American Institute of Mathematical Sciences

Advanced
April  2019, 15(2): 595-618. doi: 10.3934/jimo.2018060

Anode effect prediction based on collaborative two-dimensional forecast model in aluminum electrolysis production

Zuguo Chen , Yonggang Li , , Xiaofang Chen , Chunhua Yang and  Weihua Gui

School of Information Science and Engineering, Central South University, Changsha 410083, China

* Corresponding author: liyonggang@csu.edu.cn(Yonggang Li)

Received  October 2017 Revised  December 2017 Published  April 2019 Early access  April 2018

Fund Project: The first author is supported by by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 61621062), the State Key Program of National Natural Science of China (Grant No. 61533020), the Major Program of the National Natural Science Foundation of China (Grant No. 61590921 and 61590923), and the Fundamental Research Funds for the Central Universities of Central South University (Grant No. 502221709).

In this study, a new prediction algorithm is proposed, based on the collaborative two-dimensional forecast model (CTFM) that combines the traditional method and similarity search technique. The main idea of the algorithm is that the prediction of the change trend of the slope and the accumulated slope of the cell resistance as well as the useful knowledge obtained using the similarity search technique are used as the main criteria to calculate anode effect (AE)-prediction reliability. The accumulated mass deviation value is used as an auxiliary criterion to adjust the AE-prediction reliability. Finally, the current AE-process is marked according to the current AE-prediction reliability. The prediction model based on CTFM is tested on a real situation, in which multiple samples are extracted from the production of a 400 kA aluminum electrolysis cell. We observe that when the time advance of AE-prediction is within 20 ~ 40 min, the accuracy rate of the CTFM algorithm is greater than 95% and the applicability of the method is excellent, showing a high prediction accuracy for different aluminum electrolysis cells.

Keywords: Anode effect prediction, collaborative two-dimensional forecast model, similarity search, square-root cubature Kalman filter.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.
Citation: Zuguo Chen, Yonggang Li, Xiaofang Chen, Chunhua Yang, Weihua Gui. Anode effect prediction based on collaborative two-dimensional forecast model in aluminum electrolysis production. Journal of Industrial & Management Optimization, 2019, 15 (2) : 595-618. doi: 10.3934/jimo.2018060
References:
[1]

G. Bearne, M. Dupuis and G. Tarcy, On the anode effect in aluminum electrolysis, in Essential Readings in Light Metals: Aluminum Reduction Technology, (eds. J. Thonstad, T. A. Utigard and H. Vogt), Metals and Alloys, 2 (2013), 131-138. Google Scholar

[2]

B. Bardet, T. Foetisch, S. Renaudier, J. Rappaz, M. Flueck and M. Picasso, Alumina dissolution modeling in aluminium electrolysis cell considering MHD driven convection and thermal impact, Light Metals, Springer International Publishing, (2016), 315-319.   Google Scholar

[3]

D. S. Wong, P. Fraser, P. Lavoie and J. Kim, PFC emissions from detected versus nondetected anode effects in the aluminum industry, JOM, 67 (2015), 342-353.  doi: 10.1007/s11837-014-1265-8.  Google Scholar

[4]

L. Dion, L. I. Kiss, S. Poncsák and C. L. Lagacé, Prediction of low-voltage tetrafluoromethane emissions based on the operating conditions of an aluminium electrolysis cell, JOM, 68 (2016), 2472-2482.  doi: 10.1007/s11837-016-2043-6.  Google Scholar

[5]

L. Kong, C. Yu, K. L. Teo and C. Yang, Robust real-time optimization for blending operation of alumina production, Journal of Industrial and Management Optimization, 13 (2017), 1149-1167.   Google Scholar

[6]

M. Farrow, Prediction of AEs in aluminum reduction cells, JOM, 36 (2013), 33-34.   Google Scholar

[7]

J. Li, F. Q. Ding, M. J. Li, J. Xiao and Z. Zou, Intelligent anode effect prediction method for prebaked-anode aluminum reduction cells, Journal of Central South University of Technology, 32 (2001), 29-32.   Google Scholar

