基于模糊功能依赖网分析的体系效能评估方法

doi:10.16182/j.issn1004731x.joss.25-0464

摘要/Abstract

摘要：

功能依赖网分析法(functional dependency network analysis, FDNA)可对体系中装备的依赖关系进行建模，进而利用单个装备的效能来计算体系层面的整体效能，从而克服传统的基于树状指标体系进行评估的不足。依赖强度、依赖关键度等重要参数需要借助主观经验给出，针对主观评价偏差容易影响效能评估结果的准确性，提出了一种基于模糊功能依赖网分析(fuzzy FDNA, FFDNA)的装备体系效能评估 方法。基于装备的功能属性构建功能依赖网模型，并且考虑了对节点综合依赖关键度的计算，以提高对体系分析的准确性。对于依赖参数取值过于主观、缺乏可靠性的问题，引入三角模糊数和模糊数学计算方法对体系效能进行分析计算，从而有效减少参数取值时主观偏差对效能计算结果造成的影响。通过对具体作战场景的体系效能评估进行实验分析，对该方法的有效性和实用性进行了验证。

关键词: 体系, 效能评估, 模糊功能依赖网分析, 模糊数学

Abstract:

Functional dependency network analysis (FDNA) enables modeling functional dependencies among equipment in a system of systems (SoS) and then computing the whole SoS effectiveness based on the effectiveness of each equipment, thus overcoming the deficiency of traditional SoS effectiveness evaluation based on tree-like index systems. However, critical parameters such as strength/criticality of dependency in this methodology currently rely on subjective empirical assignments, where the deviations resulting from subjectivity may compromise the accuracy of effectiveness evaluation. To address this limitation, this paper proposes a fuzzy FDNA (FFDNA)-based SoS effectiveness evaluation method. This method constructs a functional dependency network (FDN) model based on the functional attributes of equipment, and incorporates synthesis credibility of dependency to improve analytical accuracy. More importantly, to mitigate the subjectivity of dependency parameter selection, triangular fuzzy numbers (TFN) and fuzzy mathematical calculations are introduced for effectiveness computation. Experimental validation through simulated combat scenarios confirms effectiveness and practicality of the method.

Key words: system-of-systems, effectiveness evaluation, fuzzy functional dependency network analysis, fuzzy mathematics

中图分类号:

TP391.9

苏泓嘉,张成,刘飞 . 基于模糊功能依赖网分析的体系效能评估方法[J]. 系统仿真学报, 2026, 38(5): 1224-1238.

Su Hongjia,Zhang Cheng,Liu Fei . SoS Effectiveness Evaluation Method Based on Fuzzy Functional Dependency Network Analysis[J]. Journal of System Simulation, 2026, 38(5): 1224-1238.

