考虑概率型共因失效的多阶段任务系统可靠性分析模型

doi:10.12305/j.issn.1001-506X.2022.12.35

Abstract

Abstract:

Aiming at the problem that mission reliability of phased-mission system (PMS) is affected by probabilistic common cause failure (PCCF), a reliability analysis model PCCF-PMS of PMS based on Bayesian network (BN) is proposed. Firstly, the representation method of PMS based on BN is studied, and the basic BN model of PMS without considering common cause failure is established. Secondly, the common cause space node is constructed, and the modification method of system model parameters under the influence of common cause space node is studied. Finally, the common cause node is introduced to extend the PMS-BN model to realize the quantitative reliability analysis of the PMS considering the effect of common cause failure. The correctness of the proposed model is illustrated by an example of the satellite's first orbit transfer mission. The analysis results show that the common cause failure has a significant impact on the reliability of the PMS. The PCCF-PMS model can deal with the reliability analysis problem of PMS affected by probabilistic and deterministic common cause failures. The model is applicable to the cases where common cause events are independence, dependence or mutual exclusion, and the scale of the network model is controllable.

Key words: probabilistic common cause failure (PCCF), phased-mission system (PMS), Bayesian network (BN), reliability analysis

CLC Number:

TB114.3
V37

Peng WANG, Zijing SUN, Fan ZHANG, Guosong XIAO. Reliability analysis model for phased-mission system considering probabilistic common cause failures[J]. Systems Engineering and Electronics, 2022, 44(12): 3887-3898.

