﻿ 基于抽象故障树的化工事故预警
 计算机系统应用  2018, Vol. 27 Issue (9): 151-156 PDF

Chemical Accident Early Warning Analysis Based on Abstract Fault Tree
MA Chao, DU Jun-Wei, HU Qiang
Information Science and Technology Academy, Qingdao University of Science and Technology, Qingdao 266061, China
Foundation item: National Natural Science Foundation of China (61273180); Natural Science Foundation of Shandong Province (ZR2012FL17); Key Research and Development Plan of Shandong Province (2018GGX101052, 2016GGX101031); Outstanding Young and Middle-Aged Scientists Award Foundation of Shandong Province (BS2015DX010)
Abstract: Scenarios are effective mechanisms for analyzing the occurrence, development, and possible consequences of an accident. However, lack of effective model to model or limitation of models to analysis, scenario-based early warning mechanisms are difficult to popularize in practice. Abstract fault tree is a high-level abstraction of the same kind of fault tree. Based on historical cases and expert experiences, it can characterize the mechanism, evolution process, and possible consequences of the accident, and can effectively support scenario-based early warning analysis. A method of early warning of chemical accidents based on abstract fault tree is proposed. Based on the abstract map relation, hazard degree, and importance level of nodes are calculated. The scenario-evolved cutting set model is transformed into Bayesian network model. Board method is used to measure risk of accident hazard. The ranking of defense events can be used to predict the accident risk and propose the best coping strategies based on different evolution paths of scenarios. The experimental results show the effectiveness of this method in accident analysis and early warning.
Key words: fault tree     Board method     Bayesian network     early warning

1 基于抽象故障树的事故模型

1) V代表故障树的节点集合;

2) G为逻辑门集合, $\forall g \in G$ , 定义逻辑门的类型 $Type\left( g \right) \in \left\{ {\rm{And,Or}} \right\}$ ;

3) E为抽象故障树的边集合, $E \subseteq V \times G \cup G \times V$ ;

4) v0代表根节点, ${V_L} = \{ {\rm{v}} \in V \wedge G(\nexists {\rm{g}} \in G,(v,g) \in E)\}$ 为叶子节点, ${V_M} = \{ v|v \in V \wedge (\exists g \in G,(v,g) \in E)\}$ 为中间节点.

2 基于抽象故障树的预警分析

2.1 故障树割集的贝叶斯网络转换

ev包含以x为故障树中根节点的子树ext和故障树中其他关联部分exo, 那么信念:

 $\begin{split}B{\rm{el}}(x) & = P({{x|ev}}) = P(x|{e_{xt}},{e_{xo}})\\ & = \frac{{P({{\rm{e}}_{xt}}|{e_{xo}},x)P(x|{e_{xo}})}}{{P({{\rm{e}}_{xt}}|{e_{xo}})}} = \frac{{P({e_{xt}}|x)P(x|{e_{xo}})}}{{P{\rm{(}}{{\rm{e}}_{xt}}|{e_{xo}})}}\end{split}$ (1)

$\alpha = 1/P({e_{xt}}|{e_{xo}})$ , $\lambda \left( x \right) = P\left( {{e_{xt}}|x} \right)$ , $\pi \left( x \right) = P\left( {x|{e_{xo}}} \right)$ , 此时,

 $Bel\left( x \right) = \alpha \lambda \left( x \right)\pi \left( x \right)$ (2)

Step1. 依据故障树不同逻辑门的语义, 将抽象故障树转换为贝叶斯网络模型.

Step2. 依据情景, 计算情景关联的事件集合.

Step3. 依据割集事件在贝叶斯网络中信念传递更新, 求解基于割集扩展的贝叶斯子网.

Step4. 由割集扩展得到的子网的底事件开始, 逐层进行概率运算.

Step5. 判断当前节点是否包含顶节点, 不包含执行Step6, 否者执行Step9.

Step6. 依据事件间的连接门, 计算关联节点间的连接概率P, 并计算当前事件对预测的支持π.

Step7. 由于故障树中底事件节点的概率是由历史事故统计而来, 式中λ(x)为(1, 1), 归一化因子α近似为(1, 1), 信念公式可简化为: $Bel\left( x \right) = \pi \left( x \right)$ .

Step8. 根据信念公式计算出上层事件VM的信念值, 执行Step5.

Step9. 得到当前割集发生的概率.

2.2 基于Borda序值法进行事故的预警推荐

Borda 序值法是一种经典的投票表决法, 依据投票人通过投票表达出对各候选人的偏好次序, 然后对候选人从高到低进行评分并累加, 得分最高者最终获胜. 依据2.1提供算法可以计算不同演化路径的事件发生概率及事件重要度概率, 是一个典型的两目标优化问题. 因此, 我们使用Borda序值法对事故以及其包含的节点事件进行重要度排序, 计算每种演化路径的不同风险值.

N为风险包含因素数, 设i为某一特定风险, k表示某一准则原始风险矩阵只有两个准则. 用k=1表示风险影响I, k=2表示风险概率P. 如果rik表示风险i在准则k下的风险等级, 则风险i的Borda数可由下式给出: ${b_i} = \sum {(N - {r_{ik}})}$ , 某一因素的Borda序值即为比这个风险因素的Borda数大的风险因素的个数[14].

Step1. 由事故损失和事故概率确定事故等级分布.

Step2. 由求得割集的概率和对应的历史事故损失确定割集的初步风险等级.

Step3. 由割集的概率和对应的历史事故损失, 根据border法求得每个割集对应的border数值.

Step4. 根据border数值, 计算割集对应的border序值.

Step5. 根据border序值对割集的重要度进行排序.

Step6. 得到割集对应事故的重要度排序, 即事故重要度排序.

Step7. 根据事故重要度排序, 进行事故预警推荐.

3 案例分析

 图 1 泄露着火爆炸型抽象故障树 Fig. 1 The standard FT of fire explosion

4 结论

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