复杂体系可靠性结构分析与建模GERT网络技术

doi:10.12305/j.issn.1001-506X.2024.10.20

系统工程与电子技术 ›› 2024, Vol. 46 ›› Issue (10): 3427-3436.doi: 10.12305/j.issn.1001-506X.2024.10.20

• 系统工程 • 上一篇

复杂体系可靠性结构分析与建模GERT网络技术

方志耕¹, 华晨晨¹^,*, 陈顶², 张靖如¹, 张亚东¹, 吴鸿华¹

1. 南京航空航天大学经济与管理学院, 江苏南京 211106
2. 上海机电工程研究所, 上海 201109

收稿日期:2023-04-03 出版日期:2024-09-25 发布日期:2024-10-22
通讯作者: 华晨晨
作者简介:方志耕(1962—), 男, 教授, 博士研究生导师, 博士, 主要研究方向为可靠性工程、复杂装备研制管理
华晨晨(1999—), 女, 硕士研究生, 主要研究方向为可靠性工程、效能优化
陈顶(1989—), 男, 工程师, 博士, 主要研究方向为效能评估、质量与可靠性
张靖如(1997—), 女, 博士研究生, 主要研究方向为复杂体系建模
张亚东(1996—), 男, 硕士研究生, 主要研究方向为可靠性增长
吴鸿华(1978—), 男, 副教授, 博士研究生, 主要研究方向为灰色系统理论
基金资助:
国家自然科学基金项目(72271124);国家自然科学基金项目(52232014)

GERT network technology for reliability structure analysis and modeling of complex system-of-systems

Zhigeng FANG¹, Chenchen HUA¹^,*, Ding CHEN², Jingru ZHANG¹, Yadong ZHANG¹, Honghua WU¹

1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
2. Shanghai Electro-Mechanical Engineering Institute, Shanghai 201109, China

Received:2023-04-03 Online:2024-09-25 Published:2024-10-22
Contact: Chenchen HUA

摘要/Abstract

摘要：

体系各要素(系统)连接的或然性决定了其结构框架、联系逻辑和功能表现的复杂性。复杂体系可靠性结构分析与建模是解构表征其复杂特性的重要手段, 是学术界长期以来的研究热点。然而, 有关复杂体系可靠性结构、功能逻辑、计算框架的构建问题, 却尚未有较好的解决方案。针对该问题, 运用结构函数理论和图示评审技术(graphical evaluation and review technique, GERT) 建立了一种新的复杂体系可靠性结构分析框架与建模方法。首先, 基于“和联”思想建构其基于使命与任务生态联盟、行为演化的可靠性“和联”结构框架; 其次, 基于复杂体系要素的或然性逻辑联结关系, 建立其可靠性结构GERT网络模型; 最后, 运用GERT解析算法原理, 建立其可靠度计算模型, 并考虑计算的复杂性, 为该类问题提供GERT仿真(GERT simulation, GERTS)计算解决方案。以一反舰作战侦察复杂体系进行案例研究, 结果表明所提方法有效且适应性强。

关键词: 复杂体系, 可靠性分析, 结构函数, 图示评审技术

Abstract:

The probability of linking elements (systems) of system-of-systems(SoS) determines the complexity of its structure framework, connection logic and function performance. Reliability structure analysis and modeling of complex SoS is an important means to deconstruct and represent its complex characteristics, which has long been concerned by academia. However, there is no good solution to the reliability structure, functional logic and computational framework of complex SoS. To solve this problem, a new analysis framework and modeling method of complex SoS reliability structure is established by using structure function theory and graphical evaluation and review technique (GERT). Firstly, based on the idea of "plus system", it constructs its reliability "plus system" structure frame, which is based on the ecological alliance of mission and task and the evolution of behavior. Secondly, the reliability structure GERT network model is established based on the probabilistic logic connection relationship of complex SoS elements. Finally, the GERT analytic algorithm is used to establish the reliability calculation model, and the GERT simulation (GERTS) computation solution is provided for this kind of problem considering the computational complexity. A case study of an anti-ship combat reconnaissance complex SoS shows that the proposed method is effective and adaptable.

Key words: complex system-of-systems (SoS), reliability analysis, structure function, graphical evaluation and review technique (GERT)

中图分类号:

方志耕, 华晨晨, 陈顶, 张靖如, 张亚东, 吴鸿华. 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.

