大型复杂系统多态可靠性快速评估算法

doi:10.12305/j.issn.1001-506X.2022.10.35

Abstract

Abstract:

Carrying out reliability evaluation of equipment system has important engineering application value for ehhancing performance, improving efficiency, and reducing management and control risks. Aiming at the large-scale complex equipment system, by constructing limit sequence kernel and limit reliability approximation function for different coupling structures, a multi-state reliability modeling, analysis, and fast evaluation method with low requirement of calculation resources, calculation convenience, and approximation accuracy meeting the needs of engineering is explored. The case study shows that the algorithm breaks through the bottleneck of large-scale reliability calculation technology of complex equipment system, improves the efficiency of reliability evaluation, and has good effect in evaluation and risk prediction. Moreover, the algorithm enriches the multi-state reliability modeling, analysis, and evaluation system of complex equipment system, which can provide advanced theoretical reserves and engineering technology reference for reliability engineering design, use, and management personnel.

Key words: large-scale system, limit sequence kernel, multi-state, reliability evaluation, fast algorithm

CLC Number:

TP11

Yuedong SHI, Jiashan JIN, Kai CHAI. Multi-state reliability fast evaluation algorithm for large-scale complex system[J]. Systems Engineering and Electronics, 2022, 44(10): 3282-3290.