[8]

D. G. Bell, System for predicting impending anode effects in aluminum cells, US, US. 6132571[P], (2000). Google Scholar

[9]

Y. Zhang, Study on anode effect prediction of aluminium reduction applying wavelet packet transform, International Conference on Intelligent Computing, Springer Berlin Heidelberg, (2010), 477-484.  doi: 10.1007/978-3-642-14831-6_62.  Google Scholar

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J. Xing and D. Y. Xiao, Ordered neural network and its application to prediction of anode effect, Control Engineering of China, 14 (2007), 27-36.   Google Scholar

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J. B. Harley and J. M. F. Moura, Data-driven matched field processing for Lamb wave structural health monitoring, The Journal of the Acoustical Society of America, 135 (2014), 1231-1244.   Google Scholar

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V. Y. Bazhin, A. A. Vlasov and A. V. Lupenkov, Controlling the AE in an aluminum reduction cell, Metallurgist, 55 (2011), 463-468.   Google Scholar

[13]

Y. Song, J. P. Peng, Y. W. Wang, Y. Z. Di, B. K. Li and N. X. Feng, Magneto-hydrodynamics simulation of 300 KA novel cell for aluminium electrolysis, Metalurgija, 55 (2016), 22-24.   Google Scholar

[14]

J. Yi, D. Huang, S. Fu, H. He and T. Li, Multi-objective bacterial foraging optimization algorithm based on parallel cell entropy for aluminum electrolysis production process, IEEE Transactions on Industrial Electronics, 63 (2016), 2488-2500.  doi: 10.1109/TIE.2015.2510977.  Google Scholar

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H. Viumdal and S. Mylvaganam, System identification of a non-uniformly sampled multi-rate system in aluminium electrolysis cells, Modeling Identification and Control, 35 (2014), 127-146.  doi: 10.4173/mic.2014.3.1.  Google Scholar

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A. Solheim, Entropic heat effects in aluminum electrolysis cells with inert anodes, Metallurgical and Materials Transactions -B, 47 (2016), 1274-1279.  doi: 10.1007/s11663-015-0561-1.  Google Scholar

[17]

F. Allard, G. Soucy and L. Rivoaland, Formation of deposits on the cathode surface of aluminum electrolysis cells, Metallurgical and Materials Transactions -B, 45 (2014), 2475-2485.  doi: 10.1007/s11663-014-0118-8.  Google Scholar

[18]

J. J. Li, Z. J. Wang and J. L. Zhu, Aluminum electrolysis multi-objective control system based on quantum optimized, Advanced Materials, Technology and Application: Proceedings of the 2016 International Conference on Advanced Materials, Technology and Application (AMTA2016). World Scientific, (2016), 417-423.  doi: 10.1142/9789813200470_0049.  Google Scholar

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H. Zhang, T. Li, J. Li, S. Yang and Z. Zou, Progress in aluminum electrolysis control and future direction for smart aluminum electrolysis plant, JOM, 69 (2017), 292-300.  doi: 10.1007/s11837-016-2150-4.  Google Scholar

[20]

C. K. Hu, F. B. Liu and C. F. Hu, Efficiency measures in fuzzy data envelopment analysis with common weights, Journal of Industrial and Management Optimization, 13 (2017), 237-249.   Google Scholar

[21]

H. Z. Haghighi, S. Adeli and F. H. Lotfi, Revenue congestion: An application of data envelopment analysis, Journal of Industrial and Management Optimization, 12 (2016), 1311-1322.  doi: 10.3934/jimo.2016.12.1311.  Google Scholar

[22]

A. Klos, J. Bogusz, M. Figurski and W. Kosek, On the handling of outliers in the GNSS time series by means of the noise and probability analysis, Springer Berlin Heidelberg, 143 (2015), 657-664.  doi: 10.1007/1345_2015_78.  Google Scholar

[23]

A. Katayev, J. K. Fleming, D. Luo, A. H. Fisher and T. M. Sharp, Reference intervals data mining, American Journal of Clinical Pathology, 143 (2015), 134-142.  doi: 10.1309/AJCPQPRNIB54WFKJ.  Google Scholar

