Fault diagnosis of mine drainage system based on fuzzy Bayesian network
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摘要: 矿井排水系统不断向自动化、智能化方向发展，系统结构和功能越来越复杂，单一部件的功能异常和故障问题可能会造成整个系统故障。针对现有矿井排水系统故障诊断方法实施难度较大、未考虑系统的整体性、故障诊断效率低等问题，提出一种基于模糊贝叶斯网络的矿井排水系统故障诊断方法。首先，利用故障树分析法将系统的故障原因逐层分解细化，找出系统故障的根本原因。其次，将故障树中的事件转换为贝叶斯网络的节点，逻辑门转换为贝叶斯网络的有向边及条件概率，根据故障树与贝叶斯网络之间的映射关系构建贝叶斯网络。然后，将模糊集合理论引入贝叶斯网络中，通过专家评估确定故障与征兆间的关联强度，经三角模糊数模糊化、均值化、去模糊化处理，得到模糊贝叶斯网络的条件概率。最后，根据先验概率和条件概率，利用模糊贝叶斯网络判断各根节点的故障概率。利用Genie3.0仿真软件建立模糊贝叶斯网络并进行推理分析和诊断测试，结果表明，该方法对各故障征兆的诊断准确率均在80%以上，平均准确率为82.7%。该方法不仅能确定故障源的具体位置和具体部件，还能找出矿井排水系统的薄弱点，排除潜在故障，提升系统的可靠性与安全性。Abstract: The mine drainage system is developing towards automation and intelligence. The system's structure and function are becoming more and more complex, and the abnormal function and failure of a single component may cause the failure of the whole system. The existing fault diagnosis methods of the mine drainage system have problems, such as difficult implementation, no consideration of the integrity of the system, and low fault diagnosis efficiency. In order to solve the above problems, a fault diagnosis method of mine drainage system based on fuzzy Bayesian network is proposed. Firstly, the fault tree analysis method is used to decompose the fault causes of the system layer by layer, and find out the root cause of the system fault. Secondly, the events in the fault tree are transformed into the nodes of the Bayesian network. The logic gates are transformed into the directed edges and conditional probabilities of the Bayesian network. The Bayesian network is constructed according to the mapping relationship between the fault tree and the Bayesian network. Thirdly, the fuzzy set theory is introduced into the Bayesian network. The correlation strength between fault and symptom is determined by expert evaluation. After fuzzification by triangular fuzzy number, averaging and defuzzification, the conditional probability of the fuzzy Bayesian network is obtained. Finally, according to the prior probability and conditional probability, the fuzzy Bayesian network is used to judge the probability of each root node fault. The simulation software Genie3.0 is used to establish the fuzzy Bayesian network, and the reasoning analysis and diagnosis test are carried out. The results show that the diagnosis accuracy of the method for each fault symptom is above 80%, and the average accuracy is 82.7%. The method can not only determine the specific position and specific components of the fault source, but also find out the weak nodes of the mine drainage system, eliminate potential faults, and improve the reliability and safety of the system.
