冲击环境下多状态系统可靠性评估和韧性分析

doi:10.12305/j.issn.1001-506X.2026.05.14

系统工程与电子技术 ›› 2026, Vol. 48 ›› Issue (5): 1581-1589.doi: 10.12305/j.issn.1001-506X.2026.05.14

冲击环境下多状态系统可靠性评估和韧性分析

景永峰¹, 褚嘉运², 关亮³, 焦健¹^,*, 兑红炎⁴

1. 北京航空航天大学可靠性与系统工程学院，北京 100191
2. 中国运载火箭技术研究院，北京 100076
3. 中国船舶集团有限公司，上海 200011
4. 郑州大学管理学院，河南郑州 450001

收稿日期:2024-12-31 出版日期:2026-05-27 发布日期:2026-05-27
通讯作者: 焦健
作者简介:景永峰（1997—），男，博士研究生，主要研究方向为复杂系统可靠性与安全性
褚嘉运（1995—），男，工程师，博士，主要研究方向为复杂系统及体系可靠性建模仿真
关　亮（1988—），男，高级工程师，硕士，主要研究方向为系统工程
兑红炎（1982—），男，教授，博士，主要研究方向为复杂系统可靠性与集群韧性
基金资助:
国家自然科学基金（72301296）资助课题

Multi-state system reliability evaluation and resilience analysis in shock environments

Yongfeng JING¹, Jiayun CHU², Liang GUAN³, Jian JIAO¹^,*, Hongyan DUI⁴

1. School of Reliability and Systems Engineering，Beihang University，Beijing 100191，China
2. China Academy of Launch Vehicle Technology，Beijing 100076，China
3. China State Shipping Corporation Limited，Shanghai 200011，China
4. School of Management，Zhengzhou University，Zhengzhou 450001，China

Received:2024-12-31 Online:2026-05-27 Published:2026-05-27
Contact: Jian JIAO

摘要/Abstract

摘要：

随着全球工业快速发展和智能化转型，系统结构日益复杂并呈现多状态特性，其可靠运行能力直接影响生产效率与产品质量。对此，基于状态性能分布及其转移特性评估冲击环境下的多状态系统的可靠性，进而提出综合韧性评价指标。考虑可靠性和成本约束构建多状态系统综合韧性优化模型，并以焊接机器人为例验证模型的有效性。案例结果表明，在多冲击场景下，经维修后系统综合韧性恢复至1.000，可靠性为0.953。与传统韧性分析模型相比，所提方法能够更全面地反映外部冲击、维修及更换对系统韧性的影响，为工业系统的可靠运行提供了技术途径。

关键词: 可靠性, 性能, 韧性, 多状态系统

Abstract:

With the rapid development and intelligent transformation of global industry, system structures are becoming increasingly complex and exhibit multi-state characteristics, and their reliable operation capability directly affects production efficiency and product quality. In response, based on state performance distribution and its transition characteristics, the reliability of multi-state systems under shock environments is evaluated, and then a comprehensive resilience evaluation index is proposed. A comprehensive resilience optimization model of multi-state system is constructed considering reliability and cost constraints, and the effectiveness of the model is verified by taking welding robots as an example. The case results show that under multi-shock scenarios, the comprehensive resilience of the system is restored to 1.000 after maintenance, with a reliability of 0.953. Compared with traditional resilience analysis models, the proposed method can more comprehensively reflect the impacts of external shocks, maintenance and replacement on system resilience, providing a technical approach for the reliable operation of industrial systems.

Key words: reliability, performance, resilience, multi-state system

中图分类号:

N 945

景永峰, 褚嘉运, 关亮, 焦健, 兑红炎. 冲击环境下多状态系统可靠性评估和韧性分析[J]. 系统工程与电子技术, 2026, 48(5): 1581-1589.

Yongfeng JING, Jiayun CHU, Liang GUAN, Jian JIAO, Hongyan DUI. Multi-state system reliability evaluation and resilience analysis in shock environments[J]. Systems Engineering and Electronics, 2026, 48(5): 1581-1589.

