﻿ 船舶压载水系统可靠性分析
 舰船科学技术  2023, Vol. 45 Issue (12): 35-39    DOI: 10.3404/j.issn.1672-7619.2023.12.007 PDF

1. 中国船舶集团有限公司第七〇四研究所，上海 200031;
2. 郑州大学 管理学院，河南 郑州 450001;
3. 国防科技大学 智能科学学院 装备综合保障技术重点实验室，湖南 长沙 410073

Reliability analysis of ship ballast water system
YANG Yong1, WANG Xiao2, DUI Hong-yan2, TAO Jun-yong3
1. The 704 Research Institute of CSSC, Shanghai 200031, China;
2. School of Management, Zhengzhou University, Zhengzhou 450001, China;
3. Laboratory of Science and Technology on Integrated Logistics Support, College of Intelligence Science andTechnology, National University of Defense Technology, Changsha 410073, China
Abstract: Ballast water system is an important part of the cruise ship. It can ensure the stability of the ship during navigation. However, the reliability of ballast water system is difficult to analyze because of the complexity of its structure. In order to analyze the reliability of ballast water system, a new reliability analysis method is established based on continuous Bayesian network. This method takes into account the state change of the system under continuous time. Firstly, based on the failure mechanism of ballast water system, a dynamic fault tree model is proposed. Then, using unit step function and impulse function, the dynamic fault tree model is transformed into a continuous time Bayesian network to analyze the system reliability. Finally, the ship ballast water system is simulated using the arithmetic example to obtain the reliability and the curve of remaining life with time.
Key words: ballast water system     dynamic fault tree     reliability     continuous bayesian network
0 引　言

1 船舶压载水系统故障分析

 图 1 船舶压载水系统结构图 Fig. 1 Structure drawing of ship ballast water system

 图 2 压载水系统故障树 Fig. 2 Ballast water system fault tree
2 压载水系统可靠性模型

 $v\left( {t - \eta } \right) = \left\{ \begin{gathered} 1 \quad t \gt \eta ，\\ \frac{1}{2} \quad t = \eta ，\\ 0 \quad t \lt \eta 。\\ \end{gathered} \right.$ (1)

 $\zeta \left( {t - \eta } \right) = \left\{ \begin{gathered} 0 \quad t \ne \eta ，\\ \infty \quad t = \eta 。\\ \end{gathered} \right.$ (2)

 图 3 与门转化为贝叶斯网络 Fig. 3 AND gate is converted to Bayesian networks
 $\begin{split} {f_{{Y_8}|{Y_{11}},{X_{11}}}}\left( {{y_8}|{y_{11}},{x_{11}}} \right) =& v\left( {{x_{11}} - {y_{11}}} \right)\zeta \left( {{y_8} - {x_{11}}} \right) + \\ & v\left( {{y_{11}} - {x_{11}}} \right)\zeta \left( {{y_8} - {y_{11}}} \right) ，\end{split}$ (3)

 $\begin{split} & {f_{{Y_{11}}{X_{11}}{Y_8}}}\left( {{y_{11}},{x_{11}},{y_8}} \right) = \\ & {f_{{Y_8}|{Y_{11}},{X_{11}}}}\left( {{y_8}|{y_{11}},{x_{11}}} \right){f_{{Y_{11}}}}\left( {{y_{11}}} \right){f_{{X_{11}}}}\left( {{x_{11}}} \right) ，\end{split}$ (4)

 $\begin{split} &{f_{{Y_8}}}\left( {{y_8}} \right) =\int_0^\infty {\int_0^\infty {v\left( {{x_{11}} - {y_{11}}} \right)\zeta \left( {{y_8} - {x_{11}}} \right)} } \\ & {f_{{Y_{11}}}}\left( {{y_{11}}} \right){f_{{X_{11}}}}\left( {{x_{11}}} \right){\rm{d}}{x_{11}}{\rm{d}}{y_{11}} + \\ &\int_0^\infty {\int_0^\infty {v\left( {{y_{11}} - {x_{11}}} \right)\zeta \left( {{y_8} - {y_{11}}} \right)} } {f_{{Y_{11}}}}\left( {{y_{11}}} \right){f_{{X_{11}}}}\left( {{x_{11}}} \right){\rm{d}}{x_{11}}{\rm{d}}{y_{11}} =\\ & \frac{{{\rm{d}}\left[ {{F_{{Y_{11}}}}\left( {{y_8}} \right){F_{{X_{11}}}}\left( {{y_8}} \right)} \right]}}{{{\rm{d}}{y_8}}}，\\[-17pt] \end{split}$ (5)
 ${F_{{Y_8}}}\left( t \right) = P\left( {{Y_8} \leqslant t} \right) = {F_{{Y_{11}}}}\left( t \right){F_{{X_{11}}}}\left( t \right) 。$ (6)