Figures/Tables 19

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References 31

1	XING L , AMARI S V . Reliability of phased-mission systems[M]. Berlin: Springer, 2008: 349- 368.
2	李志强, 徐廷学, 顾钧元, 等. 复杂系统相关失效分析研究综述[J]. 失效分析与预防, 2017, 12 (2): 130- 136. doi: 10.3969/j.issn.1673-6214.2017.02.012
	LI Z Q , XU T X , GU J Y , et al. Review on research on dependent failure analysis of complex systems[J]. Failure Analysis and Prevention, 2017, 12 (2): 130- 136. doi: 10.3969/j.issn.1673-6214.2017.02.012
3	HAUGE S , HOKSTAD P , HÅBREKKE S , et al. Common cause failures in safety-instrumented systems: using field experience from the petroleum industry[J]. Reliability Engineering and System Safety, 2016, 151 (7): 34- 45.
4	ZAHNG M , ZHANG Z J , MOSLEH A , et al. Common cause failure model updating for risk monitoring in nuclear power plants based on alpha factor model[J]. Journal of Risk and Reliability, 2017, 231 (3): 209- 220.
5	MATTHIAS C M , TROFFAES G W , DANA K . A robust Bayesian approach to modeling epistemic uncertainty in common-cause failure models[J]. Reliability Engineering and System Safety, 2014, 125, 13- 21. doi: 10.1016/j.ress.2013.05.022
6	孔祥芬, 王杰, 张兆民. 基于贝叶斯网络和共因失效的飞机电源系统可靠性分析[J]. 航空学报, 2020, 41 (5): 270- 279.
	KONG X F , WANG J , ZHANG Z M . Reliability analysis of aircraft eleltrical power system based on Bayesian network and common cause failure[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41 (5): 270- 279.
7	李志强, 徐廷学, 安进, 等. 冗余系统共因失效动态贝叶斯网络建模[J]. 仪器仪表学报, 2018, 39 (3): 190- 198. doi: 10.19650/j.cnki.cjsi.J1702575
	LI Z Q , XU T X , AN J , et al. Common cause failure modeling for redundant system based on dynamic Bayesian network[J]. Chinese Journal of Scientific Instrument, 2018, 39 (3): 190- 198. doi: 10.19650/j.cnki.cjsi.J1702575
8	XING L D , LEVITIN G . BDD-based reliability evaluation of phased-mission systems with internal/external common-cause failures[J]. Reliability Engineering and System Safety, 2013, 112, 145- 153. doi: 10.1016/j.ress.2012.12.003
9	LEVITIN G , XING L D , AMARI S V . Reliability of nonrepairable phased-mission systems with common cause failures[J]. IEEE Trans.on Systems, Man, and Cybernetics: Systems, 2013, 43 (4): 967- 978. doi: 10.1109/TSMCA.2012.2220761
10	LEVITIN G , XING L D , AMARI S V , et al. Reliability of non-repairable phased-mission systems with propagated failures[J]. Reliability Engineering and System Safety, 2013, 119, 218- 228. doi: 10.1016/j.ress.2013.06.005
11	XING L D, WANG W D. Probabilistic common-cause failures analysis[C]//Proc. of the Annual Reliability and Maintainability Symposium, 2009: 354-358.
12	WANG C N , XING L D , LEVITIN G . Explicit and implicit methods for probabilistic common-cause failure analysis[J]. Reliability Engineering and System Safety, 2014, 131, 175- 184. doi: 10.1016/j.ress.2014.06.024
13	WANG C N , XING L D , LEVITIN G . Probabilistic common cause failures in phased-mission systems[J]. Reliability Engineering and System Safety, 2015, 144, 53- 60. doi: 10.1016/j.ress.2015.07.004
14	WANG C N, XING L D, VOKKARANE V M, et al. A phased-mission framework for communication reliability in WSN[C]//Proc. of the Reliability & Maintainability Symposium, 2014.
15	曹文斌, 胡起伟, 苏续军, 等. 随机共因失效条件下的多阶段任务成功概率评估研究[J]. 兵工学报, 2017, 38 (4): 766- 775. doi: 10.3969/j.issn.1000-1093.2017.04.019
	CAO W B , HU Q W , SU X J , et al. Research on phased-mission success probability assessment under random common cause failures[J]. Acta Armamentarii, 2017, 38 (4): 766- 775. doi: 10.3969/j.issn.1000-1093.2017.04.019
16	吴欢, 焦健, 赵廷弟. 一种考虑共因失效的PMS可靠性建模分析方法[J]. 北京航空航天大学学报, 2018, 44 (5): 1088- 1094.
	WU H , JIAO J , ZHAO T D . A reliability modeling and analysis method for PMS considering common cause failure[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44 (5): 1088- 1094.
17	XU Z P , MO Y C , LIU Y , et al. Reliability assessment of multi-state phased-mission systems by fusing observation data from multiple phases of operation[J]. Mechanical Systems and Signal Processing, 2019, 118, 603- 622. doi: 10.1016/j.ymssp.2018.08.064
18	房丙午, 黄志球, 李勇, 等. 基于贝叶斯网络的复杂系统动态故障树定量分析方法[J]. 电子学报, 2016, 44 (5): 1234- 1239. doi: 10.3969/j.issn.0372-2112.2016.05.032
	FANG B W , HUANG Z Q , LI Y , et al. Quantitative analysis method of dynamic fault tree of complex system using Bayesian network[J]. Acta Electronica Sinica, 2016, 44 (5): 1234- 1239. doi: 10.3969/j.issn.0372-2112.2016.05.032
19	张友鹏, 杨金凤. 基于动态贝叶斯网络的CTCS-3级ATP系统可靠性分析[J]. 铁道学报, 2017, 39 (7): 79- 86. doi: 10.3969/j.issn.1001-8360.2017.07.012
	ZHANG Y P , YANG J F . Reliability analysis on ATP system of CTCS-3 based on dynamic Bayesian network[J]. Journal of the China Railway Society, 2017, 39 (7): 79- 86. doi: 10.3969/j.issn.1001-8360.2017.07.012
20	张振海, 王悦榕, 党建武. 基于证据理论和贝叶斯网络的列控车载子系统可靠性分析[J]. 铁道科学与工程学报, 2020, 17 (9): 2208- 2215.
	ZHANG Z H , WANG Y R , DANG J W . Reliability analysis of on-board subsystem of train control system based on evidence theory and Bayesian network method[J]. Journal of Railway Science and Engineering, 2020, 17 (9): 2208- 2215.
21	古莹奎, 沈延军, 张全新, 等. 基于贝叶斯网络的多状态共因失效系统可靠性分析[J]. 机械设计与研究, 2018, 34 (2): 1- 4. 1-4, 9
	GU Y K , SHEN Y J , ZHANG Q X , et al. Multi-state common cause failure system reliability analysis based on Bayesian network[J]. Machine Design and Research, 2018, 34 (2): 1- 4. 1-4, 9
22	江磊, 王小敏, 蔺伟. 基于动态贝叶斯网络的列控中心可靠性及可用性评估[J]. 交通运输系统工程与信息, 2018, 18 (3): 182- 188. 182-188, 217
	JIANG L , WANG X M , LIN W . Reliability and availability evaluation of train control center based on dynamic Bayesian network[J]. Journal of Transportation Systems Engineering and Information Technology, 2018, 18 (3): 182- 188. 182-188, 217
23	QIU S Q , HOU Y H , MING H X G . An implicit method for probabilistic common-cause failure analysis using Bayesian network[J]. IFAC PapersOnLine, 2018, 51 (24): 1037- 1042. doi: 10.1016/j.ifacol.2018.09.718
24	厉海涛, 金光, 周经伦, 等. 贝叶斯网络推理算法综述[J]. 系统工程与电子技术, 2008, 30 (5): 935- 939.
	LI H T , JIN G , ZHOU J L , et al. Survey of Bayesian network inference algorithms[J]. Systems Engineering and Electronics, 2008, 30 (5): 935- 939.
25	KIM J Y , SHAH A U A , KANG H G . Dynamic risk assessment with Bayesian network and clustering analysis[J]. Reliability Engineering and System Safety, 2020, 201, 106959.
26	ZHOU D , PAN E , ZHANG X F , et al. Dynamic model-based saddle-point approximation for reliability and reliability-based sensitivity analysis[J]. Reliability Engineering and System Safety, 2020, 201, 106972.
27	LEWIS D A , GROTH M K . A dynamic Bayesian network structure for joint diagnostics and prognostics of complex engineering systems[J]. Algorithms, 2020, 13 (3): 64.
28	LEE D , CHOI D S . Analysis of the reliability of a starter-generator using a dynamic Bayesian network[J]. Reliability Engineering and System Safety, 2020, 195, 106628.
29	XUE S S , LI X G , WANG X F . Fault diagnosis of multi-state gas monitoring network based on fuzzy Bayesian net[J]. Personal and Ubiquitous Computing, 2019, 23 (3/4): 573- 581.
30	WANG C , LIU Y P , HOU W , et al. Reliability and availability modeling of Subsea Xmas tree system using dynamic Bayesian network with different maintenance methods[J]. Journal of Loss Prevention in the Process Industries, 2020, 64, 104066.
31	ANDAS A , VASILEIOS Z , CHRISTOS S . Reliability analysis and functional design using Bayesian networks generated automatically by an "Idea Algebra" framework[J]. Reliability Engineering and System Safety, 2018, 180, 211- 225.