Zhigeng FANG, Chenchen HUA, Ding CHEN, Jingru ZHANG, Yadong ZHANG, Honghua WU. GERT network technology for reliability structure analysis and modeling of complex system-of-systems[J]. Systems Engineering and Electronics, 2024, 46(10): 3427-3436.

图/表 14

图1

图2

表1

图3

图4

图5

图6

表2

图7

图8

图9

图10

图11

图12

参考文献 32

1	胡晓峰,张斌.体系复杂性与体系工程[J].中国电子科学研究院学报,2011,6(5):446-450.
	HUX F,ZHANGB.SoS complexity and SoS engineering[J].Journal of China Academy of Electronics and Information Technology,2011,6(5):446-450.
2	MAIERM W.Architecting principles for systems-of-systems[J].Systems Engineering,1998,1(4):267-284. doi: 10.1002/(SICI)1520-6858(1998)1:4<267::AID-SYS3>3.0.CO;2-D
3	DELECOLLE A, LIMA R S, NETO V V G, et al. Architectural strategy to enhance the availability quality attribute in system-of-systems architectures: a case study[C]//Proc. of the 15th International Conference of System of Systems Engineering, 2020: 93-98.
4	葛冰峰,任长晟,赵青松,等.可执行体系结构建模与分析[J].系统工程理论与实践,2011,31(11):2191-2201.
	GEB F,RENC S,ZHAOQ S,et al.Executable architecture modeling and analysis for system-of-systems[J].Systems Engineering-Theory & Practice,2011,31(11):2191-2201.
5	王新尧,曹云峰,孙厚俊,等.基于DoDAF的有人/无人机协同作战体系结构建模[J].系统工程与电子技术,2020,42(10):2265-2274. doi: 10.3969/j.issn.1001-506X.2020.10.15
	WANGX R,CAOY F,SUNH J,et al.Modeling for cooperative combat system architecture of manned/unmanned aerial vehicle based on DoDAF[J].Systems Engineering and Electronics,2020,42(10):2265-2274. doi: 10.3969/j.issn.1001-506X.2020.10.15
6	HELA K, LAKHAL O, CONRARD B, et al. Formal approach to SoS management design[C]//Proc. of the International Conference of System of Systems Engineering, 2021: 138-143.
7	SOYEZJ,MORVANG,MERZOUKIR,et al.Multilevel agent-based modeling of system of systems[J].IEEE Systems Journal,2017,11(4):2084-2095. doi: 10.1109/JSYST.2015.2429679
8	JIN Q C, LI J C, JIANG J, et al. Research on assessment of technical importance based on weapon technology system-of-systems network model[C]//Proc. of the International Conference of System of Systems Engineering, 2020: 75-82.
9	HANQ,PANGB,LIS,et al.Evaluation method and optimization strategies of resilience for air & space defense system of systems based on kill network theory and improved self-information quantity[J].Defence Technology,2023,(21):219-239.
10	PAYUNAU,RAKSHITC,KARENM.System importance measures: definitions and application to system-of-systems analysis[J].Reliability Engineering & System Safety,2019,(191):106582.
11	李小波,王维平,林木,等.体系贡献率评估的研究框架、进展与重点方向[J].系统工程理论与实践,2019,39(6):1623-1634.
	LIX B,WANGW P,LINM,et al.The research framework, progress, and key directions of system-of systems contribution ratio evaluation[J].Systems Engineering-Theory & Practice,2019,39(6):1623-1634.
12	ZHANG H J, HUANG B Q, ZHANG P, et al. A new index for SoS reliability-viability[C]//Proc. of the International Conference on Reliability, Maintainability, and Safety, 2018: 27-30.
13	潘星,张振宇,张曼丽,等.基于SoSE的装备体系RMS论证方法研究[J].系统工程与电子技术,2019,41(8):1771-1779. doi: 10.3969/j.issn.1001-506X.2019.08.14
	PANX,ZHANGZ Y,ZHANGM L,et al.Research on RMS demonstration method of equipment SoS based on SoSE[J].Systems Engineering and Electronics,2019,41(8):1771-1779. doi: 10.3969/j.issn.1001-506X.2019.08.14
14	张喜燕. 基于Agent的区域防空体系建模与可靠性分析[D]. 武汉: 华中科技大学, 2019.
	ZHANG X Y. Agent-based modeling and reliability analysis of regional air defense system of systems[D]. Wuhan: Huazhong University of Science & Technology, 2019.