Figures/Tables 16

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References 37

1	ANATOLY L , ILIA F , YI D . Multi-state system reliability analysis and optimization for engineers and industrial managers[M]. London: Springer Press, 2010.
2	ANATOLY L , ILIA F . Recent advances in system reliability: signatures, multi-state systems and statistical inference[M]. London: Springer Press, 2012.
3	ANATOLY L , ILIA F , ALEX K . Recent advances in muti-state system reliability: theory and applications[M]. London: Springer Press, 2017.
4	宋月, 刘三阳, 冯海林. n中取相邻n-1好的多状态可修系统的可靠性分析[J]. 西安电子科技大学学报(自然科学版), 2005, 32 (6): 965- 967. doi: 10.3969/j.issn.1001-2400.2005.06.032
	SONG Y , LIU S Y , FENG H L . Reliability analysis of consecu tive n-1-out-of-n: G repairable systems with the multi-state component[J]. Journal of Xidian University, 2005, 32 (6): 965- 967. doi: 10.3969/j.issn.1001-2400.2005.06.032
5	YAMANOTO H , ZUO M J , AKIBA T , et al. Recursive for mulas for the reliability of multi-state consecutive k-out-of-n: G systems[J]. IEEE Trans.on Reliabilitiy, 2006, 55 (1): 98- 104. doi: 10.1109/TR.2005.863792
6	LIU Y W , KAPUR K C . Reliability measures for dynamic multi-sate nonrepairable systems and their applications to system performance evaluation[J]. ⅡE Transactions, 2006, 38 (6): 511- 520.
7	宋月, 刘三阳, 冯海林. 相邻k/n(F)多状态可修系统的可靠性分析[J]. 系统工程与电子技术, 2006, 28 (2): 310- 312. doi: 10.3321/j.issn:1001-506X.2006.02.039
	SONG Y , LIU S Y , FENG H L . Reliability analysis of consecut ive k-out-of-n: F repairable systems with multi-state component[J]. Systems Engineering and Electronics, 2006, 28 (2): 310- 312. doi: 10.3321/j.issn:1001-506X.2006.02.039
8	武月琴, 周泓, 官建成. 一类多状态系统的可靠性计算[J]. 北京航空航天大学学报, 2007, 33 (8): 968- 971. doi: 10.3969/j.issn.1001-5965.2007.08.024
	WU Y Q , ZHOU H , GUAN J C . Reliability estmiation of a multi-state system[J]. Journal of Beijing University of Aeronautics and Astronautics, 2007, 33 (8): 968- 971. doi: 10.3969/j.issn.1001-5965.2007.08.024
9	钱文学, 尹晓伟, 谢里阳. 多状态机械系统可靠性的离散化建模方法[J]. 东北大学学报, 2008, 29 (11): 1609- 1612.
	QIAN W X , YIN X W , XIE L Y . Discretized modeling process of reliability of multi-state mechanical systems[J]. Journal of Northeastern University, 2008, 29 (11): 1609- 1612.
10	TIAN Z G , RICHARD C , ZUO M J , et al. Reliability bounds for multi-state k-out-of-n systems[J]. IEEE Trans.on Reliability, 2008, 57 (1): 53- 58. doi: 10.1109/TR.2007.909766
11	尹晓伟, 钱文学, 谢里阳. 基于贝叶斯网络的多状态系统可靠性建模与评估[J]. 机械工程学报, 2009, 45 (2): 206- 212.
	YIN X W , QIAN W X , XIE L Y . Multi-state system reliability modeling and assessment based on Bayesian networks[J]. Journal of Mechanical Engineering, 2009, 45 (2): 206- 212.
12	XING L , DAI Y S . A new decision-diagram-based method for efficient analysis on multi-state systems[J]. IEEE Trans.on Dependable and Secure Computing, 2009, 6 (3): 161- 174. doi: 10.1109/TDSC.2007.70244
13	SHRETHA A , XING L , DAI Y S . Decision diagram based methods and complexity analysis for multi-state systems[J]. IEEE Trans.on Reliabilitiy, 2010, 59 (1): 145- 161. doi: 10.1109/TR.2009.2034946
14	AMARI S V , XING L , SHRETHA A , et al. Performabilty analysis of multi-state computing systems using multivalued decision diagram[J]. IEEE Trans.on Computers, 2010, 59 (10): 1419- 1433. doi: 10.1109/TC.2009.184
15	史跃东, 徐一帆, 金家善. 基于逻辑报酬矩阵的多状态系统可靠性评估[J]. 系统工程理论与实践, 2019, 39 (5): 1315- 1325.
	SHI Y D , XU Y F , JIN J S . Reliability assessment for multi-state system based on logic reward matrix[J]. Systems Engineering Theory & Practice, 2019, 39 (5): 1315- 1325.
16	LIMNIOS N , OPRISAN G . Semi-Markov processes and reliability[M]. London: Springer Press, 2001.
17	OURANIA C , NIKOLAOS L , SONIA M . Multi-State reliability systems under discrete time semi-Markovian hypothesis[J]. IEEE Trans.on Reliability, 2011, 60 (1): 80- 87. doi: 10.1109/TR.2010.2104210
18	尚彦龙, 蔡琦, 赵新文, 等. 基于UGF和Semi-Markov方法的反应堆泵机组多状态可靠性分析[J]. 核动力工程, 2012, 33 (1): 117- 123. doi: 10.3969/j.issn.0258-0926.2012.01.025
	SHANG Y L , CAI Q , ZHAO X W , et al. Multi-state reliability for pump group in nuclear power system based on UGF and semi-Markov process[J]. Nuclear Power Engineering, 2012, 33 (1): 117- 123. doi: 10.3969/j.issn.0258-0926.2012.01.025
19	WANG J , LI M . Redundancy allocation optimization for multistate systems with failure interactions using semi-Markov process[J]. Journal of Mechanical Design, 2015, 137 (10): 42- 52.
20	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): 445- 453.
	SHI Y D , JIN J S , XU Y F . Reliability assessment for multi-state system based on logic reward matrix[J]. Systems Engineering and Electronics, 2019, 41 (2): 445- 453.
21	LISNIANSKI A. Combined generating function and semi-Markov process technique for multi-state system reliability evaluation[C]//Proc. of the 4th International Conference on Mathematical Methods in Reliability, 2004: 21-25.
22	LEVITIN G . The universal generating function in reliabilitiy analysis and optimization[M]. London: Springer, 2005: 98- 105.
23	DING Y , LISNIANSKI A . Fuzzy universal generating functions for multi-sate system reliabilitiy assessment[J]. Fussy Sets and Systems, 2008, 159 (3): 307- 324. doi: 10.1016/j.fss.2007.06.004
24	ZHOU J Y , XIE L Y . Generating function approach to reliabilitiy analysis of structural system[J]. Science in China Series E: Technological Sciences, 2009, 52 (10): 2849- 2858. doi: 10.1007/s11431-009-0273-3
25	李春洋, 陈循, 易晓山. 基于向量通用生成函数的多性能参数多态系统可靠性分析[J]. 兵工学报, 2010, 31 (12): 1604- 1610.
	LI C Y , CHEN X , YI X S . Reliability analysis of multi-state system with multiple performance parameters based on vector-universal generating function[J]. Acta Armamentarii, 2010, 31 (12): 1604- 1610.
26	鄢民强, 杨波, 王展. 不完全覆盖的模糊多状态系统可靠性计算方法[J]. 西安交通大学学报, 2011, 45 (10): 109- 114.
	YAN M Q , YANG B , WANG Z . Reliability assessment for multistate system subject to imperfect fault coverage[J]. Journal of Xi'an Jiaotong University, 2011, 45 (10): 109- 114.
27	LI Y F , ZIO E . A multi-state model for the reliability assessment of a distributed generating system via universal gengnerating function[J]. Reliability Engineering and System Safety, 2012, 106 (12): 28- 36.
28	史跃东, 陈砚桥, 金家善. 舰船装备多状态可修复系统可靠性通用生成函数解算方法[J]. 系统工程与电子技术, 2016, 38 (9): 2215- 2220.
	SHI Y D , CHEN Y Q , JIN J S . Reliability analysis for warship armament multi-state repairable system based on universal generating function method[J]. Systems Engineering and Electronics, 2016, 38 (9): 2215- 2220.
29	史跃东, 金家善, 徐一帆, 等. 基于发生函数的模糊多状态复杂系统可靠性通用评估方法[J]. 系统工程与电子技术, 2018, 40 (1): 238- 244.
	SHI Y D , JIN J S , XU Y F , et al. Universal reliability assessment method for fuzzy multi-state complex technical system based on generating function[J]. Systems Engineering and Electronics, 2018, 40 (1): 238- 244.
30	ZIO E , PODOFILLINI L , LEVITIN G . Estimation of the importance measures of multi-sate elements by Monte Carlo simulation[J]. Reliabilitiy Engineering and System Safety, 2004, 86 (3): 191- 204.
31	RAMIREZ-MARQUEZ J E , COIT D . A Monte Carlo simulation approach for approximating multi-sate two-terminal reliabilitiy[J]. Reliabilitiy Engineering and System Safety, 2005, 87 (4): 253- 264.
32	ZIO E , MARELLA M , PODOFILLINI L . A Monte Carlo simulation approach to the availability assessment of multi-sate system with operational dependencies[J]. Reliabilitiy Engineering and System Safety, 2007, 92 (7): 871- 882.
33	KOTOWROCKI K . On asymptotic reliability functions of series-parallel and parallel-series systems with identical components[J]. Reliability Engineering and System Safety, 1993, 41 (31): 251- 257.
34	KOTOWROCKI K . On a class of limit reliability functions for series-parallel and parallel-series systems[M]. Gdynia: Maritime University Press, 1993.
35	TOSHIO N . Advanced reliability models and maintenance policies[M]. London: Springer Press, 2008.
36	KRZYSZTOF K , JOANNA S B . Reliability and safety of complex technical systems and processes[M]. London: Springer Press, 2011.
37	KOTOWROCKI K . Reliability of large systems[M]. London: Elsecier Press, 2004.