图/表 14

图1

图2

图3

图4

图5

图6

图7

图8

图 9

表1

表2

表3

图10

表4

参考文献 27

[1]	Garvey P R, Pinto C A. Introduction to Functional Dependency Network Analysis[C]//The MITRE Corporation and Old Dominion, Second International Symposium on Engineering Systems. Cambridge: MIT, 2009: 1-17.
[2]	Guariniello C, DeLaurentis D. Dependency Analysis of System-of-systems Operational and Development Networks[J]. Procedia Computer Science, 2013, 16: 265-274.
[3]	Guariniello Cesare, Ali Khalid Raz, Fang Zhemei, et al. System-of-systems Tools and Techniques for the Analysis of Cyber-physical Systems[J]. Systems Engineering, 2020, 23(4): 480-491.
[4]	陈宽, 李元元, 罗云峰, 等. 基于功能依赖网络的体系韧性分析[J]. 指挥与控制学报, 2016, 2(3): 256-260.
	Chen Kuan, Li Yuanyuan, Luo Yunfeng, et al. Evaluating System of Systems Resilience Based on Functional Dependency Network Analysis[J]. Journal of Command and Control, 2016, 2(3): 256-260.
[5]	邱禄芸, 方志耕, 陶良彦, 等. 网络体系效能评估改进FDNA模型[J]. 系统工程与电子技术, 2022, 44(12): 3728-3737.
	Qiu Luyun, Fang Zhigeng, Tao Liangyan, et al. Effectiveness Evaluation of Network SoS Based on Improved FDNA Model[J]. Systems Engineering and Electronics, 2022, 44(12): 3728-3737.
[6]	王学文, 程思齐, 武世勇, 等. 基于功能依赖网的评估指标体系构建[J]. 火力与指挥控制, 2024, 49(7): 97-103.
	Wang Xuewen, Cheng Siqi, Wu Shiyong, et al. Construction of Evaluation Index System Based on the Functional Dependency Network Analysis[J]. Fire Control & Command Control, 2024, 49(7): 97-103.
[7]	于冰倩, 李学艳, 程思齐, 等. 基于复杂网络的陆空协同作战体系效能评估方法[J]. 火力与指挥控制, 2024, 49(1): 105-110.
	Yu Bingqian, Li Xueyan, Cheng Siqi, et al. A Method for Evaluating the Effectiveness of Land-air Collaborative Warfare System Based on Complex Networks[J]. Fire Control & Command Control, 2024, 49(1): 105-110.
[8]	Wang Yushuai, Si Guangya. Modeling and Analysis Method of Dependency Network Based on Kill Chain and FDNA[C]//Proceedings of the 2024 16th International Conference on Machine Learning and Computing. New York: ACM, 2024: 734-740.
[9]	孙丽杰, 王剑波, 罗云峰, 等. 体系功能依赖网络参数获取及应用[J]. 兵工自动化, 2018, 37(1): 40-44, 54.
	Sun Lijie, Wang Jianbo, Luo Yunfeng, et al. Acquisition and Application of Functional Dependency Network Parameters for System of Systems[J]. Ordnance Industry Automation, 2018, 37(1): 40-44, 54.
[10]	陈宇奇, 徐廷学, 郝建平, 等. 基于FDN的装备体系任务能力依赖性分析[J]. 系统工程与电子技术, 2021, 43(6): 1721-1728.
	Chen Yuqi, Xu Tingxue, Hao Jianping, et al. Task Capability Dependency Analysis of Weapon System of Systems Based on FDN[J]. Systems Engineering and Electronics, 2021, 43(6): 1721-1728.
[11]	Luo Aimin, Yi Shuanghui, Liu Junxian, et al. An Improved Functional Dependency Network Model for Information Systems Effectiveness Analysis[C]//Proceedings of the 2020 International Conference on Wireless Communication and Sensor Networks. New York: ACM, 2020: 56-59.
[12]	Liu Shengyu, Wang Xichao, Yan Ci, et al. Analysis of System Capability Generation Based on Functional Dependency Networks[C]//2024 10th International Conference on Systems and Informatics (ICSAI). Piscataway: IEEE, 2024: 1-5.
[13]	王玉帅, 司光亚. 基于杀伤链和FDNA的能力依赖关系分析[J]. 系统仿真学报, 2025, 37(4): 1076-1089.
	Wang Yushuai, Si Guangya. Capability Dependency Analysis Based on Kill Chain and FDNA[J]. Journal of System Simulation, 2025, 37(4): 1076-1089.
[14]	钟庆, 周剑雄, 秦肖臻, 等. 体系效能的功能依赖网络分析[J]. 兵工自动化, 2017, 36(6): 52-55.
	Zhong Qing, Zhou Jianxiong, Qin Xiaozhen, et al. FDNA of SoS Effectiveness[J]. Ordnance Industry Automation, 2017, 36(6): 52-55.
[15]	王泉, 刘新爱, 何永鹏, 等. 基于Fuzzy-AHP的反辐射导弹作战效能评估应用研究[J]. 空天防御, 2024, 7(2): 47-51.
	Wang Quan, Liu Xinai, He Yongpeng, et al. Research on the Application of Combat Effectiveness Evaluation of Anti-radiation Missile Based on Fuzzy-AHP[J]. Air & Space Defense, 2024, 7(2): 47-51.
[16]	林意博, 蒋彦雯, 卢大威, 等. 基于改进层次分析法的相控阵雷达效能评估方法研究[J]. 火控雷达技术, 2025, 54(1): 37-42, 48.
	Lin Yibo, Jiang Yanwen, Lu Dawei, et al. Research on Effectiveness Evaluation Method of Phased Array Radar Based on Improved Analytic Hierarchy Process[J]. Fire Control Radar Technology, 2025, 54(1): 37-42, 48.
[17]	解凤娟, 李广宁, 魏圣钢. 基于AHP及模糊综合评判的弹药装填系统效能评估[J]. 火炮发射与控制学报, 2026, 47(1): 56-61.
	Xie Fengjuan, Li Guangning, Wei Shenggang. Assessment of Ammunition Loading System Effectiveness Based on Analytic Hierarchy Process and Fuzzy Comprehensive Evaluation[J]. Journal of Gun Launch & Control, 2026, 47(1): 56-61.
[18]	韩维, 郭放, 刘玉杰, 等. 基于三角模糊数作战环的航母编队作战效能评估方法[J]. 系统工程与电子技术, 2025, 47(3): 893-903.
	Han Wei, Guo Fang, Liu Yujie, et al. 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.
[19]	陈俊, 李建华. 改进模糊综合评价法的军地联合信息通信保障效能评估[J]. 空军工程大学学报, 2025, 26(2): 55-61.
	Chen Jun, Li Jianhua. An Improved Fuzzy Comprehensive Evaluation Method for Effectiveness Evaluation of Military-civilian Integrated Information and Communication Support[J]. Journal of Air Force Engineering University, 2025, 26(2): 55-61.
[20]	张旺勋. 基于复杂交互网络的武器装备体系安全性分析方法[D]. 长沙: 国防科学技术大学, 2015.
	Zhang Wangxun. A Weapon System of Systems Safety Analysis Method Based on Complex Interaction Networks[D]. Changsha: National University of Defense Technology, 2015.
[21]	浣顺启. 基于改进FDNA方法的体系效能评估[D]. 武汉: 华中科技大学, 2021.
	Huan Shunqi. System-of-systems Effectiveness Evaluation Based on Improved FDNA Method[D]. Wuhan: Huazhong University of Science & Technology, 2021.
[22]	程里春, 陈化成. 基于有界算子的三角模糊数运算[J]. 模糊系统与数学, 1993, 7(2): 33-42.
	Cheng Lichun, Chen Huacheng. Operations of Triangular Fuzzy Numbers with Composition Sup-☉[J]. Fuzzy Systems and Mathematics, 1993, 7(2): 33-42.
[23]	甘庭聪, 徐义红, 张雨涵. 三角模糊数的一种排序方法[J]. 数学的实践与认识, 2020, 50(13): 116-121.
	Gan Tingcong, Xu Yihong, Zhang Yuhan. A Ranking Method of Fuzzy Triangular Fuzzy Numbers[J]. Mathematics in Practice and Theory, 2020, 50(13): 116-121.
[24]	Liu Yan, Eckert C M, Earl C. A Review of Fuzzy AHP Methods for Decision-making with Subjective Judgements[J]. Expert Systems with Applications, 2020, 161: 113738.
[25]	邵俊. 基于杀伤网的装备组合选择方法研究[D]. 长沙: 国防科技大学, 2020.
	Shao Jun. Research on Equipment Portfolio Method Based on the Kill Web[D]. Changsha: National University of Defense Technology, 2020.
[26]	夏博远, 杨克巍, 杨志伟, 等. 基于杀伤网评估的装备组合多目标优化[J]. 系统工程与电子技术, 2021, 43(2): 399-409.
	Xia Boyuan, Yang Kewei, Yang Zhiwei, et al. Multi-objective Optimization of Equipment Portfolio Based on Kill-web Evaluation[J]. Systems Engineering and Electronics, 2021, 43(2): 399-409.
[27]	浣顺启, 方哲梅, 王剑波. 基于功能依赖网的体系效能评估方法[J]. 系统工程与电子技术, 2022, 44(7): 2191-2200.
	Huan Shunqi, Fang Zhemei, Wang Jianbo. System-of-systems Effectiveness Evaluation Method Based on Functional Dependency Network[J]. Systems Engineering and Electronics, 2022, 44(7): 2191-2200.

