考虑时间相关故障的多状态系统可靠性与任务成功性仿真评估方法

doi:10.12305/j.issn.1001-506X.2021.08.40

摘要/Abstract

摘要：

针对考虑时间相关故障、多状态性能输出、系统冗余储备等因素的系统可靠性与任务成功性评估问题使用解析法难以建模求解, 而一般仿真方法又存在抽样效率慢和估值精度低的问题, 提出具有时间相关故障抽样与统计方差减小相结合的蒙特卡罗仿真评估方法。首先，设计了非指数剩余分布抽样的数值计算方法, 实现了时间相关故障的随机事件抽样。其次，在此基础上结合受迫转移、失效偏倚等方差减小方法, 提高了小概率事件的仿真抽样效率, 改善了仿真评估方法的估值精度。最后，通过舰船航渡任务的算例, 验证了该方法对评估复杂系统行为和故障机制条件下系统可靠性及任务成功性的合理性和有效性。

关键词: 任务可靠性, 多状态系统, 非指数分布, 蒙特卡罗间接仿真法, 方差减小方法

Abstract:

Aiming at the problem of system reliability and mission success probability assessment considering time-dependent faults, multi-state performance output, and system redundancy, the analytical method is difficult to model and solve, and the general simulation method has poor sampling efficiency and low estimation accuracy. A Monte-Carlo simulation assessment method combining time-dependent faults sampling and statistical variance reduction is proposed. First, a numerical algorithm for non-exponential residual distribution sampling is designed to implement random event sampling for time-dependent faults. Then, combining with the variance reduction methods such as forced transition and failure biasing, the simulation sampling efficiency of small probability events and the estimation accuracy of the simulation method are improved. Finally, the example of the warship's sail mission verifies the rationality and effectiveness of the proposed method for assessing the system reliability and mission success probability under complex system behavior and fault mechanism.

Key words: mission reliability, multi-state system, non-exponential distribution, indirect Monte-Carlo, variance reduction method

中图分类号:

杨皓洁, 吕建伟, 徐一帆. 考虑时间相关故障的多状态系统可靠性与任务成功性仿真评估方法[J]. 系统工程与电子技术, 2021, 43(8): 2362-2372.

Haojie YANG, Jianwei LYU, Yifan XU. Simulation assessment method for multi-state system reliability and mission success probability considering time-dependent faults[J]. Systems Engineering and Electronics, 2021, 43(8): 2362-2372.

