , GUO J L . The portfolio-analysis methods for as sessing effectiveness of system of long-range operation system[J]. System Engineering, 2015, 33 (11): 140- 145.
8	马骏, 杨镜宇, 吴曦. 基于预聚类主动半监督的作战体系效能评估[J]. 系统工程与电子技术, 2022, 44 (6): 1889- 1896. doi: 10.12305/j.issn.1001-506X.2022.06.15
	MA J , YANG J Y , WU X . Evaluation of operational system of systems effectiveness based on pre-clustering active semi-supervised learning[J]. Systems Engineering and Electronics, 2022, 44 (6): 1889- 1896. doi: 10.12305/j.issn.1001-506X.2022.06.15
9	SHAO R R , FANG Z G , TAO L Y , et al. A comprehensive G-LZ-ADC effectiveness evaluation model for the single communication satellite system in the context of poor information[J]. Grey Systems: Theory and Application, 2022, 12 (2): 417- 461.
10	XU R J , LIU X , CUI D H , et al. An evaluation method of contribution rate based on fuzzy Bayesian networks for equipment system-of-systems architecture[J]. Journal of Systems Engineering and Electronics, 2023, 34 (3): 574- 587.
11	刘海洋, 胡晓峰, 刘戎翔, 等. 基于时序超网的作战体系效能指标动态测量方法[J]. 火力与指挥控制, 2020, 45 (4): 47- 58. doi: 10.3969/j.issn.1002-0640.2020.04.009
	LIU H Y , HU X F , LIU R X , et al. Dynamic measurement method of operation SoS effectiveness index based on sequential super-network[J]. Fire Control & Command Control, 2020, 45 (4): 47- 58. doi: 10.3969/j.issn.1002-0640.2020.04.009
12	FAN J R , LI D G , LI R P , et al. Analysis on MAV/UAV cooperative combat based on complex network[J]. Defence Technology, 2020, 16 (1): 150- 157.
13	WANG Z K , ZENG S K , GUO J B , et al. A Bayesian network for reliability assessment of man-machine phased-mission system considering the phase dependencies of human cognitive error[J]. Reliability Engineering & System Safety, 2021, 207, 107385.
14	柳李鹏, 曹菲, 毋凡. 基于专家集成赋权-灰色聚类法的引信抗干扰效能评估[J]. 探测与控制学报, 2018, 40 (6): 7- 13.
	LIU L P , CAO F , WU F . Fuze anti-jamming efficiency evaluation based on expert integrated weighting and grey clustering method[J]. Journal of Detection & Control, 2018, 40 (6): 7- 13.
15	HU X W, LUO P C, ZHANG X N, et al. Research on the effectiveness evaluation of big data in combat simulation[C]//Proc. of the 2nd International Conference on Big Data Research, 2018: 70-75.
16	LEE J , SHIN S , PARK M , et al. Agent-based simulation and its application to analyze combat effectiveness in network-cen tric warfare considering communication failure environments[J]. Mathematical Problems in Engineering, 2018, 2018 (1): 2730671.
17	CHEN L B , WANG C , ZENG C Y , et al. A novel method of heterogeneous combat network disintegration based on deep reinforcement learning[J]. Frontiers in Physics, 2022, 10, 1021245.
18	ZENG C Y , LIU H F , LU L N , et al. Shatter: searching hete-rogeneous combat network attack sequences through network embedding and reinforcement learning[J]. IEEE Systems Journal, 2023, 17 (3): 4497- 4508.
19	马也, 范文慧, 常天庆. 基于智能算法的无人集群防御作战方案优化方法[J]. 兵工学报, 2022, 43 (6): 1415- 1425.
	MA Y , FAN W H , CHANG T Q . Optimization method of unmanned swarm defensive combat scheme based on intelligent algorithm[J]. Acta Armamentarii, 2022, 43 (6): 1415- 1425.
20	张国辉, 高昂, 张雅楠. 基于RLoMAG+EAS的同构集群装备体系作战效能评估方法[J]. 系统仿真学报, 2024, 36 (1): 160- 169.
	ZHANG G H , GAO A , ZHANG Y N . Combat effectiveness evaluation method of homogeneous cluster equipment system based on RLoMAG+EAS[J]. Journal of System Simulation, 2024, 36 (1): 160- 169.
21	PRITSKER A A B , HAPP W W . GERT: graphical evaluation and review technique, Part Ⅰ: fundamental[J]. Journal of Industrial Engineering, 1966, 17 (5): 267- 274.
22	PRITSKER A A B . GERT networks[J]. Production Engineer, 1968, 47 (10): 499- 506.
23	AHMED A , KAYIS B , AMORNSAWADWATANA S . A review of techniques for risk management in projects[J]. Benchmarking: an International Journal, 2017, 14 (1): 22- 36.
24	KANNAN R . Graphical evaluation and review technique (GERT): the panorama in the computation and visualization of network-based project management[M]. New York: IGI Global Publishing, 2014.
25	FISHER D L , GOLDSTEIN W M . Stochastic PERT networks as models of cognition: derivation of the mean, variance, and distribution of reaction time using order-of-processing (OP) diagrams[J]. Journal of Mathematical Psychology, 1983, 27 (2): 121- 151.
26	KOSUGI T , HAYASHI A , MATSUMOTO T , et al. Time to realization: evaluation of CO₂ capture technology R&Ds by GERT (graphical evaluation and review technique) analyses[J]. Energy, 2004, 29 (9): 1297- 1308.
27	NELSON R G , AZARON A , AREF S . The use of a GERT based method to model concurrent product development processes[J]. European Journal of Operational Research, 2016, 250 (2): 566- 578.
28	WANG X L , XU J H , ZHANG L , et al. Mission success probability optimizing of phased mission system balancing the phase backup and system risk: a novel GERT mechanism[J]. Reliability Engineering & System Safety, 2023, 236, 109311.
29	TAO L Y , WU D S , 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.
30	GENG S Y , LIU S F , FANG Z G . An agent-based algorithm for dynamic routing in service networks[J]. European Journal of Operational Research, 2022, 303 (2): 719- 734.
31	方志耕, 夏悦馨, 张靖如, 等. 基于Agent的体系过程A-GERT网络"刺激-反应"学习模型[J]. 系统工程与电子技术, 2022, 44 (8): 2540- 2553. doi: 10.12305/j.issn.1001-506X.2022.08.19
	FANG Z G , XIA Y X , ZHANG J R , et al. A stimulus-response learning model for Agent-based system process A-GERT network[J]. Systems Engineering and Electronics, 2022, 44 (8): 2540- 2553. doi: 10.12305/j.issn.1001-506X.2022.08.19
32	黄路炜, 毕义明, 杨继锋. 应急作战下导弹技术测试优化方法研究[J]. 系统仿真学报, 2007, 19 (6): 1347- 1350.
	HUANG L W , BI Y M , YANG J F . Research on optimal method of missile technical test in emergent battle[J]. Journal of System Simulation, 2007, 19 (6): 1347- 1350.
33	ZHANG N , YAN S L , FANG Z G , et al. Fuzzy GERT model based on ztag and its application in weapon equipment management[J]. Journal of Intelligent & Fuzzy Systems, 2021, 40 (6): 12503- 12519.
34	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.
35	YU H Y , WU X Y , WU X Y . An extended object-oriented petri net model for mission reliability evaluation of phased-mission system with time redundancy[J]. Reliability Engineering & System Safety, 2020, 197, 106786.
36	HE Y H , CHEN Z X , ZHAO Y X , et al. Mission reliability evaluation for fuzzy multistate manufacturing system based on an extended stochastic flow network[J]. IEEE Trans.on Reliability, 2019, 69 (4): 1239- 1253.
37	WU D , YAN X B , PENG R , et al. Risk-attitude-based defense strategy considering proactive strike, preventive strike and imperfect false targets[J]. Reliability Engineering & System Safety, 2020, 196, 106778.