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Q. X. Chi and X. C. Si, Discussion for radar signal sorting method based on the grubbs' criterion, Chinese Journal of Sensors and Actuators, 6 (2006), 2625-2629.   Google Scholar

[25]

Z. N. Qu and J. L. Xie, Long-term periodicity variations of the solar radius, Astrophysical Journal, 762 (2012), 23-28.  doi: 10.1088/0004-637X/762/1/23.  Google Scholar

[26]

F. Gürbüz and P. M. Pardalos, A decision making process application for the slurry production in ceramics via fuzzy cluster and data mining, Journal of Industrial and Management Optimization, 8 (2013), 285-297.   Google Scholar

[27]

M. Kato, H. Masuyama, S. Kasahara and Y. Takahashi, Effect of energy-saving server scheduling on power consumption for large-scale data centers, Journal of Industrial and Management Optimization, 12 (2016), 667-685.   Google Scholar

[28]

Z. Gong, C. Liu and Y. Wang, Optimal control of switched systems with multiple time-delays and a cost on changing control, Journal of Industrial and Management Optimization, 14 (2018), 183-198.  doi: 10.3934/jimo.2017042.  Google Scholar

[29]

F. M. Anuar, R. Setchi and Y. K. Lai, Semantic retrieval of trademarks based on conceptual similarity, IEEE Transactions on Systems Man and Cybernetics Systems, 46 (2016), 220-233.  doi: 10.1109/TSMC.2015.2421878.  Google Scholar

[30]

Y. Xia, Convex hull of the orthogonal similarity set with applications in quadratic assignment problems, Journal of Industrial and Management Optimization, 9 (2013), 689-701.  doi: 10.3934/jimo.2013.9.689.  Google Scholar

[31]

V. Satuluri and S. Parthasarathy, Bayesian locality sensitive hashing for fast similarity search, Proceedings of the VLDB Endowment, 5 (2012), 430-441.  doi: 10.14778/2140436.2140440.  Google Scholar

[32]

H. Xiao, Similarity Search and Outlier Detection in Time Series. Department of Computer and Information Technique, Ph. D thesis, FuDan University in shanghai, 2005. Google Scholar

[33]

L. Zhang, J. Lin and R. Karim, Sliding window-based fault detection from high-dimensional data streams, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47 (2017), 289-303.  doi: 10.1109/TSMC.2016.2585566.  Google Scholar

[34]

R. Faragher, Understanding the basis of the Kalman filter via a simple and intuitive derivation, IEEE Signal processing magazine, 29 (2012), 128-132.   Google Scholar

[35]

T. Schuhmann, W. Hofmann and R. Werner, Improving operational performance of active magnetic bearings using Kalman filter and state feedback control, IEEE Transactions on Industrial Electronics, 59 (2012), 821-829.  doi: 10.1109/TIE.2011.2161056.  Google Scholar

[36]

V. F. De, A. Brandl, M. Battipede and P. Gili, Joseph covariance formula adaptation to square-root sigma-point Kalman filters, Nonlinear Dynamics, 88 (2017), 1969-1986.   Google Scholar

[37]

B. Jia, M. Xin and Y. Cheng, High-degree cubature Kalman filter, Automatica, 49 (2013), 510-518.  doi: 10.1016/j.automatica.2012.11.014.  Google Scholar

[38]

J. Shawash and D. R. Selviah, Real-time nonlinear parameter estimation using the Levenberg-Marquardt algorithm on field programmable gate arrays, IEEE Transactions on Industrial Electronics, 60 (2013), 170-176.  doi: 10.1109/TIE.2012.2183833.  Google Scholar

[39]

V. López, S. delRío, J. M. Benítez and F. Herrera, Cost-sensitive linguistic fuzzy rule based classification systems under the MapReduce framework for imbalanced big data, Fuzzy Sets and Systems, 258 (2015), 5-38.  doi: 10.1016/j.fss.2014.01.015.  Google Scholar

[40]