图/表 10

图1

图2

表1

图3

图4

图5

表2

图6

图7

表3

参考文献 32

1	杨丹辉, 邵军. 新型工业化推动构建现代化产业体系的理论逻辑与实现路径[J]. 南京社会科学, 2025, (1): 39- 48. doi: 10.15937/j.cnki.issn1001-8263.2025.01.005
	YANG D H, SHAO J. Theoretical logic and implementation path of new industrialization promoting the construction of modern industrial system[J]. Nanjing Social Sciences, 2025, (1): 39- 48. doi: 10.15937/j.cnki.issn1001-8263.2025.01.005
2	FRIEDERICH J, LAZAROVA-MOLNAR S. Reliability assessment of manufacturing systems: a comprehensive overview, challenges and opportunities[J]. Journal of Manufacturing Systems, 2024, 72, 38- 58.
3	RODA I, MACCHI M. Factory-level performance evaluation of buffered multi-state production systems[J]. Journal of Manufacturing Systems, 2019, 50, 226- 235. doi: 10.1016/j.jmsy.2018.12.008
4	XIA W F, WANG Y H, HAO Y C, et al. Reliability analysis for complex electromechanical multi-state systems utilizing universal generating function techniques[J]. Reliability Engineering & System Safety, 2024, 244, 109911. doi: 10.1016/j.ress.2023.109911
5	YAN X H, LI J L, LIU N. Refined multi-state modeling based battery energy storage system reliability indicators and evaluation[J]. Applied Energy, 2025, 393, 126038. doi: 10.1016/j.apenergy.2025.126038
6	HUANG D H. Evaluation and management of sustainable supply chain systems with carbon emissions and transport damage based on multi-state system reliability assessment[J]. Reliability Engineering & System Safety, 2025, 257, 110821. doi: 10.1016/j.ress.2025.110821
7	ZHANG C, QIAO J M, WANG S P, et al. Importance measures based on system performance loss for multi-state phased-mission systems[J]. Reliability Engineering & System Safety, 2025, 256, 110776. doi: 10.1016/j.ress.2024.110776
8	NIU Y F, WANG J F, XU X Z, et al. Reliability evaluation for a multi-commodity multi-state distribution network under transportation emission consideration[J]. Reliability Engineering & System Safety, 2025, 254, 110599. doi: 10.1016/j.ress.2024.110599
9	LI X Y, LI H, XIONG X, et al. Reliability modeling of multi-state phased mission systems with random phase durations and dynamic combined phases[J]. Reliability Engineering & System Safety, 2025, 253, 110524. doi: 10.1016/j.ress.2024.110524
10	陈童, 胡斌, 狄鹏. 舰船发电系统多状态可靠性马尔可夫报酬模型[J]. 兵工学报, 2023, 44 (10): 3177- 3186. doi: 10.12382/bgxb.2022.0558
	CHEN T, HU B, DI P. Multi-state reliability Markov reward model for ship power generation system[J]. Acta Armamentarii, 2023, 44 (10): 3177- 3186. doi: 10.12382/bgxb.2022.0558
11	史跃东, 金家善, 柴凯. 大型复杂系统多态可靠性快速评估算法[J]. 系统工程与电子技术, 2022, 44 (10): 3282- 3290.
	SHI Y D, JIN J S, CHAI K. Fast evaluation algorithm for multi-state reliability of large complex systems[J]. Systems Engineering and Electronics, 2022, 44 (10): 3282- 3290.
12	段建国, 李爱平, 谢楠, 等. 可重构制造系统多态可靠性建模与分析[J]. 机械工程学报, 2011, 47 (17): 104- 111. doi: 10.3901/JME.2011.17.104
	DUAN J G, LI A P, XIE N, et al. Multi-state reliability modeling and analysis of reconfigurable manufacturing systems[J]. Journal of Mechanical Engineering, 2011, 47 (17): 104- 111. doi: 10.3901/JME.2011.17.104
13	WANG F, TIAN J, LING J M, et al. A multi-stage resilience analysis framework of critical infrastructure systems based on component importance measures[J]. Reliability Engineering & System Safety, 2025, 256, 110720. doi: 10.1016/j.ress.2024.110720
14	HE Y X, ZIO E, YANG Z M, et al. A systematic resilience assessment framework for multi-state systems based on physics-informed neural network[J]. Reliability Engineering & System Safety, 2025, 257, 110866. doi: 10.1016/j.ress.2025.110866
15	SU J S, LI J J, WU D Q, et al. Lifetime seismic damage evolution and resilience assessment of offshore bridges under height-varying corrosion and scour[J]. Ocean Engineering, 2025, 326, 120883. doi: 10.1016/j.oceaneng.2025.120883
16	DONG S J, GAO X Y, MOSTAFAVI A, et al. Characterizing resilience of flood-disrupted dynamic transportation network through the lens of link reliability and stability[J]. Reliability Engineering & System Safety, 2023, 232, 109071. doi: 10.1016/j.ress.2022.109071