变量名称	边	S₁	S_T
COD_l165	r₃,C->r₆,D	0.123 139 3	0.041 283 4
COD_h163	r₃,C->r₄,D	0.106 715 1	0.026 327 2
COD_l170	r₃,S->r₁₅,C	0.104 752 1	0.026 639 5
COD_h172	r₃,S->r₃,C	0.081 486 1	0.030 767 8
COD_l168	r₃,D->r₂₁,I	0.080 942 6	0.029 858 7

想定	FFDNA	HI-FDNA	E-FDNA
1	5.356×10³	5.665×10³	5.560×10³
2	5.218×10³	5.510×10³	5.423×10³
3	3.668×10³	3.868×10³	3.794×10³
4	4.073×10³	4.276×10³	4.205×10³

想定	FFDNA	HI-FDNA	E-FDNA
1	1.368×10³	1.560×10³	1.520×10³
2	1.292×10³	1.476×10³	1.442×10³
3	0.948×10³	1.086×10³	1.060×10³
4	1.056×10³	1.205×10³	1.179×10³

节点ID	FFDNA 模糊值	FFDNA精确值	HI-FDNA	E-FDNA
(r₁₅,I)	<48.64,53.64,55.99>	52.98	75.00	74.58
(r₁₈,I)	<20.11,23.45,23.45>	22.61	50.00	50.00
(r₁₉,I)	<0.00,10.00,10.00>	7.50	50.00	50.00
(r₂₀,I)	<27.50,32.50,32.50>	31.25	50.00	50.00
(r₂₁,I)	<27.50,32.50,32.50>	31.25	50.00	50.00