图/表 20

图1

图2

图3

图4

图5

图6

图7

表1

图8

表2

表3

图9

表4

图10

图11

图12

图13

图14

表5

图15

参考文献 30

1	CHANG Y R , AMARI S V , KUO S Y . OBDD-based evaluation of reliability and importance measures for multistate systems subject to imperfect fault coverage[J]. IEEE Trans.on Depen-dable and Secure Computing, 2005, 2 (4): 336- 347. doi: 10.1109/TDSC.2005.51
2	XING L D . Reliability analysis of nonrepairable cold-standby systems using sequential binary decision diagrams[J]. IEEE Trans.on Systems Man and Cybernetics Part A, 2012, 42 (3): 715- 726. doi: 10.1109/TSMCA.2011.2170415
3	LEUNG K N F , ZHANG Y L , LAI K K . Analysis for a two-dissimilar-component cold standby repairable system with repair priority[J]. Reliability Engineering and System Safety, 2011, 96 (11): 1542- 1551. doi: 10.1016/j.ress.2011.06.004
4	史跃东, 金家善, 徐一帆. 半马尔可夫跃迁历程下装备复杂系统多状态可靠性分析与评估[J]. 系统工程与电子技术, 2019, 41 (2): 222- 230.
	SHI Y D , JIN J S , XU Y F . Multi-state reliability analysis and assessment for complex technical system under semi-Markov process[J]. Systems Engineering and Electronic, 2019, 41 (2): 222- 230.
5	WANG C , XING L , AMARI S V . A fast approximation method for reliability analysis of cold-standby systems[J]. Reliability Engineering and System Safety, 2012, 106- 119, 126.
6	LI S M , SUN S D , SI S B , et al. Decision diagram based methods and reliability analysis for k-out-of-n: G systems[J]. Journal of Mechanical Science and Technology, 2014, 28 (10): 3917- 3923. doi: 10.1007/s12206-014-0902-z
7	SHRESTHA A , XING L D , DAI Y W . Decision diagram based methods and complexity analysis for multi-state systems[J]. IEEE Trans.on Reliability, 2010, 59 (1): 145- 161. doi: 10.1109/TR.2009.2034946
8	ZHAI Q Q , XING L D , PENG R , et al. Multi-valued decision diagram-based reliability analysis of k-out-of-n cold standby systems subject to scheduled backups[J]. IEEE Trans.on Reliability, 2015, 64 (4): 1310- 1324. doi: 10.1109/TR.2015.2404891
9	AOKI H, YAMASHITA S, MINATO S. An efficient algorithm for constructing a sequence binary decision diagram representing a set of reversed sequences[C]//Proc. of the Granular Computing, 2011.
10	SHRESTHA A , XING L D . A logarithmic binary decision diagram-based method for multistate system analysis[J]. IEEE Trans.on Reliability, 2008, 57 (4): 595- 606. doi: 10.1109/TR.2008.2006038
11	LI Y F, ZIO E. A multi-state power model for adequacy assessment of distributed generation via universal generating function[EB/OL]. [2020-06-16]. http://arxiv.org/abs/1206.6808.
12	LI Y F , ZIO E . A multi-state model for the reliability assessment of a distributed generation system via universal generating function[J]. Reliability Engineering & System Safety, 2012, 106 (1): 28- 36.
13	GE D C , LI D , LIN M , et al. SFRs-based numerical simulation for the reliability of highly-coupled DFTS[J]. Eksploatacja I Niezawodnosc Maintenance and Reliability, 2015, 17 (2): 199- 206. doi: 10.17531/ein.2015.2.5
14	LEVITIN G , XING L , ZONOUZ A E , et al. Heterogeneous warm standby multi-phase systems with variable mission time[J]. IEEE Trans.on Reliability, 2016, 65 (1): 381- 393. doi: 10.1109/TR.2015.2451271
15	LIANG X F, HONG Y, ZHANG Y F, et al. A numerical simu lation approach for reliability analysis of fault-tolerant repairable system[C]//Proc. of the International Conference on Reliability, 2009.
16	苏续军, 吕学志. 基于离散事件仿真的多状态多阶段任务系统可靠性分析[J]. 兵工学报, 2017, 38 (4): 776- 784. doi: 10.3969/j.issn.1000-1093.2017.04.020
	XU X J , LYU X Z . Reliability analysis of phased-mission system with multiple states based on discrete event simulation[J]. Acta Armamentarii, 2017, 38 (4): 776- 784. doi: 10.3969/j.issn.1000-1093.2017.04.020
17	JIA X , GUO B . Analysis of non-repairable cold-standby systems in Bayes theory[J]. Journal of Statistical Computation & Simulation, 2016, 86 (11): 2089- 2112.
18	OZGE D , EMMANUEL R M J . A generic method for estimating system reliability using Bayesian networks[J]. Reliability Engineering and System Safety, 2017, 94 (2): 542- 550.
19	WU X Y , WU X Y . Extended object-oriented Petri net model for mission reliability simulation of repairable PMS with common cause failures[J]. Reliability Engineering and System Safety, 2015, 136 (4): 109- 119.
20	FAULIN J , JUAN A A , MARTORELL S , et al. Simulation methods for reliability and availability of complex systems[M]. Berlin: Springer Series in Reliability Engineering, 2010.
21	LEWIS E E, BOEH M. Monte Carlo simulation of complex system mission reliability[C]//Proc. of the Winter Simulation Conference, 1989.
22	XIAO G , LI Z Z , LI T . Dependability estimation for non-Markov consecutive-k-out-of-n: F repairable systems by fast simulation[J]. Reliability Engineering & System Safety, 2007, 92 (3): 293- 299.
23	ZIO E . The Monte Carlo simulation method for system reliability and risk analysis[M]. Berlin: Springer Series in Reliability Engineering, 2013.
24	ESTECAHANDY M , BORDES L , COLLAS S , et al. Some acce-leration methods for Monte Carlo simulation of rare events[J]. Reliability Engineering & System Safety, 2015, 144, 296- 310.
25	梁善勇, 王江安, 张峰. 基于舰船尾流激光雷达的Monte Carlo模型及方差消减方法研究[J]. 物理学报, 2013, 62 (1): 266- 273.
	LIANG S Y , WANG J A , ZHANG F . Monte Carlo model and variance reduction method based on lidar of ship wake[J]. Acta Physica Sinica, 2013, 62 (1): 266- 273.
26	许双伟, 武小悦. 单测控站测控任务可靠性仿真的高效方法[J]. 系统工程理论与实践, 2012, 32 (6): 1385- 1390. doi: 10.3969/j.issn.1000-6788.2012.06.026
	XU S W , WU X Y . Efficient reliability simulation method for TT&C mission executed by single TT&C station[J]. System Engineering-Theory & Practice, 2012, 32 (6): 1385- 1390. doi: 10.3969/j.issn.1000-6788.2012.06.026
27	BLANCHET J, LAM H. Rare event simulation techniques[C]//Proc. of the Winter Simulation Conference, 2011.
28	肖刚, 吴俊. 剩余分布抽样及其在非马尔可夫可修系统可靠性数字仿真中的应用[J]. 强度与环境, 1997, (3): 58- 65.
	XIAO G , WU J . The sampling method for remain distribution and its application in the simulation of non-Markov repairable system[J]. Structure & Environment Engineering, 1997, (3): 58- 65.
29	吕建伟, 郭顺合, 徐一帆, 等. 基于多智能体仿真的舰船动力系统航渡任务成功性研究[J]. 系统工程与电子技术, 2019, 41 (8): 1896- 1902.
	LYU J W , GUO S H , XU Y F , et al. Research on mission success-ability of ship propulsion system based on multi-agent simulation[J]. Systems Engineering & Electronic, 2019, 41 (8): 1896- 1902.
30	吕建伟, 余鹏, 杨建军. 舰船航渡过程中的松弛时间与航渡策略问题[J]. 海军工程大学学报, 2012, 24 (2): 25- 28.
	LYU J W , YU P , YANG J J . Relaxation time and sailing strategy of naval vessel in voyage[J]. Journal of Naval University of Engineering, 2012, 24 (2): 25- 28.