17	葛路琨, 朱乐为, 侯恺, 等. 基于可靠性指标复用的地震灾害配电网韧性评估方法[J]. 电力系统及其自动化学报, 2024, 36 (10): 1- 10.
	GE L K, ZHU L W, HOU K, et al. Resilience assessment method for earthquake disaster distribution network based on reliability index reuse[J]. Journal of Power System and Automation, 2024, 36 (10): 1- 10.
18	程杉, 冉涛, 喻磊, 等. 考虑配电网全过程韧性提升的多类型韧性资源分布鲁棒机会约束规划[J]. 电网技术, 2025, (1): 157- 166. doi: 10.13335/j.1000-3673.pst.2024.0256
	CHENG S, RAN T, YU L, et al. Robust opportunity-constrained planning for distribution of multi-type resilience resources considering whole-process resilience enhancement of distribution network[J]. Power System Technology, 2025, (1): 157- 166. doi: 10.13335/j.1000-3673.pst.2024.0256
19	YOUNESI A, SHAYEGHI H, SAFARI A, et al. Assessing the resilience of multi microgrid based widespread power systems against natural disasters using Monte Carlo Simulation[J]. Energy, 2020, 207, 118220. doi: 10.1016/j.energy.2020.118220
20	SHEHADEH A, ALSHBOUL O, SALEH E. Enhancing safety and reliability in multistory construction: a multi-state system assessment of shoring/reshoring operations using interval-valued belief functions[J]. Reliability Engineering & System Safety, 2024, 252, 110458. doi: 10.1016/j.ress.2024.110458
21	KOZYRA P M. A parallel algorithm for reliability assessment of multi-state flow networks based on simultaneous finding of all multi-state minimal paths and performing state space decomposition[J]. Reliability Engineering & System Safety, 2024, 251, 110376. doi: 10.1016/j.ress.2024.110376
22	GEURTSEN M, ADAN I, ATAN Z. Planning of multi-production line maintenance[J]. Journal of Manufacturing Systems, 2024, 75, 174- 193. doi: 10.1016/j.jmsy.2024.06.003
23	BO Y M, BAO M L, DING Y, et al. A DNN-based reliability evaluation method for multi-state series-parallel systems considering semi-Markov process[J]. Reliability Engineering & System Safety, 2024, 242, 109604. doi: 10.1016/j.ress.2023.109604
24	LYU H, QU H C, XIE H L, et al. Reliability analysis of the multi-state system with nonlinear degradation model under Markov environment[J]. Reliability Engineering & System Safety, 2023, 238, 109411. doi: 10.1016/j.ress.2023.109411
25	WU B, LIMNIOS N. A comparative study of numerical methods for reliability assessment based on semi-Markov processes[J]. Reliability Engineering & System Safety, 2024, 252, 110431. doi: 10.1016/j.ress.2024.110431
26	MITTAL N, IVANOVA N, JAIN V, et al. Reliability and availability analysis of high-altitude platform stations through semi-Markov modeling[J]. Reliability Engineering & System Safety, 2024, 252, 110419. doi: 10.1016/j.ress.2024.110419
27	DUI H Y, LU Y, WU S M. Competing risks-based resilience approach for multi-state systems under multiple shocks[J]. Reliability Engineering & System Safety, 2024, 242, 109773. doi: 10.1016/j.ress.2023.109773
28	TAN Z Z, WU B, CHE A. Resilience modeling for multi-state systems based on Markov processes[J]. Reliability Engineering & System Safety, 2023, 235, 109207. doi: 10.1016/j.ress.2023.109207
29	DUAN Y T, HU B, RI S, et al. A hybrid multi-criteria decision-making model for waste facilities location considering system resilience[J]. Computers & Industrial Engineering, 2024, 193, 110326. doi: 10.1016/j.cie.2024.110326
30	陈茂爱, 任文建, 蒋元宁. 焊接机器人技术[M]. 2版. 北京: 化学工业出版社, 2023.
	CHEN M A, REN W J, JIANG Y N. Welding robot technology[M]. 2nd ed. Beijing: Chemical Industry Press, 2023.
31	WANG Y, WANG X W, CHEN S Y, et al. Integrated scheduling for ring layout multi-station multi-robot welding system with dual function robots and jump stations operations[J]. Journal of Manufacturing Systems, 2025, 80, 976- 994. doi: 10.1016/j.jmsy.2025.04.012
32	陈志伟, 王靖, 谷长超, 等. 考虑动态重构的装备体系可用性及弹性分析[J]. 系统工程与电子技术, 2021, 43 (8): 2347- 2354. doi: 10.12305/j.issn.1001-506X.2021.08.38
	CHEN Z W, WANG J, GU C C, et al. Availability and resilience analysis of equipment system considering dynamic reconfiguration[J]. Systems Engineering and Electronics, 2021, 43 (8): 2347- 2354. doi: 10.12305/j.issn.1001-506X.2021.08.38