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图 2 故障树与模糊贝叶斯网络的转换流程
Figure 2. The conversion process of fault tree to fuzzy Bayesian network
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图 3 故障树逻辑门与模糊贝叶斯网络的转换关系
Figure 3. Transformation relationship between logic gate of fault tree and fuzzy Bayesian network
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图 6 根节点先验概率与后验概率对比
Figure 6. Comparison of prior probability and posterior probability of root node
表 1 矿井排水系统故障树各符号意义
Table 1 Significance of symbols of fault tree of mine drainage system
符号 故障 符号 故障 T 排水系统故障 X7 淤塞 E1 流量异常 X8 散热不良 E2 温度异常 X9 润滑不良 E3 振动信号异常 X10 短路 E4 负压不足 X11 轴承故障 E5 正压不足 X12 叶轮卡死 Y1 管道故障 X13 联轴器故障 Y2 电动机故障 X14 紧固件松动 Y3 水泵故障 X15 水泵汽蚀 Y4 压力水故障 X16 水泵轴故障 Y5 射流装置故障 X17 管道缺水 Y6 真空管道故障 X18 引水阀故障 X1 管道破裂 X19 射流阀故障 X2 闸阀故障 X20 射流器故障 X3 电压过低 X21 真空阀故障 X4 转速过低 X22 真空管堵塞 X5 叶轮损坏 X23 电动机卡死 X6 轴封漏气 X24 电动机缺相 
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表 2 语言变量与三角模糊数之间的对应关系
Table 2 Correspondence between linguistic variables and triangular fuzzy numbers
序号 语言变量 符号 三角模糊数 1 很低 VL （0，0，0.2） 2 低 L （0.1，0.2，0.4） 3 中等 M （0.3，0.5，0.7） 4 高 H （0.6，0.8，0.9） 5 很高 VH （0.8，1.0，1.0）
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表 3 各根节点的先验概率
Table 3 The prior probability of each root node
故障 符号 先验概率 管道破裂 X1 0.02 闸阀故障 X2 0.10 电压过低 X3 0.08 转速过低 X4 0.20 叶轮损坏 X5 0.14 轴封漏气 X6 0.09 淤塞 X7 0.22
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表 4 专家评估结果
Table 4 Expert evaluation results
条件概率 专家评估结果 专家1 专家2 专家3 专家4 P(Y1=1|X1=1,X2=0) VL VL M VL P(Y1=1|X1=0,X2=1) L M L L P(Y2=1|X3=0,X4=1) M L M M P(Y2=1|X3=1,X4=0) VL L L VL P(Y3=1|X6=0,X7=0,X5=1) L M L VL P(Y3=1|X6=0,X7=1,X5=0) M M L M P(Y3=1|X6=0,X7=1,X5=1) M H M M P(Y3=1|X6=1,X7=0,X5=0) L VL VL L P(Y3=1|X6=1,X7=0,X5=1) L L VL VL P(Y3=1|X6=1,X7=1,X5=0) VH M H VH P(E1=1|Y1=0,Y2=0,Y3=1) VH H M H P(E1=1|Y1=0,Y2=1,Y3=0) L H M H P(E1=1|Y1=0,Y2=1,Y3=1) M VH VH VH P(E1=1|Y1=1,Y2=0,Y3=0) L L VL VL P(E1=1|Y1=1,Y2=0,Y3=1) VL L L M P(E1=1|Y1=1,Y2=1,Y3=0) M M L M
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表 5 各叶节点的条件概率
Table 5 Conditional probability of each leaf node
故障 故障征兆 条件概率 X2;X1 Y1 P(Y1=1|X1=1,X2=0)=0.1625 X2;X1 Y1 P(Y1=1|X1=0,X2=1)=0.3125 X3;X4 Y2 P(Y2=1|X3=0,X4=1)=0.4375 X3;X4 Y2 P(Y2=1|X3=1,X4=0)=0.1500 X6;X7;X5 Y3 P(Y3=1|X6=0,X7=0,X5=1)=0.2625 X6;X7;X5 Y3 P(Y3=1|X6=0,X7=1,X5=0)=0.4375 X6;X7;X5 Y3 P(Y3=1|X6=0,X7=1,X5=1)=0.5625 X6;X7;X5 Y3 P(Y3=1|X6=1,X7=0,X5=0)=0.1500 X6;X7;X5 Y3 P(Y3=1|X6=1,X7=0,X5=1)=0.1500 X6;X7;X5 Y3 P(Y3=1|X6=1,X7=1,X5=0)=0.7875 Y1;Y2;Y3 E1 P(E1=1|Y1=0,Y2=0,Y3=1)=0.7375 Y1;Y2;Y3 E1 P(E1=1|Y1=0,Y2=1,Y3=0)=0.5625 Y1;Y2;Y3 E1 P(E1=1|Y1=0,Y2=1,Y3=1)=0.8375 Y1;Y2;Y3 E1 P(E1=1|Y1=1,Y2=0,Y3=0)=0.1500 Y1;Y2;Y3 E1 P(E1=1|Y1=1,Y2=0,Y3=1)=0.2625 Y1;Y2;Y3 E1 P(E1=1|Y1=1,Y2=1,Y3=0)=0.4375
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表 6 故障诊断测试结果
Table 6 Fault diagnosis test results
故障征兆 诊断总次数 诊断正确次数 准确率/% 流量异常 72 60 83.3 振动信号异常 30 24 80.0 正压不足 35 30 85.7 负压不足 46 38 82.6 温度异常 54 44 81.5
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