﻿ 基于动态贝叶斯网络的可修GO法模型算法
 文章快速检索 高级检索

Algorithm based-on dynamic Bayesian networks for repairable GO methodology model
FAN Dongming, REN Yi, LIU Linlin, LIU Shuzheng, FAN Jian, WANG Zili
School of Reliability and Systems Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Abstract: GO methodology was an effective method of evaluating the reliability and the security of complex systems. Besides the capability to describe the sequence characteristics of multi-states, GO methodology was also capable of expressing complex dynamic repair behavior of the systems. For GO methodology models whose systems containing the dynamic repairable characteristic, a new algorithm based on the Bayesian networks was presented. The algorithm firstly mapped the repairable and unrepairable operators into dynamic Bayesian networks, and then mapped the whole model into Bayesian networks software to solve the problem. With the support of the mature algorithm and software, this new algorithm is capable not only of figuring out the curves of reliability that is changed over time but also the reliability index on the determined time point without caring about the shared signals. This new algorithm based on the Bayesian networks theory is governed by unified simple rules and it is quite convenient to apply in engineering.
Key words: GO methodology     dynamic Bayesian networks     repairable model     reliability modelling     model algorithm

GO法(GO methodology)[1]是一种以成功为导向的系统概率分析技术,对于多状态、有时序的系统,尤其对有实际物流如气流、液流、电流等过程系统具有很强的可靠性、安全性建模描述能力.在工程系统中,组成部件和设备经常是可修复的,现有的可修算法[2]是以可修操作符的概率公式为基础,先求得可修系统的等效故障率和等效维修率,然后再考虑操作符之间的相关性参数,最终通过一系列转换求得等效操作符的可用度.在该方法中,如果输入信号存在共有信号则需先将共有信号分离出去[3],进行操作符逻辑计算后,再将共有信号合并,再考虑停工相关、维修相关等复杂参数.这些问题都影响了GO法在实际工程中的广泛应用.

 图 1 GO法操作符类型 Fig. 1 Type of GO methodology operators

1) 逻辑操作符:此类操作符没有状态概率数据,仅代表一种逻辑运算规则.逻辑操作符包括第2、9、10、11、13、14、15类操作符.

2) 功能操作符:此类操作符包含自身状态值及运算逻辑.功能操作符包括第1、3、4、5、6、7、8、12、16、17类操作符.

GO法应用于可修系统时,操作符代表的单元是可修系统,因此操作符的成功状态概率P(1)就是可修系统的可用度,操作符的故障状态概率P(2)就是可修系统的不可用度,同时其故障率和维修率分别为λ、μ[2].在工程系统中,λμ一般服从指数分布,其值为常数.

1.2 动态贝叶斯网络基本原理

 图 2 “与”逻辑对应的动态贝叶斯网络 Fig. 2 Dynamic Bayesian network of logic “AND”

1.3 可修部件的动态贝叶斯网络建模

 图 3 操作符动态贝叶斯网络 Fig. 3 Dynamic Bayesian network of operator

2 动态贝叶斯网络映射 2.1 操作符到动态贝叶斯网络的一般映射规则[19]

1) 将操作符(非逻辑门操作符)及其输入信号流映射为动态贝叶斯网络的初始网络根节点,并同时建立相应的各初始网络根节点的转移网络子节点,再建立初始网络中的父节点和转移网络中的对应子节点连接关系.

2) 将每一路输出信号流(除第5类操作符)映射为转移网络的一个节点,并建立与步骤1)中转移网络中的所有节点的父子关联关系(前者为子,后者为父).

3) 根据操作符的状态概率确定初始网络根节点的先验概率,并同时确定对应转移网络中子节点的条件概率表.

4) 根据操作符的运算逻辑给出所有输出信号流对应的转移网络子节点的条件概率表.

2.2 逻辑操作符的动态贝叶斯网络映射

 图 4 第11类操作符及对应动态贝叶斯网络 Fig. 4 Type 11 operator and its dynamic Bayesian network

2.3 功能操作符的动态贝叶斯网络映射

1) 第1、3、8类操作符.

 图 5 第1类操作符及对应动态贝叶斯网络 Fig. 5 Type 1 operator and its dynamic Bayesian network

2) 第5类操作符.

 图 6 第5类操作符及对应动态贝叶斯网络 Fig. 6 Type 5 operator and its dynamic Bayesian network

3) 第6、7类操作符.

 图 7 第6类操作符及对应动态贝叶斯网络 Fig. 7 Type 6 operator and its dynamic Bayesian network

2.4 操作符相关性及其动态贝叶斯网络映射

1) 停工相关:可修系统由于某些单元的故障而停工维修时,没有发生故障的单元随系统的停工而停止工作,且不再发生故障.这种相关性定义为停工相关.