冲击等级及维修	子系统A（机械本体和减速器）状态转移的时间分布函数
Ⅱ	$ {\varPhi }_{\left(1{,}2\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.018t\right)}^{2}}} $，$ {\varPhi}_{\left(2{,}3\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.014t\right)}^{2.3}}} $，$ {\varPhi }_{\left(3{,}4\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.013t\right)}^{2.7}}} $，$ {\varPhi }_{\left(4{,}5\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.013t\right)}^{2.9}}} $
Ⅲ	$ {\varPhi }_{\left(1{,}3\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.021t\right)}^{2.3}}} $，$ {\varPhi }_{\left(2{,}4\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.02t\right)}^{2.5}}} $，$ {\varPhi }_{\left(3{,}5\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.023t\right)}^{2.7}}} $，$ {\varPhi }_{\left(4{,}5\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-(0.02t)}^{3.5}}} $
Ⅳ	$ {\varPhi }_{\left(1{,}4\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.03t\right)}^{2.5}}} $，$ {\varPhi }_{\left(2{,}5\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.03t\right)}^{3.0}}} $，$ {\varPhi }_{\left(3{,}5\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.03t\right)}^{3.0}}} $，$ {\varPhi }_{\left(3{,}4\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-(0.035t)}^{3.2}}} $
维修时	$ {\varPhi }_{\left(3{,}2\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.05t\right)}^{2}}} $，$ {\varPhi }_{\left(4{,}3\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.032t\right)}^{2}}} $，$ {\varPhi }_{\left(4{,}2\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-\left(0.022t\right)}^{2}}} $，$ {\varPhi }_{\left(5{,}1\right)}\left(t\right)=1-{{\mathrm{e}}}^{{{-(0.05t)}^{3}}} $

时间点	事件	综合韧性	可靠性	总成本
20	第1次II级冲击发生	1.000	1.000	120.132
121.364	第2次II冲击发生	0.471	0.904	465.323
172.614	第2次II级冲击结束	0.278	0.761	1482.173
172.614	第1次预防性维修开始	0.278	0.761	1482.173
188.121	第1次预防性维修结束	0.511	0.887	1593.793
225.312	第3次II冲击发生	0.511	0.887	1815. 413
276.812	第3次II冲击结束	0.322	0.771	2038.147
276.812	第2次预防性维修开始	0.322	0.771	2038.147
291.648	第2次预防性维修结束	0.513	0.912	2185.954
365	仿真结束	0.513	0.912	2373.286