15	CHEN Z W, ZHAO T D, JIAO J, et al. System of systems architecture modeling and mission reliability analysis based on DoDAF and petri net[C]//Proc. of the Annual Reliability and Maintainability Symposium, 2019.
16	GARROA,TUNDISA.On the reliability analysis of systems and SoS: the RAMSAS method and related extensions[J].IEEE Systems Journal,2015,9(1):232-241. doi: 10.1109/JSYST.2014.2321617
17	IMAMURA M, FERREIRA F H, FERNANDES J C, et al. System-of-systems reliability: an exploratory study in a Brazilian public organization[C]//Proc. of the XVⅡ Brazilian Symposium on Information Systems, 2021.
18	TSILIPANOSK,NEOKOSMIDISI,VAROUTASD.A system of systems framework for the reliability assessment of telecommunications networks[J].IEEE Systems Journal,2013,7(1):114-124. doi: 10.1109/JSYST.2012.2207274
19	WANGH B,FEIH H,YUQ,et al.A motifs-based maximum entropy Markov model for realtime reliability prediction in system of systems[J].Journal of Systems and Software,2019,(151):180-193.
20	PRITSKER A A B. GERT-graphical evaluation and review technique[R]. Washting D. C: NASA-CR-74140, 1966.
21	BELLASC J,SAMLIA C.Improving new product planning with GERT simulation[J].California Management Review,1973,15(4):14-21. doi: 10.2307/41164453
22	CLAYTONE R,COOLEYJ W.Use of Q-GERT network simulation in reliability analysis[J].IEEE Trans.on Reliability,1981,R-30(4):321-324. doi: 10.1109/TR.1981.5221101
23	陶良彦,刘思峰,方志耕,等.GERT网络的矩阵式表达及求解模型[J].系统工程与电子技术,2017,39(6):1292-1297. doi: 10.3969/j.issn.1001-506X.2017.06.17
	TAOL Y,LIUS F,FANGZ G,et al.Matrix representation model and its solution of GERT network[J].Systems Engineering and Electronics,2017,39(6):1292-1297. doi: 10.3969/j.issn.1001-506X.2017.06.17
24	董文杰,刘思峰,陶良彦,等.多参量CF-GERT网络作用下的复杂系统风险管控[J].运筹与管理,2021,30(11):92-98.
	DONGW J,LIUS F,TAOL Y,et al.Risk management of complex system under CF-GERT network of multi-parameter variables[J].Operations Research and Management Science,2021,30(11):92-98.
25	ZHANGN,YANS L,FANGZ G,et al.Fuzzy GERT model based on z-tag and its application in weapon equipment management[J].Journal of Intelligent & Fuzzy Systems,2021,40(6):12503-12519.
26	陈达强,张少博,王海燕,等.食品质量链风险传递耦合网络研究[J].系统工程理论与实践,2022,42(4):1093-1106.
	CHEND Q,ZHANGS B,WANGH Y,et al.Research on food quality chain risk propagation with multilayer coupling network[J].Systems Engineering-Theory & Practice,2022,42(4):1093-1106.
27	ZHAOJ L,XUEZ,LIT,et al.An energy and time prediction model for remanufacturing process using graphical evaluation and review technique (GERT) with multivariant uncertainties[J].Environmental Science and Pollution Research,2021,1-13.
28	DONGW J,LIUS F,FANGZ G,et al.A model based on hidden graphic evaluation and review technique network to evaluate reliability and lifetime of multi-state systems[J].Proc.of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability,2019,233(3):369-378.
29	FANGZ G,WUS,ZHANGX 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.
30	WANGZ,LIUS F,FANGZ G.Research on SoS-GERT network model for equipment system of systems contribution eva-luation based on joint operation[J].IEEE Systems Journal,2020,14(3):4188-4196.
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
	FANGZ G,XIAY X,ZHANGJ 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	郭位, 朱晓岩. 系统重要性测度原理与应用[M]. 苗强, 王冬, 译. 北京: 国防工业出版社, 2014: 11-14.
	GUO W, ZHU X Y. Importance measures in reliability, risk and optimization: principles and applications[M]. MIAO Q, WANG D. Trans. Beijing: National Defense Industry Press, 2014: 11-14.