状态v	钢缕丝状态说明	钢缕丝与钢索系统状态约束关系
0	钢缕丝出现破损或腐蚀, 且相关数量超过钢缕丝总数的40%。	$ \begin{gathered}T(v, z)= \\\min _i \max _j T_{i j}(v, z), \\i \in\{1, 2, \cdots, 12\}, \\j \in\{1, 2, \cdots, 26\}\end{gathered}$
1	钢缕丝出现破损或腐蚀, 且相关数量超过钢缕丝总数的20%, 但小于40%。
2	钢缕丝出现破损或腐蚀, 但相关数量不超过钢缕丝总数的20%。
3	全部钢缕丝状态完好, 没有任何形式的功能缺陷。

工况z	年均持续时间/h	转运载荷范围/t	发生概率q_z
0	8 080	0~5	0.922 4
1	120	5~20	0.013 7
2	320	20~40	0.036 5
3	240	40~60	0.027 4

状态v	工况z	α(v, z)	β(v, z)	备注
1	0	3	0.003	α(v, 0)≡3 β(v, 0)=0.003v
2	0	3	0.006
3	0	3	0.009
1	1	2.8	0.007	α(v, 1)≡2.8 β(v, 1)=0.007v
2	1	2.8	0.014
3	1	2.8	0.021
1	2	1.9	0.092	α(v, 2)≡1.9 β(v, 2)=0.092v
2	2	1.9	0.184
3	2	1.9	0.276
1	3	1.4	0.260	α(v, 3)≡1.4 β(v, 3)=0.260v
2	3	1.4	0.520
3	3	1.4	0.780

〈Φ(12, v, z), Ψ(12, v, z)〉	z=0	z=1	z=2	z=3
v=1	〈0.654 7, 8.321 7〉	〈0.594 7, 7.153 5〉	〈0.573 7, 4.682 8〉	〈0.643 4, 3.869 9〉
v=2	〈0.512 5, 6.604 9〉	〈0.464 3, 5.584 8〉	〈0.398 3, 3.251 4〉	〈0.392 2, 2.358 7〉
v=3	〈0.447 7, 5.769 9〉	〈0.401 7, 4.831 9〉	〈0.321 8, 2.626 6〉	〈0.293 6, 1.765 6〉

统计量	v=0	v=1	v=2	v=3
M(v)	10	8.637 2	6.813 4	5.933 3
σ(v)	0	1.198 0	1.086 4	1.009 7
${\bar M}$(v)	1.362 8	1.823 8	0.880 1	5.933 3

Multi-state reliability fast evaluation algorithm for large-scale complex system

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References 37

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序号	k	m	R(t, v)		耗时
序号	k	m	逼近/ms	解析/ms	耗时
1	12	26	0.071 5	0.468 5	6.55
2	24	52	0.075 8	0.496 1	6.54
3	72	156	0.076 6	0.512 3	6.68
4	288	624	0.079 8	0.538 1	6.74

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