节点	单阶段	多阶段
元件节点	X(元件X节点, X依据实际系统选择)	X_j(阶段j中的元件X节点)
模块节点	M_i(第i个模块)	M_ji(阶段j中的第i个模块节点)
子系统节点	S_k(第k个子系统)	S_jk(阶段j中的第k个子系统节点)
阶段节点	—	T_j(阶段j节点)
系统节点	S(系统节点)	S(系统节点)

共因事件CC_i间关系	共因空间CCE_k的概率P_CCEk
共因事件间相互独立或集合{CC_i}中不存在互斥事件(i∈S)	$P_{\mathrm{CCE}_k}=\left[\prod\limits_{i \in S} P_{\mathrm{CC}_i}\right] \cdot \\ \left[\prod\limits_{i \notin S}\left(1-P_{\mathrm{CC}_i}\right)\right]$
集合{CC_i}中存在至少两共因事件互斥(i∈S)	P_{CCE_k=0}
所有共因事件中至少存在两共因事件CC_i与CC_j相关(i≠j)	$P_{\mathrm{CCE}_k}=\left[\prod\limits_{i \in S} P_{\mathrm{CC}_i \mid \mathrm{CC}_j}\right] \cdot\\ \left[\prod\limits_{i \notin S}\left(1-P_{ \mathrm{CC}_i \mid \overline{\mathrm{CC}_j}}\right) \right]$

共因空间	发生概率
$\mathrm{CCE}_0=\overline{\mathrm{CC}_1} \cap \overline{\mathrm{CC}_2} \cap \overline{\mathrm{CC}_3}$	$P_{\mathrm{CCE}_0}=\left(1-P_{\mathrm{CC}_1}\right)\left(1-P_{\mathrm{CC}_2}\right)\left(1-P_{\mathrm{CC}_3 \mid \overline{\mathrm{CC}_2}}\right)$
$\mathrm{CCE}_1=\mathrm{CC}_1 \cap \overline{\mathrm{CC}_2} \cap \overline{\mathrm{CC}_3}$	$P_{\mathrm{CCE}_1}=P_{\mathrm{CC}_1}\left(1-P_{\mathrm{CC}_3\mid \overline{\mathrm{CC}_2}} \right)$
$\mathrm{CCE}_2=\overline{\mathrm{CC}_1} \cap \mathrm{CC}_2 \cap \overline{\mathrm{CC}_3}$	P_CCE₂=P_CC₂(1-P_CC₃\|CC₂)
$\mathrm{CCE}_3=\overline{\mathrm{CC}_1} \cap \overline{\mathrm{CC}_2} \cap \mathrm{CC}_3$	$P_{\mathrm{CCE}_3}=\left(1-P_{\mathrm{CC}_1}\right)\left(1-P_{\mathrm{CC}_2}\right) P_{\mathrm{CC}_3 \mid \overline{\mathrm{CC}_2}}$
$\mathrm{CCE}_4=\mathrm{CC}_1 \cap \mathrm{CC}_2 \cap \overline{\mathrm{CC}_3}$	P_CCE₄=0
$\mathrm{CCE}_5=\mathrm{CC}_1 \cap \overline{\mathrm{CC}_2} \cap \mathrm{CC}_3$	$P_{\mathrm{CCE}_5}=P_{\mathrm{CC}_1} P_{\mathrm{CC}_3\mid \overline{\mathrm{CC}_2}} $
$\mathrm{CCE}_6=\overline{\mathrm{CC}_1} \cap \mathrm{CC}_2 \cap \mathrm{CC}_3$	P_CCE₆=P_CC₂P_CC₃\|CC₂
CCE₇=CC₁∩CC₂∩CC₃	P_CCE₇=0