(i, j)	活动	效能	时间分布	矩母函数	传递函数
(0, 1)	预警卫星侦察威胁目标	0.4	N(0.85, 0.03)	e^{0.85s+0.03s²}	0.4e^{0.85s+0.03s²}
(0, 3)	目标搜索雷达侦察威胁目标	0.5	N(0.7, 0.03)	e^0.7s+0.03s²	0.5e^0.7s+0.03s²
(0, 10)	未侦察到目标	0.1	N(0.6, 0.07)	e^0.6s+0.07s²	0.1e^0.6s+0.07s²
(1, 2)	预警卫星将目标信息传送至预警机	0.4	N(0.65, 0.01)	e^{0.65s+0.01s²}	0.4e^{0.65s+0.01s²}
(1, 10)	预警卫星未能成功传送目标信息	0.6	N(0.8, 0.02)	e^0.8s+0.02s²	0.6e^0.8s+0.02s²
(2, 4)	预警机将目标信息传送至指控中心	0.8	N(0.65, 0.05)	e^{0.65s+0.05s²}	0.8e^{0.65s+0.05s²}
(2, 10)	预警机未能成功传送目标信息	0.2	N(0.8, 0.03)	e^0.8s+0.03s²	0.2e^0.8s+0.03s²
(3, 4)	目标搜索雷达将目标信息传送至指控中心	0.8	N(0.7, 0.05)	e^0.7s+0.05s²	0.8e^0.7s+0.05s²
(3, 10)	目标搜索雷达未能成功传送目标信息	0.2	N(0.75, 0.06)	e^{0.75s+0.06s²}	0.2e^{0.75s+0.06s²}
(4, 5)	指控中心下令作战	0.7	N(0.6, 0.07)	e^0.6s+0.07s²	0.7e^0.6s+0.07s²
(4, 10)	指控中心未下令作战	0.3	N(0.8, 0.01)	e^0.8s+0.01s²	0.3e^0.8s+0.01s²
(5, 5)	导弹发射失败, 再次发射	0.3	N(0.65, 0.02)	e^{0.65s+0.02s²}	0.3e^{0.65s+0.02s²}
(5, 6)	导弹发射车发射导弹成功	0.7	N(0.6, 0.04)	e^0.6s+0.04s²	0.7e^0.6s+0.04s²
(6, 7)	导弹击中目标	0.9	N(0.7, 0.02)	e^0.7s+0.02s²	0.9e^0.7s+0.02s²
(6, 8)	导弹未击中目标	0.1	N(0.8, 0.03)	e^0.8s+0.03s²	0.1e^0.8s+0.03s²
(7, 9)	防御作战任务成功	1	N(0.9, 0.01)	e^0.9s+0.01s²	e^0.9s+0.01s²
(8, 5)	导弹击中未目标, 启动下一次发射	1	0	1	1

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MS-GERT model for effectiveness evaluation of multi-stage offensive and defensive adversarial system-of-systems

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