Abnormal Condition Identification Based on Bayesian Network Parameter Transfer Learning for the Electro-fused Magnesia
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摘要:
在贝叶斯网络(Bayesian network, BN)参数学习中, 如果数据不够充分, 将无法建立准确的BN模型来分析和解决问题. 针对电熔镁炉熔炼过程的异常工况识别建模, 提出一种新的BN参数迁移学习方法来改进异常工况识别精度. 该方法可以解决源域BN与目标域BN在结构不一致情况下的参数迁移学习问题. 在实验部分, 首先在著名的Asia网络上对该方法进行了验证, 然后将其应用于电熔镁炉熔炼过程排气异常工况识别BN模型的参数学习. 实验结果表明, 与小数据下建立的目标域BN模型相比, 该方法较大地提高了异常工况识别的准确性.
Abstract:In Bayesian network (BN) parameter learning, if the data is not sufficient, an accurate BN model cannot be established to analyze and solve the problem. Aiming at the abnormal condition identification modeling of the electro-fused magnesia, a new BN parameter transfer learning method is proposed in this paper to improve the accuracy of abnormal condition identification. This method can solve the parameter transfer learning problem when the structure of the source domain BN and the target domain BN are inconsistent. In the experimental section, the method is first verified by the well-known Asia network. Then, it is applied to the parameter learning of the BN model for identifying abnormal conditions of exhaust gas in the smelting process of the electro-fused magnesia. Experimental results show that compared with the target domain BN model established under small data, the proposed method greatly improves the accuracy of abnormal condition identification.
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图 2 电熔镁炉熔炼过程示意图
Fig. 2 Schematic diagram of the electro-fused magnesia furnace smelting process
图 3 电熔镁炉排气异常工况的BN模型结构
Fig. 3 BN model structure for the abnormal exhausting condition of the electro-fused magnesia furnace
图 4 提出的BN参数迁移学习方法流程图
Fig. 4 Flow diagram of the proposed BN parameter transfer learning method
图 8 不同权重
$\eta $ 下的KL散度值Fig. 8 The values of KL divergence under the different weights
$\eta $ 
图 9 电熔镁炉仿真平台
Fig. 9 Construction of simulation platform for electric-fused magnesium furnace
表 1 各节点物理意义
Table 1 Physical meaning of the nodes
节点 物理意义 A 排气异常工况 B 异常声音信息 C 异常图像信息 D 异常电流信息 E 在飞溅特征频率下的短时能量 F 在飞溅特征频率下的幅值 G 平均灰度 H 灰度方差 I 灰度丰度 J 电流变化率 K 电流跟踪误差 
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表 2 节点
$\underline{\underline {\rm A}} $ 和$\underline{\underline {\rm S}} $ 的CPTsTable 2 The CPTs of nodes
$\underline{\underline {\rm A}}$ and$\underline{\underline {\rm S}} $ $\underline{\underline {\rm A}} $ (i = 1) $\underline{\underline {\rm S}} $ (i = 2) 0 (k = 1) 0.99 0.5 1 (k = 2) 0.01 0.5
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表 3 节点
$\underline{\underline {\rm T}} $ 的CPTTable 3 The CPT of node
$\underline{\underline {\rm T}} $ $\underline{\underline {\rm A}} $ 0 (j = 1) 1 (j = 2) $\underline{\underline {\rm T}} $ (i = 3) 0 (k = 1) 0.99 0.95 1 (k = 2) 0.01 0.05
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表 4 节点
$\underline{\underline {\rm L}} $ 的CPTTable 4 The CPT of node
$\underline{\underline {\rm L}} $ $\underline{\underline {\rm S}} $ 0 (j = 1) 1 (j = 2) $\underline{\underline {\rm L}} $ (i = 4) 0 (k = 1) 0.99 0.9 1 (k = 2) 0.01 0.1