元件X	P(X=0\|CCE_i=1)	P(X=1\|CCE_i=1)
CCE₀=1	1-q_jx	q_jx
CCE₁=1	$\left\{\begin{array}{l}\left(1-q_{j x}\right)\left(1-q_{j 1 x}\right), \mathrm{CC}_1 \text { 发生在阶段} j \text { 且影响元件} X \\ 1-q_{j x}, \mathrm{CC}_1 \text { 末发生在阶段} j \text { 或不影响元件} X\end{array}\right.$	$\left\{\begin{array}{l}1-\left(1-q_{j x}\right)\left(1-q_{j 1 x}\right), \mathrm{CC}_1 \text { 发生在阶段} j \text { 且影响元件} X \\ q_{j, x}, \mathrm{CC}_1 \text { 末发生在阶段} j \text { 或不影响元件} X\end{array}\right.$
CCE₂=1	$\left\{\begin{array}{l}\left(1-q_{j x}\right)\left(1-q_{j 1 x}\right), \mathrm{CC}_2 \text { 发生在阶段} j \text { 且影响元件} X \\ 1-q_{j x}, \mathrm{CC}_2 \text { 末发生在阶段} j \text { 或不影响元件} X\end{array}\right.$	$\left\{\begin{array}{l}1-\left(1-q_{j x}\right)\left(1-q_{j 1 x}\right), \mathrm{CC}_2 \text { 发生在阶段} j \text { 且影响元件} X \\ q_{j x}, \mathrm{CC}_2 \text { 末发生在阶段} j \text { 或不影响元件} X\end{array}\right.$
$\vdots$	$\vdots$	$\vdots$
$\mathrm{CCE}_{2-1}^n=1$	$\left(1-q_{j X}\right) \prod\limits_{i=1}^m\left(1-q_{j i X}\right)$	$1-\left(1-q_{j X}\right) \prod\limits_{i=1}^m\left(1-q_{j i X}\right)$

子系统	组件/元件	备注	运行阶段
姿轨控	A: 姿轨控计算机	A_a、A_b共2台, 冷备份	T₁、T₂、T₃、T₄、T₅
	B: 陀螺	B_a、B_b、B_c共3台, 3取2	T₁、T₂、T₄
	C: 数字太阳敏感器	C_a、C_b、C_c、C_d共4台, C_a、C_b热备份	C_a、C_b: T₃C_c、C_d: T₁、T₂、T₄
	D: 红外地球敏感器	D_a、D_b共2台, 热备份	T₃
	E: 星敏感器	E_a、E_b、E_c共3台, 3取2	—
推进	F: 发动机	F一台	T₅
推进	G: 推进器	G_a、G_b共2台, 热备份	T₁、T₂、T₃、T₄

Reliability analysis model for phased-mission system considering probabilistic common cause failures