 图 8 操作符之间的停工相关 Fig. 8 Shutdown dependence between operators

2) 备用相关:假设冗余单元处于备用状态时不会发生故障或发生故障率较小,那么冗余备用单元发生故障就和其余单元是否处于故障状态有关,这种相关性定义为备用相关.

 图 9 操作符之间的备用相关 Fig. 9 Standby dependence between operators

3) 维修相关:当可修系统有多个单元同时处于故障状态,而维修工不足,即有些单元在发生故障后不能及时维修.这种相关性定义为维修相关.

 图 10 操作符之间的维修相关 Fig. 10 Repair dependence between operators

3 案例验证

 图 11 核电站高压注水系统GO图 Fig. 11 High-pressure-water-infusion system GO graph of nuclear power station

 编号 类型 单元名称 故障率/a-1 平均维修时间/h 3-5 1 隔离阀A-E 0.21 8.0 8-10 1 上冲离心泵A-C 2.80 8.0 13-15 1 逆止阀A-E 0.08 8.0 注:故障率每年按8 760 h计算.

 编号 类型 单元名称 故障率/a-1 平均维修时间/h 1 5 水箱 0 2 1 主阀门 0.38 8.0 6,7 1 隔离阀D-E 0.21 8.0 11,12 1 安全阀A-B 2.80 8.0 16,17 1 逆止阀D-E 1.92 8.0 18 11 冗余3取2 0.08 8.0 19 2 或门 20,22 1 隔离阀F-H 0.21 8.0 23 2 或门

 图 12 核电站高压注水系统动态贝叶斯网络转移图 Fig. 12 Dynamic Bayesian network transition diagram of high-pressure-water-infusion system of nuclear power station

 操作符名称 t=0 h t=1 h PR(1) PR(2) 主阀门 PR(1) 0.999 957 0.000 043 PR(2) 0 1 隔离阀D-E PR(1) 0.999 976 0.000 024 PR(2) 0 1 安全阀A-B PR(1) 0.999 781 0.000 219 PR(2) 0 1 逆止阀D-E PR(1) 0.999 990 0.000 010 PR(2) 0 1 隔离阀F-H PR(1) 0.999 976 0.000 024 PR(2) 0 1 隔离阀A-C PR(1) 0.999 976 0.000 024 PR(2) 0.882 5 0.117 5 上冲离心泵A-C PR(1) 0.999 680 0.000 320 PR(2) 0.882 5 0.117 5 逆止阀A-C PR(1) 0.999 99 0.000 01 PR(2) 0.882 5 0.117 5

 系统可靠性参数 热端注水 冷端注水 工作概率 0.942 161 0.953 521 停工概率 0.057 839 0.046 479 故障率λ/10-4 0.433 90 0.683 66 平均工作时间MTBF/h 23 046.6 14 627.1

 图 13 核电站高压注水系统动态可用度 Fig. 13 Dynamic availability of high-pressure-water-infusion system of nuclear power station

4 结 论

1) 新算法无需考虑共有信号问题,可根据系统的组成结构直接将操作符转换成为动态贝叶斯网络模型.

2) 新算法可通过成熟的贝叶斯网络软件对可修复操作符直接进行定量求解.

3) 新算法计算简便且转换过程简单直观,易于理解,便于GO法在工程中的推广应用.