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表 5 节点
$\underline{\underline {\rm B}}$ 的CPTTable 5 The CPT of node
$\underline{\underline {\rm B}} $ $\underline{\underline {\rm S}} $ 0 (j = 1) 1 (j = 2) $\underline{\underline {\rm B}} $ (i = 5) 0 (k = 1) 0.99 0.9 1 (k = 2) 0.01 0.1
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表 6 节点
$\underline{\underline {\rm E}} $ 的CPTTable 6 The CPT of node
$\underline{\underline {\rm E}} $ $\underline{\underline {\rm T}} $ 0 1 $\underline{\underline {\rm L}} $ 0 (j = 1) 1 (j = 2) 0 (j = 3) 1 (j = 4) $\underline{\underline {\rm E}} $ (i = 6) 0 (k = 1) 1 0 0 0 1 (k = 2) 0 1 1 1
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表 7 节点
$\underline{\underline {\rm X}} $ 的CPTTable 7 The CPT of node
$\underline{\underline {\rm X}}$ $\underline{\underline {\rm E}} $ 0 (j = 1) 1 (j = 2) $\underline{\underline {\rm X}} $ (i = 7) 0 (k = 1) 0.95 0.02 1 (k = 2) 0.05 0.98
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表 8 节点
$\underline{\underline {\rm D}} $ 的CPTTable 8 The CPT of node
$\underline{\underline {\rm D}} $ $\underline{\underline {\rm E}} $ 0 1 $\underline{\underline {\rm B}} $ 0 (j = 1) 1 (j = 2) 0 (j = 3) 1 (j = 4) $\underline{\underline {\rm D}} $ (i = 8) 0 (k = 1) 0.9 0.2 0.3 0.1 1 (k = 2) 0.1 0.8 0.7 0.9
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表 9 Asia网络专家知识形式二
Table 9 The expert knowledge form two for the Asia network
序号 约束 得分 1 $\theta _{321}^t > 0.8$ 1 2 $0.85 < \theta _{421}^t < 0.95$ 1 3 $0.35 < \theta _{521}^t < 0.45$ 1 4 $0.85 < \theta _{811}^t < 0.95$ 1 5 $\theta _{321}^t > 0.9$ 2 6 $0.88 < \theta _{421}^t < 0.92$ 2 7 $0.38 < \theta _{521}^t < 0.42$ 2 8 $0.88 < \theta _{811}^t < 0.92$ 2
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表 10 节点A的参数表达形式
Table 10 The parameters expression of node A
A (i = 1) 1 (k = 1) $\theta _{1\_1}^t$ 2 (k = 2) $\theta _{1\_2}^t$ 3 (k = 3) $\theta _{1\_3}^t$ 4 (k = 4) $\theta _{1\_4}^t$
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表 11 节点B的参数表达形式
Table 11 The parameters expression of node B
A (i = 1) 1 (j = 1) 2 (j = 2) 3 (j = 3) 4 (j = 4) 1 (k = 1) $\theta _{211}^t$ $\theta _{221}^t$ $\theta _{231}^t$ $\theta _{241}^t$ B (i = 2) 2 (k = 2) $\theta _{212}^t$ $\theta _{222}^t$ $\theta _{232}^t$ $\theta _{242}^t$ 3 (k = 3) $\theta _{213}^t$ $\theta _{223}^t$ $\theta _{233}^t$ $\theta _{243}^t$
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表 12 排气异常工况识别模型的专家知识形式一
Table 12 The expert knowledge form one for the abnormal exhausting condition model
序号 约束 1 $\theta _{232}^t < \theta _{233}^t$ 2 $\theta _{333}^t < \theta _{332}^t$ 3 $\theta _{434}^t < \theta _{433}^t$ 4 $\theta _{521}^t < \theta _{522}^t$ 5 $\theta _{831}^t < \theta _{833}^t$ 6 $\theta _{1031}^t < \theta _{1032}^t$
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表 13 排气异常工况识别模型的专家知识形式二
Table 13 The expert knowledge form two for the abnormal exhausting condition model
序号 约束 得分 1 $0.03 < \theta _{341}^t < 0.07$ 1 2 $0.01 < \theta _{512}^t < 0.05$ 1 3 $0.13 < \theta _{923}^t < 0.17$ 1 4 $0.78 < \theta _{1122}^t < 0.82$ 1 5 $0.04 < \theta _{341}^t < 0.06$ 2 6 $0.02 < \theta _{512}^t < 0.04$ 2 7 $0.14 < \theta _{923}^t < 0.16$ 2 8 $0.79 < \theta _{1122}^t < 0.81$ 2
