基于改进生成函数的多元状态复杂系统可靠性重要度分析

doi:10.12382/bgxb.2024.0604

摘要/Abstract

摘要：

研究多元状态复杂系统的可靠性重要度,有助于分析并确定系统设计的潜在技术薄弱环节,对于实现系统状态性能的精细化管理意义重大。通过引入改进生成函数模型,并构建面向特定“状态可达门限”的系统层级生成函数,给出一类能够适应“多元”状态复杂任务功能系统的可靠性重要度通用化封闭解算体系与高精度分析算法。工程案例验证结果表明:新算法适用范围广、可靠性重要度分辨精度高,更便于实现复杂系统可靠状态的精细化管理;新算法程式化运算资源要求低,可规避大维度复杂系统状态微分解算的技术瓶颈,工程应用价值更突出。研究结果可拓展应用于多元状态复杂系统其他通用质量特性的重要度分析与精细化管理,对于科学筹措配套保障资源、合理规划预防性维修工作具有重要技术指导作用。

关键词: 复杂系统, 多元状态, 可靠性, 重要度分析, 改进生成函数, 精细化管理

Abstract:

Study on the reliability importance of multi-state complex system can help analyze and identify the potential technical weaknesses in system design, and is of great significance for achieving the refined management of system state performance. By introducing an improved generating function model and constructing a system-level generating function for specific state reachable threshold, a generalized closed solution system and a high-precision analysis algorithm for reliability importance that can adapt to complex task functional systems with multiple states are proposed. Engineering case verification shows that the proposed algorithm has a high accuracy in distinguishing reliability importance, and is more conducive to achieving the refined management of reliable states in complex system. Meanwhile, the proposed algorithm has low requirements for programmatic computing resources and can avoid the technical bottleneck of state differential calculation in high-dimensional complex system. Its engineering application value is more prominent. The research results can be used for the importance analysis and refined management of other general quality characteristics in multi-state complex system, and have important technical guidance for scientifically allocating support resources and reasonably planning preventive maintenance work.

Key words: complex system, multi-state, reliability, importance analysis, improved generating function, refined management

中图分类号:

TP11

史跃东, 钱超, 邵松世, 胡俊波. 基于改进生成函数的多元状态复杂系统可靠性重要度分析[J]. 兵工学报, 2025, 46(5): 240604-.

SHI Yuedong, QIAN Chao, SHAO Songshi, HU Junbo. Importance Analysis for Multi-state Complex System Reliability Based on Improved Generating Function[J]. Acta Armamentarii, 2025, 46(5): 240604-.

图/表 11

图1 “多元”状态复杂能量传输系统任务可靠性框图

Fig.1 Task reliability block diagram of multi-state complex energy transfer systems

表1 内置单元的多元状态性能gih

Table 1 Multi-state performance gih of built-in units

状态h	单元i
状态h	1	2	3	4	5	6
1	0	0	0	0	0	0
2	0.6	0.6	0.8	0.85	1	1
3	0.9	0.9	1

表2 内置单元的状态跃迁强度 ζ m j i

Table 2 State transition strength ζ m j i of built-in units year-1

状态		单元i
m	j	1	2	3	4	5	6
1	2	60	60	50	10	10	10
2	3	30	30	20
3	2	4	4	3
2	1	12	12	10	2	1.2	1.2

表3 内置单元的多元状态稳态概率分布Pih

Table 3 Steady-state probability distribution Pih of built-in units

状态 h	单元i
状态 h	1	2	3	4	5	6
1	0.0205	0.0205	0.0197	0.2153	0.0722	0.0722
2	0.1079	0.1079	0.1089	0.7847	0.9278	0.9278
3	0.8716	0.8716	0.8714

表4 不同内置单元间的逻辑构型函数ψij(·)

Table 4 Logical configuration function between different built-in units

i	k_i	j	k_j	逻辑构型函数ψ_ij(·)	备注
1	3	2	3	max(g_in, g_jm)	n=1,2,…,k_i
3	3	5	2	min(g_in, g_jm)	m=1,2,…,k_j
4	2	6	2	min(g_in, g_jm)

图2 不同需求w下的系统可用度A变化

Fig.2 Change of system availability A under different requirements w

图3 不同需求w下的系统期望性能输出E变化

Fig.3 Change of system expected performance E under different requirements w

图4 不同需求w下的系统期望性能失效D变化

Fig.4 Change of system expected performance deficiency D under different requirements w

