﻿ 基于专家综合评估的模糊动态故障树分析
 舰船科学技术  2019, Vol. 41 Issue (10): 192-197 PDF

1. 中国舰船研究设计中心，湖北 武汉 430060;
2. 海装装备技术合作中心，北京 100841

Fuzzy dynamic fault tree analysis based on expert comprehensive evaluation
LI Pei-chang1, ZHOU Hai-jun2, ZHOU Guo-jing1
1. China Ship Development and Design Center, Wuhan 430064, China;
2. Naval Equipment Department Equipment Technology Cooperation Center, Beijing 100841, China
Abstract: For new shipdynamic system, the component failure data is often difficult to obtain, and depends on the experts fuzzy language judgment. In order to overcome the problem for shipsystem quantitative assessment, a new Fuzzy Dynamic Fault Tree Analysis method is proposed based on Expert Comprehensive Evaluation, which transforms experts language information into quantitative data, and synthesize expert opinions to evaluate shipsystem reliability.
Key words: expert comprehensive evaluation     fuzzy dynamic fault tree analysis     reliability evaluation
0 引　言

1 基本概念 1.1 动态故障树分析（DFTA）

1.2 顺序二元决策图（SBDD）

1.3 模糊数

 $\begin{array}{l} {\mu _{\mathop{\rm A}\nolimits} }:\;\;U \to [0,\;1]\text{，}\\ \;\;\;\;\;\;\;\;u \to {\mu _{\mathop{\rm A}\nolimits} }(u)\text{。} \end{array}$

2 专家综合评估方法

1）专家信息收集

2）模糊化

3）专家意见归一化

1）计算任2位专家间的认可度 ${S_{ij}}$

 ${S_{ij}} = S({\tilde A_i},{\tilde A_j}) = 1 - \frac{1}{4}\sum\limits_{k = 1}^4 {|{a_{ik}} - {a_{jk}}|}\text{。}$ (1)

2）计算所有专家的认可矩阵M和每位专家的平均认可度 $A({E_i})$

 ${ M} = \left[ {\begin{array}{*{20}{c}} {{s_{11}}}&{\;{s_{12}}}& \ldots &{{s_{1n}}} \\ {{s_{21}}}&{{s_{22}}}& \cdots &{{s_{2n}}} \\ \vdots & \vdots & \ddots & \vdots \\ {{s_{n1}}}&{{s_{n2}}}& \cdots &{{s_{nn}}} \end{array}} \right]\text{。}$ (2)

 $A({E_i}) = \frac{1}{{n - 1}}\sum\limits_{j = 1,j \ne i}^n {{S_{ij}}}\text{。}$ (3)

3）计算专家的相对认可度 $R({E_i})$

 $R({E_i}) = A({E_i})/\sum\limits_{i = 1}^n {A({E_i})} \text{。}$ (4)

4）计算专家的重要度 $IM({E_i})$

 $IM({E_i}) = \frac{{score(i)}}{{\sum\limits_{i = 1}^n {score(i)} }}\text{。}$ (5)

5）计算专家的权重系数 $w({E_i})$

 $w({E_i}) = \alpha IM({E_i}) + (1 - \alpha )R({E_i})\text{。}$ (6)

6）专家意见归一化结果

 ${\tilde \lambda _j} = \sum\limits_{i = 1}^n {{w_i} \cdot } {\tilde \lambda _{ij}},\;\;j = 1,2, \cdots m\text{。}$ (7)

4）去模糊化

COG是一种基于隶属函数重心的去模糊化方法，是目前使用最广泛的方法，其表达式为：

 ${{COG}} (A) = \frac{{\int_{ - \infty }^{ + \infty } {x{\mu _A}(x){\rm d}x} }}{{\int_{ - \infty }^{ + \infty } {{\mu _A}(x){\rm d}x} }}\text{。}$ (8)

 ${{COG}} (A) = \frac{{\int_a^b {x \cdot \frac{{x - a}}{{b - a}}dx + \int_b^c {x \cdot \frac{{c - x}}{{c - b}}dx} } }}{{\int_a^b {\frac{{x - a}}{{b - a}}dx + \int_b^c {\frac{{c - x}}{{c - b}}dx} } }} = \frac{{a + b + c}}{3}\text{。}$ (9)

 $PV = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{{{{10}^{{{(1 - CPS)}^{1/3}} \times 2.301}}}},\;\;CPS \ne 0} ;\\ {\;\;\;\;\;\;\;\;0 ,\;\;\;\;\;\;\;\;\;\;\;\;\;CPS = 0} \text{。} \end{array}} \right.$ (10)

3 基于专家综合评估的系统模糊动态故障树分析

1）顶事件发生概率计算

2）系统重要度分析

 $IM(i) = {P_T}(t) - {P_{T/i}}(t)\text{。}$ (11)

4 案例分析

A，密封件失效；B，火工品失效；C，关键电子器件失效；D，关键备用电子器件失效；E，陀螺仪驱动装置失效；F，激光探测器失效。考虑各种失效模式之间的时间相关、功能相关，建立了弹药控制系统的动态故障树，如图1所示。

 图 1 弹药控制系统动态故障树 Fig. 1 Dynamic fault tree of ammunition control system
4.1 弹药控制系统专家综合评估

1）专家信息收集

2）模糊化

3）专家意见归一化

 ${ M} = \left[ {\begin{array}{*{20}{c}} 1&{0.63}&{0.86}&{0.63}&1 \\ {0.63}&1&{0.77}&1&{0.63} \\ {0.86}&{0.77}&1&{0.77}&{0.86} \\ {0.63}&1&{0.77}&1&{0.63} \\ 1&{0.63}&{0.86}&{0.63}&1 \end{array}} \right]\text{。}$

4.2 弹药控制系统动态故障树分析

1）系统可靠性评估

 $\begin{array}{l} {P_1} = P({\rm{A}} \to {\rm{B}})\text{，}\\ {P_2} = [1 - P({\rm{A}} \to {\rm{B}})] \cdot P({\rm{C}} \to {\rm{D}})\text{，}\\ {P_3} = [1 - P({\rm{A}} \to {\rm{B}})] \cdot P({\rm{D}} \to {\rm{C}})\text{，}\\ {P_4} = [1 - P({\rm{A}} \to {\rm{B}})] \cdot [1 - P({\rm{C}} \to {\rm{D}}) - P({\rm{D}} \to {\rm{C}})] \cdot P({\rm{F}})\text{，}\\ {P_5} = \{ [1 - P({\rm{A}})] \cdot P({\rm{B}}) + P({\rm{B}} \to {\rm{A}})\} \cdot \\ \;\;\;\;\;\;\;[1 - P({\rm{C}} \to {\rm{D}}) - P({\rm{D}} \to {\rm{C}})] \cdot [1 - P({\rm{F}})] \cdot P({\rm{E}})\text{。} \end{array}$

 ${P_T} = {P_1} + {P_2} + {P_3} + {P_4} + {P_5}\text{。}$

 图 2 系统可靠性随时间变化曲线 Fig. 2 System reliability curve with time

2）系统重要度分析

5 结　语

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