C. C. Jiang, R. F. Zhu, G. Y. Xiao, L. L. Wang, Y. Z. Zheng and Y. P. Lu, Communication-effect of nano-alumina concentration on the microstructure and corrosion resistance of phosphate chemical conversion coating, Journal of The Electrochemical Society, 163 (2016), C339-C341.  doi: 10.1149/2.0131607jes.  Google Scholar

[41]

S. Zhang, X. Chen and Y. Yin, An ELM based online soft sensing approach for alumina concentration detection, Mathematical Problems in Engineering, 2015 (2015), Article ID 268132, 8 pages. doi: 10.1155/2015/268132.  Google Scholar

[42]

G. Bearne, M. Dupuis and G. Tarcy, Pseudo resistance curves for aluminium cell control -alumina dissolution and cell dynamics, in Essential Readings in Light Metals: Aluminum Reduction Technology, Volume 2 (eds. H. Kvande, B. P. Moxnes, J. Skaar and P. A. Solli), Metals and Alloys, (2013), 760-766. Google Scholar

[43]

Q. Zhai, J. Yang, M. Xie and Y. Zhao, Generalized moment-independent importance measures based on Minkowski distance, European Journal of Operational Research, 239 (2014), 449-455.  doi: 10.1016/j.ejor.2014.05.021.  Google Scholar

[44]

J. Torres-Sospedra, R. Montoliu, S. Trilles, $\mathit{Ó}$. Belmonte and J. Huerta, Comprehensive analysis of distance and similarity measures for Wi-Fi fingerprinting indoor positioning systems, Expert Systems with Applications, 42 (2015), 9263-9278.  doi: 10.1016/j.eswa.2015.08.013.  Google Scholar

[45]

G. H. B. Foo, X. Zhang and D. M. Vilathgamuwa, A sensor fault detection and isolation method in interior permanent-magnet synchronous motor drives based on an extended Kalman filter, IEEE Transactions on Industrial Electronics, 60 (2013), 3485-3495.  doi: 10.1109/TIE.2013.2244537.  Google Scholar

show all references

References:
[1]

G. Bearne, M. Dupuis and G. Tarcy, On the anode effect in aluminum electrolysis, in Essential Readings in Light Metals: Aluminum Reduction Technology, (eds. J. Thonstad, T. A. Utigard and H. Vogt), Metals and Alloys, 2 (2013), 131-138. Google Scholar

[2]

B. Bardet, T. Foetisch, S. Renaudier, J. Rappaz, M. Flueck and M. Picasso, Alumina dissolution modeling in aluminium electrolysis cell considering MHD driven convection and thermal impact, Light Metals, Springer International Publishing, (2016), 315-319.   Google Scholar

[3]

D. S. Wong, P. Fraser, P. Lavoie and J. Kim, PFC emissions from detected versus nondetected anode effects in the aluminum industry, JOM, 67 (2015), 342-353.  doi: 10.1007/s11837-014-1265-8.  Google Scholar

[4]

L. Dion, L. I. Kiss, S. Poncsák and C. L. Lagacé, Prediction of low-voltage tetrafluoromethane emissions based on the operating conditions of an aluminium electrolysis cell, JOM, 68 (2016), 2472-2482.  doi: 10.1007/s11837-016-2043-6.  Google Scholar

[5]

L. Kong, C. Yu, K. L. Teo and C. Yang, Robust real-time optimization for blending operation of alumina production, Journal of Industrial and Management Optimization, 13 (2017), 1149-1167.   Google Scholar

[6]

M. Farrow, Prediction of AEs in aluminum reduction cells, JOM, 36 (2013), 33-34.   Google Scholar

[7]

J. Li, F. Q. Ding, M. J. Li, J. Xiao and Z. Zou, Intelligent anode effect prediction method for prebaked-anode aluminum reduction cells, Journal of Central South University of Technology, 32 (2001), 29-32.   Google Scholar

[8]

D. G. Bell, System for predicting impending anode effects in aluminum cells, US, US. 6132571[P], (2000). Google Scholar

[9]