图5 不同需求下面向可用度参数的重要度变化

Fig.5 Importance change of system availability under different requirements

图6 不同内置单元间的Birnbaum重要度对比

Fig.6 Comparison of Birnbaum importances of differentbuilt-in units

图7 不同内置单元间的Fussel-Vesely重要度对比

Fig.7 Comparison of Fussel-Vesely importances of different built-in units

参考文献 27

[1]	LISNIANSKI A, FRENKEL I, DING Y. Multi-state system reliability analysis and optimization for engineers and industrial managers[M]. London,UK: Springer, 2010.
[2]	史跃东, 徐一帆, 金家善. 装备复杂系统多状态可靠性分析与评估技术[M]. 北京: 科学出版社, 2017.
	SHI Y D, XU Y F, JIN J S. Multistate reliability analysis and evaluation technology for complex equipment systems[M]. Beijing: Science Press, 2017. (in Chinese)
[3]	BIRNBAUM Z W. On the importance of different components in a multicomponent system[J]. Multivariate Analysis II, 1969,1:581-592.
[4]	MIZIULA P, NAVARRO J. Birnbaum importance measure for reliability systems with dependent components[J]. IEEE Transactions on Reliability, 2019, 68:39-50.
[5]	DO P, B’ERENGUER C. Conditional reliability-based importance measures[J]. Reliability Engineering and System Safety, 2020, 193:106633.
[6]	SI S B, LIU M L, JIANG Z Y, et al. System reliability allocation and optimization based on generalized Birnbaum importance measure[J]. IEEE Transactions on Reliability, 2019, 68:831-843.
[7]	MESHKAT R S, MAHMOUDI E. Joint reliability and weighted importance measures of a k-out-of-n system with random weights for components[J]. Journal of Computational and Applied Mathematics, 2017, 326:273-283.
[8]	何爱民, 赵先, 崔利荣, 等. 线形可重叠的m-consecutive-k-out-of-n:F系统可靠性和单元重要度研究[J]. 兵工学报, 2009, 30(增刊): 135-138.
	HE A M, ZHAO X, CUI L R, et al. A study on reliability and component importance of linear overlapping m-consecutive-k-out-of-n: F system[J]. Acta Armamentarii, 2009, 30(S): 135-138. (in Chinese)
[9]	吕弘, 袁海文, 张莉, 等. 基于模式重要度的航空电源系统可靠性估计[J]. 航空学报, 2010, 31(3):609-613.
	LÜ H, YUAN H W, ZHANG L, et al. Aircraft electrical power system reliability estimation based on pattern importance[J]. Acta Aeronautica et Astronautica Sinica, 2010, 31(3):609-613. (in Chinese)
[10]	白光晗, 张弛, 兑红炎, 等. 无人机集群任务可靠性建模及重要度分析[J]. 机械工程学报, 2022, 58(10):361-373. doi: 10.3901/JME.2022.10.361
	BAI G H, ZHANG C, DUI H Y, et al. Mission reliability modeling and importance analysis of UAV swarm[J]. Journal of Mechanical Engineering, 2022, 58(10):361-373. (in Chinese) doi: 10.3901/JME.2022.10.361
[11]	MOHAM L R, DAOUD A K. A new integrated strategy for optimizing the maintenance cost of complex systems using reliability importance measures[J]. Journal of Production Research, 2024, 62(11):4143-4164.
[12]	王成, 许建新, 张振明, 等. 基于成本效益重要度的复杂系统可靠性保障策略[J]. 西北工业大学学报, 2020, 38(6):1316-1321.
	WANG C, XU J X, ZHANG Z M, et al. Reliability guarantee strategy for complex system based on cost-benefit importance[J]. Journal of Northwestern Polytechnical University, 2020, 38(6):1316-1321. (in Chinese)
[13]	LIU M L, WANG D, ZHAO J B, et al. Importance measure construction and solving algorithm oriented to the cost-constrained reliability optimization model[J]. Reliability Engineering and System Safety, 2022, 222:108406.
[14]	LIU M L, WANG D, SI S B. Mixed reliability importance-based solving algorithm design for the cost-constrained reliability optimization model[J]. Reliability Engineering and System Safety, 2023, 237:109363.
[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. (in Chinese)
[16]	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. Study on multi-state reliability analysis and assessment for complex technical system under semi-Markov processes[J]. Systems Engineering and Electronics, 2019, 41(2):445-453. (in Chinese)
[17]	史跃东, 金家善, 柴凯. 大型复杂系统可靠性快速评估算法[J]. 系统工程与电子技术, 2022, 44(10):3282-3290. doi: 10.12305/j.issn.1001-506X.2022.10.35
	SHI Y D, JIN J S, CHAI K. Multi-state reliability fast evaluation for large-scale complex system[J]. Systems Engineering and Electronics, 2022, 44(10):3282-3290. (in Chinese)
[18]	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 system reliability analysis for ship power generation system based on Markov reward model[J]. Acta Armamentaii, 2023, 44(10):3177-3186. (in Chinese)
[19]	XU Y F, SHI Y D, XIONG Z H, et al. Multi-state reliability assessment for shipboard hybrid turbine-diesel generation system with redundancy and aging effects[J]. Quality and Reliability Engineering International, 2023, 39(3): 1001-1023.
[20]	SIBEL Y, OZGE E G. Reliability analysis of repairable multistate phased mission systems with Markov approach based on states[J]. Engineering Computations, 2023, 40(5): 1041-1062.
[21]	YIN J, YE Z S, CUI L R. Reliability and optimal replacement policy of a multistate system under Markov renewal shock model[J]. IEEE Transactions on Reliability, 2024, 73:1-12.
[22]	HUANG C H, HUANG D H, LIN Y K. A novel approach to predict network reliability for multistate networks by a deep neural network[J]. Quality Technology & Quantitative Management, 2022, 19(3):362-378.
[23]	PAWEL M K. An efficient algorithm for the reliability evaluation of multistate flow networks under budget constraints[J]. IISE Transactions, 2023, 55(11):1091-1102.
[24]	YANG L C, WANG C X, LING C Y, et al. Reliability evaluation of an imprecise multistate system with mixed uncertainty[J]. IEEE Transactions on Reliability, 2024, 73:478-491.
[25]	CHANKO V M. On birnbaum type joint importance measures for multistate reliability systems[J]. Communications in Statistics Theory and Methods, 2023, 52(9):2799-2818.
[26]	田宏, 陈宝智, 五穹, 等. 多态系统可靠性及元素的不确定性重要度[J]. 东北大学学报(自然科学版), 2000, 21(6):634-638.
	TIAN H, CHEN B Z, WU Q, et al. Multistate system reliability and uncertain importance of its component[J]. Journal of Northeastern and University(Natural Science), 2000, 21(6):634-638. (in Chinese)
[27]	LEVITIN G. The universal generating function in reliability analysis and optimization[M]. London, UK:Springer, 2005.