类型	任务成功性	目标①任务结束时刻舰船位置	目标②任务结束时刻舰船状态
到达目标区	任务成功	到达目标区域	总体可用, 各分系统、设备完好
到达目标区	任务成功	到达目标区域	总体可用, 某分系统或设备处于降级、一般或致命故障
航速超限	任务失败	未到达目标区域	总体可用
维修超时	任务失败	是否到达不确定	由于一般故障导致的舰船总体不可用, 宕机
致命故障	任务失败	未到达目标区域	由于致命故障导致的舰船总体不可用, 宕机

设备	降级λ_{·, 2}		一般故障λ_{·, 1}		致命故障λ_{·, 0}		修复μ_{·, 3}
设备	η	b	η	b	η	b	η	b
柴油机	2 500	1.5	2 500	1.5	25 000	1.0	8.0	5.0
燃气轮机	4 000	1.3	4 000	1.3	40 000	1.0	32.0	6.0
监控设备	-	-	10 000	2.0	-	-	0.5	6.5
辅助设备	-	-	3 000	1.2	-	-	5.0	5.9
轴系、螺旋桨	-	-	1 500	1.5	15 000	1.0	18.0	4.5
柴油发电机组	-	-	2 000	1.5	20 000	1.0	40.0	5.3

柴油机1	柴油机2	燃气轮机	功率输出系数/%
3	3	-	100.0
-	-	3	100.0
2	3	小于3	60.0
3	2	小于3	60.0
小于3	-	2	60.0
-	小于3	2	60.0
2	2	小于2	0.0
小于2	-	小于2	0.0
-	小于2	小于2	0.0

任务结束类型	受迫转移 & 失效偏倚	蒙特卡罗间接仿真
任务成功概率	0.996 1	0.996 1
航速超限概率(10^-3)	3.012 4	3.080 0
维修超时概率(10^-4)	8.571 4	8.000 0
致命故障概率(10^-5)	2.135 4	1.000 0

任务结束类型	威布尔分布	指数分布
任务成功概率	0.996 1	0.991 6
航速超限概率(10^-3)	3.012 4	6.335 2
维修超时概率(10^-4)	8.571 4	20.202 0
致命故障概率(10^-5)	2.135 4	2.789 5