 图 4 或门转化为贝叶斯网络 Fig. 4 Or gate is converted to Bayesian networks
 $\begin{split} {f_{{Y_6}|{X_6},{X_7}}}\left( {{y_6}|{x_6},{x_7}} \right) = &v\left( {{x_6} - {x_7}} \right)\zeta {y_6}\left( {{y_7} - {x_7}} \right) + \\ & v\left( {{x_7} - {x_6}} \right)\zeta \left( {{y_6} - {x_6}} \right)。\end{split}$ (7)

 ${f_{{X_6}{X_7}{Y_6}}}\left( {{x_6},{y_7},{y_6}} \right) = {f_{{Y_6}|{X_6},{X_7}}}\left( {{y_6}|{x_6},{x_7}} \right){f_{{X_6}}}\left( {{x_6}} \right){f_{{X_7}}}\left( {{x_6}} \right) ，$ (8)

 $\begin{split} & {f_{{Y_6}}}\left( {{y_6}} \right) = \\ & \int_0^\infty {\int_0^\infty {{f_{_{{Y_6}}|{X_6},{X_7}}}} } \left( {{y_6}|{x_6},{x_7}} \right){f_{{X_6}}}\left( {{x_6}} \right){f_{{X_7}}}\left( {{x_7}} \right){\rm{d}}{x_6}{\rm{d}}{x_7}= \\ & {f_{{X_6}}}\left( {{y_6}} \right) + {f_{{X_7}}}\left( {{y_6}} \right) - \frac{{{\rm{d}}\left[ {{F_{{X_6}}}\left( {{y_6}} \right){F_{{X_7}}}\left( {{y_6}} \right)} \right]}}{{d{y_6}}} 。\end{split}$ (9)

 ${F_{{Y_6}}}\left( t \right) = P\left( {{Y_6} \leqslant t} \right)t = {F_{{X_6}}}\left( t \right) + {F_{{X_7}}}\left( t \right) - {F_{{X_6}}}\left( t \right){F_{{X_7}}}\left( t \right) 。$ (10)

 图 5 热备门转化为贝叶斯网络 Fig. 5 Hot spare gate is converted to Bayesian network
 ${f_{{X_5}|{X_4}}}\left( {{x_5}|{x_4}} \right) = {f_{{X_5}}}\left( {{x_5}} \right) ，$ (11)

 $\begin{split} & {f_{{Y_4}|{X_4},{X_5}}}\left( {{y_4}|{x_4},{x_5}} \right) = v\left( {{x_5} - {x_4}} \right)\zeta \left( {{y_4} - {x_5}} \right) + \\ & v\left( {{x_4} - {x_5}} \right)\zeta \left( {{y_4} - {x_4}} \right) 。\end{split}$ (12)

 $\begin{split} &{f_{{X_4}{X_5}{Y_{\text{4}}}}}\left( {{x_4},{x_5},{y_4}} \right) = {f_{{Y_4}|{X_{\text{4}}},{X_5}}}\left( {{y_4}|{x_4},{x_5}} \right){f_{{X_{\text{5}}}{\text{|}}{X_4}}}\left( {{x_5}{\text{|}}{x_4}} \right)，\\ &{f_{{X_4}}}\left( {{x_4}} \right) = {f_{{Y_4}|{X_{\text{4}}},{X_5}}}\left( {{y_4}|{x_4},{x_5}} \right){f_{{X_5}}}\left( {{x_5}} \right){f_{{X_4}}}\left( {{x_4}} \right)。\\[-10pt] \end{split}$ (13)

