Semi-supervised Classification of Semi-molten Working Condition of Fused Magnesium Furnace Based on Image and Current Features
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摘要: 针对电熔镁炉异常工况识别任务, 在半监督学习框架下提出一种将电流与图像两类特征融合的解决方案. 主要贡献为: 使用多元图像分析(Multivariate image analysis, MIA)技术代替人眼, 更为准确客观地对镁炉火焰进行特征提取; 利用基于熵正则化(Entropy regularization, ER)的半监督学习框架, 同时使用具有强互补性的生产图像与电流数据进行工况分类, 从而弥补了基于单一特征分类的某些缺点; 采用交叉熵方法(Cross-entropy method, CEM)优化分类器目标函数, 较传统优化方法显著地提升了训练速度. 通过仿真数据与公开数据集测试并讨论了本文算法的优势, 并通过工业数据验证了所提方法的有效性、应用价值与良好的鲁棒性.Abstract: Aiming at the task of identifying abnormal working conditions of fused magnesium furnace, this paper proposes a solution that combines the two types of features of current and image under the framework of semi-supervised learning. The main contributions of this paper are: Using multivariate image analysis (MIA) technology to replace the human eyes, and extracting features of magnesium furnace flames more accurately and objectively; using a semi-supervised learning framework based on entropy regularization (ER), and at the same time using strong complementary production images and current data to classify working conditions, thereby making up for some shortcomings in classification based on single feature; the cross-entropy method (CEM) is used to optimize the objective function of the classifier, which significantly improves the training speed compared with the traditional optimization method. The advantages of the algorithm in this paper are tested and discussed through simulation data and public data sets; and the effectiveness, application value and good robustness of the method proposed in this paper are verified through industrial data.
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图 4 特征融合前后分类实验结果对比
Fig. 4 Comparison of classification experiment results before and after feature fusion
表 1 分类准确率结果比较(97%与95%无标记占比)
Table 1 Comparison of classification accuracy (97% and 95% unlabeled)
数据 无标记占比: 97% 无标记占比: 95% CEM-ER Sf-T S3VM Co-T CPLE LaN CEM-ER Sf-T S3VM Co-T CPLE LaN 1 $56.8{\pm4.2}$ $53.8{\pm6.8}$ $52.2{\pm5.7}$ $49.7{\pm6.3}$ $56.0{\pm3.0}$ $52.3{\pm4.7}$ $59.9{\pm5.7}$ $48.0{\pm7.8}$ $50.5{\pm5.8}$ $50.8{\pm8.0}$ $53.7{\pm3.6}$ $53.9{\pm5.8}$ 2 $63.2{\pm15.0}$ $65.5{\pm20.0}$ $50.2{\pm16.0}$ $64.8{\pm21.0}$ $75.7{\pm3.6}$ $57.5{\pm16.0}$ $64.0{\pm8.1}$ $50.6{\pm22.0}$ $49.9{\pm13.0}$ $60.9{\pm13.0}$ $76.1{\pm2.3}$ $60.5{\pm11.0}$ 3 $51.9{\pm9.0}$ $51.7{\pm12.0}$ $52.7{\pm13.0}$ $41.2{\pm13.0}$ $28.5{\pm3.3}$ $53.0{\pm10.1}$ $62.3{\pm7.7}$ $60.1{\pm17.0}$ $53.6{\pm11.0}$ $56.2{\pm9.8}$ $30.9{\pm3.5}$ $58.8{\pm8.8}$ 4 $72.9{\pm6.4}$ $61.3{\pm16.0}$ $69.7{\pm6.7}$ $59.1{\pm12.0}$ $60.9{\pm3.8}$ $45.0{\pm7.5}$ $73.2{\pm11.0}$ $57.6{\pm13.0}$ $75.7{\pm9.2}$ $65.7{\pm11.0}$ $35.8{\pm11.0}$ $47.5{\pm10.0}$ 5 $57.9{\pm5.9}$ $51.8{\pm8.3}$ $56.7{\pm8.3}$ $57.3{\pm8.0}$ $45.7{\pm8.8}$ $52.7{\pm6.6}$ $58.9{\pm4.8}$ $52.5{\pm11.0}$ $57.8{\pm9.0}$ $56.4{\pm10.0}$ $47.6{\pm4.2}$ $52.5{\pm6.5}$ 6 $67.2{\pm9.7}$ $67.8{\pm12.0}$ $70.1{\pm8.7}$ $69.8{\pm16.0}$ $42.7{\pm5.3}$ $54.7{\pm9.8}$ $62.1{\pm5.0}$ $60.9{\pm8.9}$ $71.4{\pm5.1}$ $75.7{\pm6.3}$ $46.4{\pm4.4}$ $57.7{\pm7.5}$ 7 $53.5{\pm5.8}$ $51.0{\pm7.0}$ $56.9{\pm3.0}$ $52.4{\pm4.6}$ $61.1{\pm1.3}$ $47.8{\pm6.0}$ $50.0{\pm4.2}$ $51.7{\pm4.6}$ $57.6{\pm6.0}$ $49.7{\pm2.2}$ $62.2{\pm1.2}$ $52.0{\pm5.2}$ 8 $93.1{\pm1.5}$ $96.2{\pm1.6}$ $96.6{\pm1.4}$ $94.1{\pm1.7}$ $68.8{\pm 5.3}$ $89.5{\pm1.8}$ $94.0{\pm1.0}$ $96.5{\pm1.3}$ $96.3{\pm1.2}$ $93.7{\pm1.5}$ $70.7{\pm4.8}$ $89.7{\pm1.5}$ 平均 64.56 62.38 63.14 61.01 54.93 56.56 65.54 59.73 64.08 63.61 52.91 59.07 
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表 3 分类准确率结果比较(80%与60%无标记占比)
Table 3 Comparison of classification accuracy (80% and 60% unlabeled)
数据 无标记占比: 80% 无标记占比: 60% CEM-ER Sf-T S3VM Co-T CPLE LaN CEM-ER Sf-T S3VM Co-T CPLE LaN 1 $65.1{\pm5.5}$ $47.8{\pm8.8}$ $50.9{\pm5.5}$ $45.5{\pm6.3}$ $59.0{\pm2.8}$ $56.7{\pm6.1}$ $63.7{\pm3.6}$ $55.7{\pm5.9}$ $49.8{\pm6.6}$ $52.9{\pm4.3}$ $56.6{\pm3.3}$ $58.7{\pm4.6}$ 2 $64.9{\pm3.9}$ $50.2{\pm13.0}$ $64.9{\pm8.0}$ $71.7{\pm6.8}$ $72.2{\pm1.9}$ $68.0{\pm7.0}$ $68.8{\pm4.3}$ $53.2{\pm5.4}$ $65.9{\pm3.5}$ $72.1{\pm5.4}$ $67.6{\pm2.6}$ $71.6{\pm4.8}$ 3 $66.4{\pm8.0}$ $50.8{\pm19.0}$ $59.8{\pm9.7}$ $58.4{\pm10.0}$ $34.7{\pm2.7}$ $67.4{\pm8.5}$ $64.4{\pm7.2}$ $44.1{\pm23.0}$ $62.6{\pm11.0}$ $58.6{\pm7.5}$ $39.2{\pm19.0}$ $69.6{\pm8.9}$ 4 $80.8{\pm3.0}$ $68.5{\pm3.9}$ $83.8{\pm4.4}$ $74.9{\pm8.1}$ $39.5{\pm13.0}$ $67.9{\pm4.7}$ $81.6{\pm2.8}$ $73.7{\pm3.0}$ $85.9{\pm3.0}$ $83.9{\pm4.9}$ $67.5{\pm20.0}$ $77.4{\pm3.1}$ 5 $60.0{\pm7.4}$ $61.6{\pm8.0}$ $70.5{\pm7.2}$ $66.8{\pm5.7}$ $54.6{\pm6.8}$ $57.1{\pm7.2}$ $66.5{\pm5.8}$ $61.9{\pm7.6}$ $73.0{\pm6.7}$ $72.4{\pm6.8}$ $58.1{\pm7.7}$ $58.7{\pm6.4}$ 6 $76.3{\pm2.7}$ $71.0{\pm3.6}$ $78.2{\pm5.4}$ $80.0{\pm2.9}$ $52.4{\pm8.8}$ $71.6{\pm6.1}$ $81.0{\pm2.9}$ $76.1{\pm4.2}$ $82.8{\pm4.8}$ $83.0{\pm3.9}$ $64.6{\pm6.8}$ $80.3{\pm4.8}$ 7 $59.7{\pm2.2}$ $34.7{\pm3.5}$ $60.4{\pm3.1}$ $51.4{\pm4.2}$ $65.3{\pm2.7}$ $55.6{\pm3.2}$ $61.1{\pm2.1}$ $36.8{\pm3.9}$ $61.5{\pm2.8}$ $58.3{\pm2.5}$ $64.2{\pm3.0}$ $56.9{\pm2.9}$ 8 $96.0{\pm1.0}$ $96.7{\pm1.2}$ $96.8{\pm1.3}$ $96.2{\pm1.4}$ $80.4{\pm9.3}$ $96.2{\pm1.9}$ $95.9{\pm1.0}$ $96.7{\pm1.0}$ $96.9{\pm0.8}$ $96.8{\pm1.0}$ $90.6{\pm3.1}$ $97.1{\pm1.0}$ 平均 71.15 60.15 70.64 68.11 57.26 67.57 72.86 62.28 72.29 72.24 63.56 71.27
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表 2 分类准确率结果比较(92%与90%无标记占比)
Table 2 Comparison of classification accuracy (92% and 90% unlabeled)
数据 无标记占比: 92% 无标记占比: 90% CEM-ER Sf-T S3VM Co-T CPLE LaN CEM-ER Sf-T S3VM Co-T CPLE LaN 1 $59.1{\pm5.5}$ $51.3{\pm8.9}$ $48.2{\pm7.1}$ $49.0{\pm6.5}$ $56.7{\pm2.8}$ $53.4{\pm6.6}$ $61.1{\pm5.6}$ $48.4{\pm9.0}$ $47.4{\pm7.1}$ $47.3{\pm5.7}$ $58.4{\pm4.6}$ $53.8{\pm5.8}$ 2 $65.6{\pm7.7}$ $50.1{\pm21.0}$ $58.1{\pm15.0}$ $72.6{\pm11.0}$ $73.7{\pm1.6}$ $63.1{\pm9.5}$ $64.7{\pm5.5}$ $49.4{\pm15.0}$ $58.2{\pm11.0}$ $72.2{\pm4.2}$ $77.9{\pm2.3}$ $65.8{\pm6.5}$ 3 $60.3{\pm8.4}$ $53.8{\pm23.0}$ $61.7{\pm11.0}$ $51.7{\pm11.0}$ $28.2{\pm3.0}$ $52.4{\pm8.8}$ $62.0{\pm10.0}$ $44.4{\pm13.0}$ $56.3{\pm6.7}$ $56.9{\pm10.4}$ $27.5{\pm3.5}$ $57.6{\pm7.8}$ 4 $73.3{\pm11.0}$ $61.8{\pm13.0}$ $82.7{\pm9.5}$ $68.4{\pm10.0}$ $38.5{\pm11.0}$ $57.8{\pm11.0}$ $78.4{\pm10.0}$ $57.5{\pm19.0}$ $80.7{\pm6.9}$ $72.2{\pm4.4}$ $37.6{\pm6.6}$ $64.2{\pm9.5}$ 5 $57.1{\pm6.5}$ $56.7{\pm8.6}$ $65.7{\pm8.0}$ $56.7{\pm8.4}$ $47.3{\pm9.7}$ $51.1{\pm8.5}$ $59.5{\pm6.8}$ $54.3{\pm7.0}$ $66.7{\pm9.9}$ $58.7{\pm9.2}$ $48.4{\pm4.8}$ $55.6{\pm8.7}$ 6 $70.4{\pm5.0}$ $66.9{\pm8.5}$ $77.4{\pm3.5}$ $79.8{\pm5.2}$ $44.7{\pm7.8}$ $58.5{\pm6.5}$ $71.0{\pm4.2}$ $71.1{\pm4.7}$ $78.6{\pm4.6}$ $80.5{\pm6.2}$ $50.2{\pm8.5}$ $65.4{\pm5.5}$ 7 $54.2{\pm4.3}$ $49.3{\pm4.5}$ $51.7{\pm6.0}$ $51.4{\pm2.5}$ $65.6{\pm2.1}$ $54.2{\pm5.8}$ $58.2{\pm3.3}$ $49.9{\pm4.5}$ $59.0{\pm3.5}$ $57.6{\pm4.7}$ $61.4{\pm3.3}$ $54.9{\pm4.7}$ 8 $94.1{\pm1.3}$ $96.4{\pm1.5}$ $96.2{\pm2.0}$ $94.9{\pm1.9}$ $70.2{\pm4.6}$ $91.9{\pm1.9}$ $95.7{\pm1.3}$ $97.2{\pm1.4}$ $96.8{\pm1.1}$ $96.0{\pm1.5}$ $69.1{\pm3.0}$ $95.7{\pm2.2}$ 平均 66.76 60.77 67.74 65.56 53.11 60.30 68.82 59.00 67.96 67.68 53.79 64.12
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表 4 分类器训练速度比较(UCI数据集)
Table 4 Comparison of classifiers′ training speed (UCI dataset)