 [1] Shen Z P, Gao J, Huang X R.A new quantification algorithm for the GO methodology[J].Reliability Engineering & System Safety, 2000, 67(3):241-247. Click to display the text [2] 沈祖培,黄祥瑞.GO法原理及应用:一种系统可靠性分析方法[M].北京:清华大学出版社, 2004:14-40. Shen Z P, Huang X R.Principle and application of GO methodology[M].Beijing:Tsinghua University Press, 2004:14-40(in Chinese). [3] Shen Z P, Wang Y, Huang X R.A quantification algorithm for a repairable system in the GO methodology[J].Reliability Engineering & System Safety, 2003, 80(3):293-298. Click to display the text [4] Weber P, Jouffe L.Reliability modelling with dynamic Bayesian network[C]//5th IFAC Symposium on Fault Detection Supervision and Safety of Technical Processes.Washington, D.C.:Elsevier Science, 2003. Click to display the text [5] Boudali H, Dugan J B.A new Bayesian network approach to solve dynamic fault trees[C]//51st Annual Reliability and Maintainability Symposium, RAMS 2005:The International Symposium on Product Quality and Integrity.Piscataway, NJ:IEEE Press, 2005:451-456. Click to display the text [6] Portinale L, Raiteri D C, Montani S.Supporting reliability engineers in exploiting the power of dynamic Bayesian networks[J].International Journal of Approximate Reasoning, 2009, 51(2):179-195. Click to display the text [7] 周忠宝,马超群,周经伦,等.基于动态贝叶斯网络的动态故障树分析[J].系统工程理论与实践, 2008, 2(2):35-42. Zhou Z B, Ma C Q, Zhou J L, et al.Dynamic fault tree analysis based on dynamic Bayesian networks[J].Systems Engineering-Theory & Practice, 2008, 2(2):35-42(in Chinese). Cited By in Cnki (35) [8] 苏傲雪,范明天,李仲来,等.基于动态贝叶斯网络的配电系统可靠性分析[J].华东电力, 2012, 11(11):1912-1915. Su A X, Fan M T, Li Z L, et al.Reliability analysis of distribution system based on dynamic Bayesian network[J].East China Electric Power, 2012, 11(11):1912-1915(in Chinese). Cited By in Cnki (2) [9] 姚成玉,陈东宁,王斌.基于T-S故障树和贝叶斯网络的模糊可靠性评估方法[J].机械工程学报, 2014, 50(2):193-201. Yao C Y, Chen D N, Wang B.Fuzzy reliability assessment method based on T-S fault tree and Bayesian network[J].Journal of Mechanical Engineering, 2014, 50(2):193-201(in Chinese). Cited By in Cnki (14) [10] 周忠宝,董豆豆,周经伦.贝叶斯网络在可靠性分析中的应用[J].系统工程理论与实践, 2006, 6(6):95-98. Zhou Z B, Dong D D, Zhou J L.Application of Bayesian networks in reliability analysis[J].Systems Engineering-Theory & Practice, 2006, 6(6):95-98(in Chinese). Cited By in Cnki (14) [11] 邓鑫洋,邓勇,章雅娟,等.一种信度马尔科夫模型及应用[J].自动化学报, 2012, 38(4):666-668. Deng X Y, Deng Y, Zhang Y J, et al.A belief Markov model and its application[J].Acta Automatica Sinica, 2012, 38(4):666-668(in Chinese). Cited By in Cnki (19) [12] Druzdzel M J.SMILE:Structural modeling, inference, and learning engine and GeNIe:A development environment for graphical decision-theoretic models[C]//Proceedings of the National Conference on Artificial Intelligence.Orlando, Florida:AAAI/IAAI, 1999:900-901. Click to display the text [13] Doguc O, Ramirez-Marquez J E.An automated method for estimating reliability of grid systems using Bayesian networks[J].Reliability Engineering & System Safety, 2012, 104(1):96-105. Click to display the text [14] Chu B B.GO methodology:Overview manual, EPRI NP-3123[R].Kansas City:Electric Power Research Institute, 1983:125-130. [15] 李海军.贝叶斯网络理论在装备故障诊断中的应用[M].北京:国防工业出版社, 2009:60-82. Li H J.Application of Bayesian network in fault diagnosis of military equipment[M].Beijing:National Defense Industry Press, 2009:60-82(in Chinese). [16] Mi J, Li Y, Huang H Z, et al.Reliability analysis of multi-state systems with common cause failure based on Bayesian networks[C]//Proceedings of 2012 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering.Piscataway, NJ:IEEE Press, 2012:1117-1121. Click to display the text [17] 马德仲,周真,于晓洋,等.基于模糊概率的多状态贝叶斯网络可靠性分析[J].系统工程与电子技术, 2012, 34(12):2607-2611. Ma D Z, Zhou Z, Yu X Y, et al.Reliability analysis of multi-state Bayesian networks based on fuzzy probability[J].Systems Engineering and Electronics, 2012, 34(12):2607-2611(in Chinese). Cited By in Cnki (11) [18] 周忠宝.基于贝叶斯网络的概率安全评估方法及应用研究[D].长沙:国防科学技术大学, 2006. Zhou Z B.Research on methods and application of probabilistic safety assessment based on Bayesian networks[D].Changsha:National University of Defense Technology, 2006(in Chinese). Cited By in Cnki (59) [19] 刘林林,任翌,王自力,等.基于贝叶斯网络的GO法模型算法[J].系统工程与电子技术, 2015, 37(1):212-218. Liu L L, Ren Y, Wang Z L, et al.Algorithm based-on Bayesian networks for GO methodology[J].Systems Engineering and Electronics, 2015, 37(1):212-218(in Chinese). Cited By in Cnki

#### 文章信息

FAN Dongming, REN Yi, LIU Linlin, LIU Shuzheng, FAN Jian, WANG Zili

Algorithm based-on dynamic Bayesian networks for repairable GO methodology model

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(11): 2166-2176.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0767