 $\begin{split} &{f_{{Y_1}}}\left( y \right) = \\ & \int_0^\infty {\int_0^\infty {{f_{{Y_{\text{1}}}|{X_{\text{1}}},{X_{\text{2}}}}}\left( {y|{x_{\text{1}}},{x_{\text{2}}}} \right){f_{{X_{\text{2}}}}}\left( {{x_{\text{2}}}} \right){f_{{X_1}}}\left( {{x_1}} \right)} } {\rm{d}}{x_2}{\rm{d}}{x_1} =\\ & \frac{{{\rm{d}}\left[ {{F_{{X_{\text{1}}}}}\left( y \right){F_{{X_2}}}\left( y \right)} \right]}}{{{\rm{d}}y}} 。\\[-10pt] \end{split}$ (14)
 ${F_{{Y_4}}}\left( t \right) = P\left( {{Y_4} \leqslant t} \right) = {F_{{X_4}}}\left( t \right){F_{{X_5}}}\left( t \right) 。$ (15)
3 算例分析

 图 6 连续贝叶斯网络模型 Fig. 6 Continuous Bayesian network model

 图 7 系统可靠性变化曲线 Fig. 7 System reliability change curve

 图 8 系统寿命变化曲线 Fig. 8 System life curve

4 结　语

 [1] 杨泽宇, 乔红宇. 基于 InTouch 的船舶压载水监控系统[J]. 中国造船, 2010, 51(3): 185-190. YANG Z Y, Q H Y. Design of ship ballast monitor based on intouch[J]. Shipbuilding of China, 2010, 51(3): 185-190. [2] 张迪, 朱发新, 雷建, 等. 基于模糊故障树的压载水系统可靠性分析[J]. 造船技术, 2012(5): 20-23. DOI:10.3969/j.issn.1000-3878.2012.05.006 [3] 李佩昌, 周海军, 周国敬. 基于专家综合评估的模糊动态故障树分析[J]. 舰船科学技术, 2019, 41(19): 192-197. [4] 白旭, 汤荣铿, 罗小芳, 等. 基于故障树分析和贝叶斯网络方法的半潜式钻井平台系统多状态可靠性分析[J]. 中国造船, 2020, 61(2): 220-228. DOI:10.3969/j.issn.1000-4882.2020.02.021 [5] 易静. 基于贝叶斯网络的舰船故障建模方法研究[J]. 舰船科学技术, 2019, 41(4): 43-45. [6] 苏艳琴, 徐廷学, 张文娟. 粗糙集和贝叶斯网络融合故障诊断方法[J]. 舰船科学技术, 2013, 35(3): 91-93. SU Y Q, XU T X, ZHANG W J. Research on one fusion fault diagnosis method based on rough set theory and bayesian network[J]. Ship Science and Technology, 2013, 35(3): 91-93. [7] 姚成玉, 韩丁丁, 陈东宁, 等. 考虑共因失效的新型连续时间动态贝叶斯网络可靠性分析方法[J]. 仪器仪表学报, 2022, 43(6): 174-184. [8] MAMDIKAR M R, KUMAR V, SINGH P. Dynamic reliability analysis framework using fault tree and dynamic Bayesian network: A case study of NPP[J]. Nuclear Engineering and Technology, 2022, 54(4): 1213-1220. DOI:10.1016/j.net.2021.09.038 [9] 王晓明, 李彦锋, 李爱峰, 等. 模糊数据下基于连续时间贝叶斯网络的整流回馈系统可靠性建模与评估[J]. 机械工程学报, 2015, 51(14): 167-174. DOI:10.3901/JME.2015.14.167 [10] CODETTA-RAITERI D, PORTINALE L. Generalized continuous time bayesian networks as a modelling and analysis formalism for dependable systems[J]. Reliability Engineering & System Safety, 2017, 167: 639-651. [11] 张大信, 郭基联. 动态故障树顶事件概率计算流程[J]. 信息工程大学学报, 2021, 22(5): 566-570+605. DOI:10.3969/j.issn.1671-0673.2021.05.008 [12] LEI X, MACKENZIE C A. Assessing risk in different types of supply chains with a dynamic fault tree[J]. Computers & Industrial Engineering, 2019, 137: 106061. [13] 隆奇芮, 郭智威, 白秀琴, 等. 大型邮轮压载水系统设计技术研究[J]. 舰船科学技术, 2020, 42(5): 85-91. LONG Q R, GUO Z W, BAI X Q, et al. Research on the design technology of ballast water system for large cruise ships[J]. Ship Science and Technology, 2020, 42(5): 85-91. DOI:10.3404/j.issn.1672-7649.2020.05.017