时间点	事件	综合韧性	可靠性	总成本
25	第1次IV级冲击发生	1.000	1.000	286.439
53.562	第1次IV级冲击结束	0.661	0.824	674.423
53.562	第1次事后维修开始	0.661	0.824	674.423
73.639	第1次事后维修结束	0.837	0.943	872.832
124.684	第2次II级冲击发生	0.837	0.943	1026.532
171.742	第2次II级冲击结束	0.572	0.825	1208.493
171.742	预防性维修开始	0.572	0.825	1208.493
188.783	预防性维修结束	0.780	0.907	1327.063
228.106	第3次III级冲击发生	0.780	0.907	1725.392
269.482	第3次III级冲击结束	0.458	0.785	2638.156
269.482	第2次事后维修开始	0.458	0.785	2638.156
298.952	第2次事后维修结束	0.739	0.894	2846.832
301.407	更换维修开始	0.000	0.894	3658.738
310.407	更换维修结束	1.000	0.953	4106.843
365	仿真结束	1.000	0.953	4106.843

[1]	贾祥, 潘正强, 程志君. 面向数字装备性能鉴定的试验样本量确定方法[J]. 系统工程与电子技术, 2026, 48(6): 1965-1971.
[2]	王昱, 邱浩波, 何小二, 王铭靖, 蒋琛, 高亮. 基于相似产品先验的产品Bayes可靠性验证[J]. 系统工程与电子技术, 2026, 48(6): 1972-1979.
[3]	谭诗翰, 石全, 胡起伟, 白永生, 朱敦祥, 张芳, 柯鹏. 考虑多种故障模式和多阶段故障过程的装备预防性维修策略优化模型[J]. 系统工程与电子技术, 2026, 48(3): 908-917.
[4]	李肖肖, 翟琛, 常莉莉, 邵方芳. 多状态部件的预防性维修策略解算方法[J]. 系统工程与电子技术, 2026, 48(3): 962-969.
[5]	刘瑞华, 鹿繁鹏, 马赞. 国产民机导航系统MBSE建模及终端区RNP运行仿真[J]. 系统工程与电子技术, 2026, 48(2): 588-602.
[6]	杨克巍, 徐任杰, 姜九瑶, 李际超, 杨志伟, 宫琳. 面向作战的体系韧性评估方法研究综述及展望[J]. 系统工程与电子技术, 2026, 48(1): 157-171.
[7]	褚健, 潘星, 呼伦呼, 魏金鹏, 刘振祥. 基于不确定随机Bow-tie模型的航空保障人因风险评估[J]. 系统工程与电子技术, 2025, 47(9): 3022-3030.
[8]	柳佳豪, 徐任杰, 孙茂桐, 姜九瑶, 李际超, 杨克巍. 基于强化学习的装备体系韧性优化方法[J]. 系统工程与电子技术, 2025, 47(7): 2216-2223.
[9]	李明华, 潘星, 张耐民, 胡彭炜, 党宇恒. 装备体系可靠性理论及航天工程实践[J]. 系统工程与电子技术, 2025, 47(7): 2304-2313.
[10]	李毅恒, 夏群利, 王明凯. 基于高阶固定时间观测器的高超变体飞行器预设性能控制[J]. 系统工程与电子技术, 2025, 47(5): 1627-1637.
[11]	贾朝波, 于雷, 位寅生. 多准则联合的频谱兼容波形快速优化方法[J]. 系统工程与电子技术, 2025, 47(4): 1036-1047.
[12]	关旗龙, 杭春进, 李胜利, 唐晓玖, 于丹, 丁颖. 深空环境下电子器件可靠性研究进展[J]. 系统工程与电子技术, 2025, 47(4): 1184-1194.
[13]	孙正阳, 杜晔. 基于改进萤火虫算法的卫星网络路由优化方法[J]. 系统工程与电子技术, 2025, 47(4): 1346-1354.
[14]	沈夏闰, 李若楠, 张昊田. 基于CVAE-LSTM的服务器KPI异常检测[J]. 系统工程与电子技术, 2025, 47(3): 1019-1027.
[15]	汪兵, 张圣鹋, 杨益川, 周黎明, 顾杰, 高昭昭. 非相干两点源比幅测角性能分析[J]. 系统工程与电子技术, 2025, 47(10): 3179-3187.

冲击环境下多状态系统可靠性评估和韧性分析

Multi-state system reliability evaluation and resilience analysis in shock environments

RichHTML

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

图/表 10

参考文献 32

相关文章 15

编辑推荐

Metrics

本文评价