节点	节点含义
	r₁表示节点u第1次实现要求完成的引入活动数; r₂表示节点u第2次以及以后各次实现要求完成的引入活动数; u为节点编号; 肯定型输出
	r₁表示节点u第1次实现要求完成的引入活动数; r₂表示节点u第2次以及以后各次实现要求完成的引入活动数; u为节点编号; 概率型输出

[1]	曾颖, 李彦锋, 王弘毅, 钱华明, 黄洪钟. 联合MRGP和PSO的工业机器人驱动器可靠性分析[J]. 系统工程与电子技术, 2023, 45(8): 2643-2650.
[2]	李军亮, 祝华远, 王正, 王利明, 张鑫磊. 基于混合Gamma分布的机载产品可靠性建模[J]. 系统工程与电子技术, 2023, 45(2): 614-620.
[3]	方志耕, 夏悦馨, 张靖如, 熊仪, 陈静邑. 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.
[4]	李懿凡, 钱华明, 黄洪钟, 张庭瑜, 黄土地. 基于广义连续时间贝叶斯网络的指挥控制网络系统可靠性分析[J]. 系统工程与电子技术, 2022, 44(12): 3880-3886.
[5]	王鹏, 孙紫荆, 张帆, 肖国松. 考虑概率型共因失效的多阶段任务系统可靠性分析模型[J]. 系统工程与电子技术, 2022, 44(12): 3887-3898.
[6]	毛泽龙, 王治华, 吴琼, 刘成瑞. 双指标阶段性退化建模及可靠性分析[J]. 系统工程与电子技术, 2021, 43(12): 3725-3731.
[7]	方志耕, 邵瑞瑞, 王召, 刘思峰, 游伟青, 高素. 高轨卫星通信星座PS-GERT效能评估模型[J]. 系统工程与电子技术, 2020, 42(10): 2356-2365.
[8]	陈宇奇, 徐廷学, 李志强, 李海君. 基于证据GO法的复杂多态系统动态可靠性分析[J]. 系统工程与电子技术, 2020, 42(1): 230-237.
[9]	李孝鹏, 黄洪钟, 李福秋. 基于PRA的复杂航天多阶段任务系统可靠性分析[J]. 系统工程与电子技术, 2019, 41(9): 2141-2147.
[10]	杨乐昌, 郭艳玲. 基于贝叶斯混合概率分布融合的系统可靠性分析与预测方法[J]. 系统工程与电子技术, 2018, 40(7): 1660-1668.
[11]	兰杰, 袁宏杰, 夏静. 基于离散时间贝叶斯网络的动态故障树分析的改良方法[J]. 系统工程与电子技术, 2018, 40(4): 948-953.
[12]	曹颖赛, 刘思峰, 方志耕, 张秦. 多态系统可靠性分析广义灰色贝叶斯网络模型[J]. 系统工程与电子技术, 2018, 40(1): 231-237.
[13]	陶良彦, 刘思峰, 方志耕, 陈顶. GERT网络的矩阵式表达及求解模型[J]. 系统工程与电子技术, 2017, 39(6): 1292-1297.
[14]	刘红旗1,2, 方志耕1,2, 陶良彦1,2. 复杂装备研制项目进度规划GERT网络“反问题”模型[J]. 系统工程与电子技术, 2015, 37(12): 2758-2763.
[15]	闫华, 武小悦. 航天测控通信系统可靠性分析的改进Krylov投影算法[J]. Journal of Systems Engineering and Electronics, 2012, 34(10): 2180-2186.

复杂体系可靠性结构分析与建模GERT网络技术

GERT network technology for reliability structure analysis and modeling of complex system-of-systems

RichHTML

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

图/表 14

参考文献 32

相关文章 15

编辑推荐

Metrics

本文评价

状态	b₁₁	b₂₁	b₂₂	c	Ψ₂
1	0	0	0	0	0
2	1	0	0	0	0
3	0	1	0	0	0
4	0	0	1	0	0
5	0	0	0	1	0
6	1	1	0	0	0
7	1	0	1	0	0
8	1	0	0	1	0
9	0	1	1	0	0
10	0	1	0	1	0
11	0	0	1	1	0
12	1	1	1	0	0
13	1	1	0	1	0
14	1	0	1	1	1
15	0	1	1	1	1
16	1	1	1	1	1