数据集 无标记 97% 无标记 95% 无标记 92% 无标记 90% 无标记 80% 无标记 60% ER CEM-ER ER CEM-ER ER CEM-ER ER CEM-ER ER CEM-ER ER CEM-ER Bupa 6.94 1.77 6.95 1.77 6.73 1.71 6.94 1.73 7.17 1.75 7.12 1.79 Blood 20.06 2.34 20.31 2.36 20.22 2.41 20.16 2.45 20.14 2.36 19.44 2.47 Haberman 8.31 2.55 7.58 2.25 7.28 1.92 7.66 2.27 6.31 2.27 6.97 1.91 Ionosphere 9.16 1.92 8.98 1.80 7.59 2.22 8.98 2.55 8.63 1.80 7.95 1.80 Sonar 6.19 2.25 5.05 1.83 5.16 1.80 5.67 1.92 5.23 1.86 5.55 1.70 Statlog (Heart) 6.19 2.16 6.05 1.89 5.81 2.05 5.97 1.86 6.31 1.77 5.64 1.81 Tic-tac-toe 31.00 2.97 28.75 2.88 20.03 2.89 30.14 3.11 32.36 3.08 32.58 3.20 WBC 28.66 5.16 21.76 3.02 21.58 2.78 19.69 2.56 20.91 2.56 16.45 2.64 平均值 14.56 2.64 13.18 2.22 11.80 2.22 13.15 2.31 13.38 2.18 12.71 2.17
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表 5 电熔镁炉生产数据实验结果
Table 5 Experimental results of fused magnesium furnace production data
无标记占比 $\phi_v^{{\rm{SSL}}}$准确率 $\phi_{vc}^{{\rm{SSL}}}$准确率 准确率提升 97% 66.72% 86.77% 30.05% 95% 67.79% 91.84% 35.49% 92% 70.72% 93.01% 31.51% 90% 71.67% 93.98% 31.14% 80% 72.86% 94.30% 29.43% 60% 74.00% 94.68% 27.93%
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表 6 过渡态样本准确率测试
Table 6 Accuracy of the test on transition state samples
无标记占比 CEM-ER Sf-T ${\rm{S}}^3$VM Co-T CPLE LaN 97% 52.22% 48.89% 48.89% 46.67% 50.00% 49.53% 95% 50.00% 49.17% 47.78% 48.61% 50.00% 49.07% 92% 48.33% 47.50% 47.78% 46.94% 50.00% 50.00% 90% 49.72% 48.61% 50.83% 49.17% 50.00% 54.17% 80% 50.83% 45.00% 48.33% 47.50% 50.00% 50.27% 60% 52.22% 50.56% 50.83% 46.39% 50.00% 50.92%
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表 7 分类器鲁棒性测试结果
Table 7 Classifier robustness test results
无标记占比 原准确率 新测试集准确率 97% 86.77% 84.06% 95% 91.84% 86.63% 92% 93.01% 88.32% 90% 93.98% 89.75% 80% 94.30% 91.02% 60% 94.68% 91.14%
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表 8 分类器训练速度测试(生产数据)
Table 8 Comparison of classifiers′ training speed (production data)
无标记占比 ER CEM-ER 速度提升 97% 94.57 4.12 95.64% 95% 86.63 4.06 95.31% 92% 83.92 4.15 95.05% 90% 73.48 4.18 94.31% 80% 59.47 4.24 92.87% 60% 15.21 4.39 71.14%
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表 9 优化算法准确率对比测试结果
Table 9 Comparison of accuracy in different optimization algorithms
无标记占比 ER CEM-ER 97% 88.33% 92.04% 95% 89.62% 90.80% 92% 91.00% 93.11% 90% 92.16% 93.16% 80% 93.76% 93.58% 60% 94.50% 94.15%
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