Y. Zhang, Study on anode effect prediction of aluminium reduction applying wavelet packet transform, International Conference on Intelligent Computing, Springer Berlin Heidelberg, (2010), 477-484.  doi: 10.1007/978-3-642-14831-6_62.  Google Scholar

[10]

J. Xing and D. Y. Xiao, Ordered neural network and its application to prediction of anode effect, Control Engineering of China, 14 (2007), 27-36.   Google Scholar

[11]

J. B. Harley and J. M. F. Moura, Data-driven matched field processing for Lamb wave structural health monitoring, The Journal of the Acoustical Society of America, 135 (2014), 1231-1244.   Google Scholar

[12]

V. Y. Bazhin, A. A. Vlasov and A. V. Lupenkov, Controlling the AE in an aluminum reduction cell, Metallurgist, 55 (2011), 463-468.   Google Scholar

[13]

Y. Song, J. P. Peng, Y. W. Wang, Y. Z. Di, B. K. Li and N. X. Feng, Magneto-hydrodynamics simulation of 300 KA novel cell for aluminium electrolysis, Metalurgija, 55 (2016), 22-24.   Google Scholar

[14]

J. Yi, D. Huang, S. Fu, H. He and T. Li, Multi-objective bacterial foraging optimization algorithm based on parallel cell entropy for aluminum electrolysis production process, IEEE Transactions on Industrial Electronics, 63 (2016), 2488-2500.  doi: 10.1109/TIE.2015.2510977.  Google Scholar

[15]

H. Viumdal and S. Mylvaganam, System identification of a non-uniformly sampled multi-rate system in aluminium electrolysis cells, Modeling Identification and Control, 35 (2014), 127-146.  doi: 10.4173/mic.2014.3.1.  Google Scholar

[16]

A. Solheim, Entropic heat effects in aluminum electrolysis cells with inert anodes, Metallurgical and Materials Transactions -B, 47 (2016), 1274-1279.  doi: 10.1007/s11663-015-0561-1.  Google Scholar

[17]

F. Allard, G. Soucy and L. Rivoaland, Formation of deposits on the cathode surface of aluminum electrolysis cells, Metallurgical and Materials Transactions -B, 45 (2014), 2475-2485.  doi: 10.1007/s11663-014-0118-8.  Google Scholar

[18]

J. J. Li, Z. J. Wang and J. L. Zhu, Aluminum electrolysis multi-objective control system based on quantum optimized, Advanced Materials, Technology and Application: Proceedings of the 2016 International Conference on Advanced Materials, Technology and Application (AMTA2016). World Scientific, (2016), 417-423.  doi: 10.1142/9789813200470_0049.  Google Scholar

[19]

H. Zhang, T. Li, J. Li, S. Yang and Z. Zou, Progress in aluminum electrolysis control and future direction for smart aluminum electrolysis plant, JOM, 69 (2017), 292-300.  doi: 10.1007/s11837-016-2150-4.  Google Scholar

[20]

C. K. Hu, F. B. Liu and C. F. Hu, Efficiency measures in fuzzy data envelopment analysis with common weights, Journal of Industrial and Management Optimization, 13 (2017), 237-249.   Google Scholar

[21]

H. Z. Haghighi, S. Adeli and F. H. Lotfi, Revenue congestion: An application of data envelopment analysis, Journal of Industrial and Management Optimization, 12 (2016), 1311-1322.  doi: 10.3934/jimo.2016.12.1311.  Google Scholar

[22]

A. Klos, J. Bogusz, M. Figurski and W. Kosek, On the handling of outliers in the GNSS time series by means of the noise and probability analysis, Springer Berlin Heidelberg, 143 (2015), 657-664.  doi: 10.1007/1345_2015_78.  Google Scholar

[23]

A. Katayev, J. K. Fleming, D. Luo, A. H. Fisher and T. M. Sharp, Reference intervals data mining, American Journal of Clinical Pathology, 143 (2015), 134-142.  doi: 10.1309/AJCPQPRNIB54WFKJ.  Google Scholar

[24]