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表 14 三种模型描述
Table 14 Descriptions of the three models
模型 建模方法描述 模型一 仅使用目标域的稀缺数据学习目标域 BN 模型参数 模型二 使用本文提出的方法学习目标域 BN 模型参数 模型三 只考虑结构一致下的相关源域来辅助学习目标域 BN 模型参数
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表 15 排气异常工况的典型事件
Table 15 The typical scenarios for the abnormal exhausting condition
编号 1 2 3 4 5 6 7 8 9 E 1 2 2 3 3 3 3 2 1 F 1 2 3 2 3 3 2 3 1 G 1 1 1 1 1 1 1 1 3 H 1 1 1 1 1 1 1 1 3 I 1 1 1 1 1 1 1 1 3 J 1 1 1 1 1 2 2 2 3 K 1 1 1 1 1 2 2 2 2 编号 10 11 12 13 14 15 16 17 18 E 1 1 1 1 1 1 1 1 1 F 1 1 1 1 1 1 1 1 1 G 3 3 3 3 2 2 2 2 2 H 3 3 3 3 2 2 2 2 2 I 3 3 3 3 2 2 2 2 2 J 3 2 3 2 3 2 2 3 3 K 4 3 3 4 2 3 4 3 4
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表 16 排气异常工况识别模型一的识别结果
Table 16 The identification results of abnormal scenarios for model one
事件编号 1 2 3 4 5 6 7 8 9 节点A的状态 1 0.5167 0.3887 0.3730 0.3721 0.3572 0.3123 0.2964 0.2849 0.0026 2 0.2471 0.3554 0.4089 0.4307 0.4865 0.2547 0.2055 0.1871 0.0182 3 0.2341 0.2546 0.2170 0.1962 0.1555 0.4243 0.4878 0.5174 0.5426 4 0.0021 0.0013 0.0011 0.0010 0.0008 0.0087 0.0103 0.0106 0.4366 事件编号 10 11 12 13 14 15 16 17 18 节点A的状态 1 0.0017 0.0009 0.0009 0.0042 0.1208 0.0429 0.2268 0.0402 0.0815 2 0.0275 0.0457 0.0314 0.0277 0.0282 0.0784 0.0515 0.0483 0.0433 3 0.5241 0.5530 0.4765 0.7157 0.1490 0.1677 0.2354 0.1295 0.1461 4 0.4467 0.4004 0.4912 0.2524 0.7020 0.7110 0.4863 0.7820 0.7291
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表 17 排气异常工况识别模型二的识别结果
Table 17 The identification results of abnormal scenarios for model two
事件编号 1 2 3 4 5 6 7 8 9 节点A的状态 1 0.8481 0.0495 0.1105 0.1287 0.1772 0.0433 0.0394 0.0342 0.0075 2 0.1266 0.8739 0.7589 0.7377 0.6344 0.1895 0.2761 0.2878 0.0079 3 0.0234 0.0746 0.1293 0.1323 0.1877 0.7629 0.6738 0.6668 0.1440 4 0.0019 0.0020 0.0013 0.0013 0.0007 0.0043 0.0107 0.0112 0.8406 事件编号 10 11 12 13 14 15 16 17 18 节点A的状态 1 0.0018 0.0017 0.0012 0.0039 0.0245 0.0059 0.0130 0.0039 0.0060 2 0.0046 0.0041 0.0041 0.0058 0.0421 0.0223 0.0313 0.0227 0.0257 3 0.0774 0.0793 0.0713 0.1014 0.1523 0.0873 0.1098 0.0786 0.0851 4 0.9162 0.9149 0.9234 0.8889 0.7811 0.8845 0.8459 0.8948 0.8832
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表 18 排气异常工况识别模型三的识别结果
Table 18 The identification results of abnormal scenarios for model three
事件编号 1 2 3 4 5 6 7 8 9 节点A的状态 1 0.7987 0.0412 0.1368 0.1362 0.1259 0.0421 0.0049 0.0052 0.0021 2 0.1881 0.8275 0.7570 0.7498 0.6411 0.1922 0.3574 0.3757 0.0072 3 0.0076 0.1281 0.1034 0.1112 0.2309 0.7593 0.6240 0.6046 0.1293 4 0.0056 0.0032 0.0028 0.0028 0.0021 0.0064 0.0137 0.0145 0.8614 事件编号 10 11 12 13 14 15 16 17 18 节点A的状态 1 0.0003 0.0003 0.0002 0.0006 0.0172 0.0031 0.0063 0.0020 0.0031 2 0.0014 0.0016 0.0011 0.1026 0.1015 0.0278 0.0429 0.0196 0.0250 3 0.1142 0.1168 0.1137 0.5782 0.2461 0.1735 0.1852 0.1473 0.1504 4 0.8841 0.8813 0.8850 0.3186 0.6352 0.7956 0.7656 0.8311 0.8215
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