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CCE节点	P_{CCE_k}
CCE₀	$P_{\mathrm{CCE}_0}=\left(1-P_{\mathrm{CC}_{41}}\right)\left(1-P_{\mathrm{CC}_{52}}\right)\left(1-P_{\mathrm{CC}_{52} \mid \overline{\mathrm{CC}_{51}}} \right)=0.09$
CCE₁	$P_{\mathrm{CCE}_1}=P_{\mathrm{CC}_{41}}\left(1-P_{\mathrm{CC}_{51}}\right)\left(1-P_{\mathrm{CC}_{52} \mid \overline{\mathrm{CC}_{51}}}\right)=0.21$
CCE₂	P_CCE₂=(1－P_CC₄₁)P_CC₅₁(1－P_CC₅₂\|CC₅₁)=0.048
CCE₃	$P_{\mathrm{CCE}_3}=\left(1-P_{\mathrm{CC}_{41}}\right)\left(1-P_{\mathrm{CC}_{51}}\right) P_{\mathrm{CC}_{52} \mid\mid \overline{\mathrm{CC}_{51}}} =0.09$
CCE₄	P_CCE₄=P_CC₄₁P_CC₅₁(1－P_{CC₅₂\|CC₅₁})=0.112
CCE₅	$P_{\mathrm{CCE}_5}=P_{\mathrm{CC}_{41}}\left(1-P_{\mathrm{CC}_{51}}\right) P_{\mathrm{CC}_{52}\mid \overline{\mathrm{CC}_{51}}} =0.21$
CCE₆	P_CCE₆=(1－P_CC₄₁)P_CC₅₁P_{CC₅₂\|CC₅₁}=0.072
CCE₇	P_CCE₇=P_CC₄₁P_CC₅₁P_{CC₅₂\|CC₅₁}=0.168

相关元件	共因事件
	CC₄₁			CC₅₁			CC₅₂
	A₄	C₄	G₄	B₅	D₅	F₅	A₅	C₅	G₅
CCE₀	2.928E-6	7.32E-6	1.464E-6	6.954E-07	1.390 8E-06	9.804E-07	1.390 8E-06	3.477E-6	6.954E-07
CCE₁	0.024 002 858	0.036 007 056	0.084 001 341	6.954E-07	1.390 8E-06	9.804E-07	1.390 8E-06	3.477E-6	6.954E-07
CCE₂	2.928E-6	7.32E-6	1.464E-6	0.005 700 691	0.011 401 375	0.017 100 964	1.390 8E-06	3.477E-6	6.954E-07
CCE₃	2.928E-6	7.32E-6	1.464E-6	6.954E-07	1.390 8E-06	9.804E-07	0.028 501 351	0.034 203 358	0.022 800 68
CCE₄	0.024 002 858	0.036 007 056	0.084 001 341	0.005 700 691	0.011 401 375	0.017 100 964	1.390 8E-06	3.477E-6	6.954E-07
CCE₅	0.024 002 858	0.036 007 056	0.084 001 341	6.954E-07	1.390 8E-06	9.804E-07	0.028 501 351	0.034 203 358	0.022 800 68
CCE₆	2.928E-6	7.32E-6	1.464E-6	0.005 700 691	0.011 401 375	0.017 100 964	0.028 501 351	0.034 203 358	0.022 800 68
CCE₇	0.024 002 858	0.036 007 056	0.084 001 341	0.005 700 691	0.011 401 375	0.017 100 964	0.028 501 351	0.034 203 358	0.022 800 68

方法	是否适用PCCF	是否适用PMS	是否适用系统动态行为	共因事件间关系	是否涉及模型转换	补充
基于BDD的显式模型^{[8, 12]}	√	√	—	相互独立	需进行系统故障树与BDD模型的转换	—
基于BDD的隐式模型^[12]	√	√	—	独立、互斥、相关	需进行系统故障树与BDD模型的转换	转换后待计算的BDD模型数量2n(n为共因事件数量)
模块化分析方法^[16]	√	√	√	独立、互斥、相关	需进行系统动态/静态模块划分, 以及故障树与BDD模型、Markov模型的转换	转换后待计算的问题数量与系统故障树的模块划分情况相关
基于BN的系统CCF模型^[6]	—	—	√	相互独立	可直接建立系统BN模型, 或由系统故障树模型进行转换	对不考虑CCF的系统BN模型进行扩展, 新增节点数量为2ⁿ-n-1(n为受共因事件影响的元件数量)
基于BN的PCCF-PMS模型	√	√	√	独立、互斥、相关	可直接建立系统BN模型, 或由系统故障树模型进行转换	对不考虑CCF的系统BN模型进行扩展, 新增一个节点表示共因事件空间

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[13]	YAN Hua, WU Xiao-yue. Improved Krylov subspace projection algorithm for reliability analysis of TT&C and communication system [J]. Journal of Systems Engineering and Electronics, 2012, 34(10): 2180-2186.
[14]	HU Tao， YU Jian. Reliability optimization model of n/k(G) phased mission systems [J]. Journal of Systems Engineering and Electronics, 2012, 34(1): 217-220.
[15]	JIANG Ying-jie, SUN Zhi-qiang, XIE Hong-wei, GONG Er-ling. Human error probability quantification method based on Bayesian information fusion [J]. Journal of Systems Engineering and Electronics, 2011, 33(4): 949-953.