Q. X. Chi and X. C. Si, Discussion for radar signal sorting method based on the grubbs' criterion, Chinese Journal of Sensors and Actuators, 6 (2006), 2625-2629.   Google Scholar

[25]

Z. N. Qu and J. L. Xie, Long-term periodicity variations of the solar radius, Astrophysical Journal, 762 (2012), 23-28.  doi: 10.1088/0004-637X/762/1/23.  Google Scholar

[26]

F. Gürbüz and P. M. Pardalos, A decision making process application for the slurry production in ceramics via fuzzy cluster and data mining, Journal of Industrial and Management Optimization, 8 (2013), 285-297.   Google Scholar

[27]

M. Kato, H. Masuyama, S. Kasahara and Y. Takahashi, Effect of energy-saving server scheduling on power consumption for large-scale data centers, Journal of Industrial and Management Optimization, 12 (2016), 667-685.   Google Scholar

[28]

Z. Gong, C. Liu and Y. Wang, Optimal control of switched systems with multiple time-delays and a cost on changing control, Journal of Industrial and Management Optimization, 14 (2018), 183-198.  doi: 10.3934/jimo.2017042.  Google Scholar

[29]

F. M. Anuar, R. Setchi and Y. K. Lai, Semantic retrieval of trademarks based on conceptual similarity, IEEE Transactions on Systems Man and Cybernetics Systems, 46 (2016), 220-233.  doi: 10.1109/TSMC.2015.2421878.  Google Scholar

[30]

Y. Xia, Convex hull of the orthogonal similarity set with applications in quadratic assignment problems, Journal of Industrial and Management Optimization, 9 (2013), 689-701.  doi: 10.3934/jimo.2013.9.689.  Google Scholar

[31]

V. Satuluri and S. Parthasarathy, Bayesian locality sensitive hashing for fast similarity search, Proceedings of the VLDB Endowment, 5 (2012), 430-441.  doi: 10.14778/2140436.2140440.  Google Scholar

[32]

H. Xiao, Similarity Search and Outlier Detection in Time Series. Department of Computer and Information Technique, Ph. D thesis, FuDan University in shanghai, 2005. Google Scholar

[33]

L. Zhang, J. Lin and R. Karim, Sliding window-based fault detection from high-dimensional data streams, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47 (2017), 289-303.  doi: 10.1109/TSMC.2016.2585566.  Google Scholar

[34]

R. Faragher, Understanding the basis of the Kalman filter via a simple and intuitive derivation, IEEE Signal processing magazine, 29 (2012), 128-132.   Google Scholar

[35]

T. Schuhmann, W. Hofmann and R. Werner, Improving operational performance of active magnetic bearings using Kalman filter and state feedback control, IEEE Transactions on Industrial Electronics, 59 (2012), 821-829.  doi: 10.1109/TIE.2011.2161056.  Google Scholar

[36]

V. F. De, A. Brandl, M. Battipede and P. Gili, Joseph covariance formula adaptation to square-root sigma-point Kalman filters, Nonlinear Dynamics, 88 (2017), 1969-1986.   Google Scholar

[37]

B. Jia, M. Xin and Y. Cheng, High-degree cubature Kalman filter, Automatica, 49 (2013), 510-518.  doi: 10.1016/j.automatica.2012.11.014.  Google Scholar

[38]

J. Shawash and D. R. Selviah, Real-time nonlinear parameter estimation using the Levenberg-Marquardt algorithm on field programmable gate arrays, IEEE Transactions on Industrial Electronics, 60 (2013), 170-176.  doi: 10.1109/TIE.2012.2183833.  Google Scholar

[39]

V. López, S. delRío, J. M. Benítez and F. Herrera, Cost-sensitive linguistic fuzzy rule based classification systems under the MapReduce framework for imbalanced big data, Fuzzy Sets and Systems, 258 (2015), 5-38.  doi: 10.1016/j.fss.2014.01.015.  Google Scholar

[40]

C. C. Jiang, R. F. Zhu, G. Y. Xiao, L. L. Wang, Y. Z. Zheng and Y. P. Lu, Communication-effect of nano-alumina concentration on the microstructure and corrosion resistance of phosphate chemical conversion coating, Journal of The Electrochemical Society, 163 (2016), C339-C341.  doi: 10.1149/2.0131607jes.  Google Scholar

[41]

S. Zhang, X. Chen and Y. Yin, An ELM based online soft sensing approach for alumina concentration detection, Mathematical Problems in Engineering, 2015 (2015), Article ID 268132, 8 pages. doi: 10.1155/2015/268132.  Google Scholar

[42]

G. Bearne, M. Dupuis and G. Tarcy, Pseudo resistance curves for aluminium cell control -alumina dissolution and cell dynamics, in Essential Readings in Light Metals: Aluminum Reduction Technology, Volume 2 (eds. H. Kvande, B. P. Moxnes, J. Skaar and P. A. Solli), Metals and Alloys, (2013), 760-766. Google Scholar

[43]

Q. Zhai, J. Yang, M. Xie and Y. Zhao, Generalized moment-independent importance measures based on Minkowski distance, European Journal of Operational Research, 239 (2014), 449-455.  doi: 10.1016/j.ejor.2014.05.021.  Google Scholar

[44]

J. Torres-Sospedra, R. Montoliu, S. Trilles, $\mathit{Ó}$. Belmonte and J. Huerta, Comprehensive analysis of distance and similarity measures for Wi-Fi fingerprinting indoor positioning systems, Expert Systems with Applications, 42 (2015), 9263-9278.  doi: 10.1016/j.eswa.2015.08.013.  Google Scholar

[45]

G. H. B. Foo, X. Zhang and D. M. Vilathgamuwa, A sensor fault detection and isolation method in interior permanent-magnet synchronous motor drives based on an extended Kalman filter, IEEE Transactions on Industrial Electronics, 60 (2013), 3485-3495.  doi: 10.1109/TIE.2013.2244537.  Google Scholar

Figure 1.  A sketch of the main features of an alumina reduction cell
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Figure 2.  The overview of CTFM algorithm
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Figure 3.  The overview of CTFM algorithm
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Figure 4.  The results of the cell resistance at different times are obtained by the search algorithm
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Figure 5.  The five most similar curves of the cell resistance with current data are obtained from historical data set
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Figure 6.  The results of the alumina feeding are obtained by the search algorithm at different times
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Figure 7.  The five most similar curves the alumina feeding with current are obtained from historical data set (the red curve, the green curve, the blue curve the turquoise curve and the carmine curve in the first box are five most similar curves, respectively. The green curve in the second box is current data curve)
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Figure 8(a) presents prediction result of the EKF algorithm for the slope of cell resistance. Figure 8(b) shows prediction result of the SRCKF algorithm for the slope of cell resistance. Figure 8(c) gives Prediction result of the LMSRCKF algorithm for the slope of cell resistance.)">Figure 8.  The prediction results of the three algorithms for the slope of cell resistance. (Figure 8(a) presents prediction result of the EKF algorithm for the slope of cell resistance. Figure 8(b) shows prediction result of the SRCKF algorithm for the slope of cell resistance. Figure 8(c) gives Prediction result of the LMSRCKF algorithm for the slope of cell resistance.)
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Figure 9.  Absolute error between actual value and prediction value for the slope of cell resistance using the three algorithms
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Figure 10.  The relative errors between actual value and prediction value obtained by the three algorithms for the slope of cell resistance
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Figure 11(a) is on prediction result obtained by the EKF algorithm for the accumulated slope of cell resistance. Figure 11(b) is on prediction result obtained by the SRCKF algorithm for the accumulated slope of cell resistance. Figure 11(c) is on prediction result obtained by the LMSRCKF algorithm for the accumulated slope of cell resistance.)">Figure 11.  The prediction results obtained by the three algorithms for the accumulated slope of cell resistance (Figure 11(a) is on prediction result obtained by the EKF algorithm for the accumulated slope of cell resistance. Figure 11(b) is on prediction result obtained by the SRCKF algorithm for the accumulated slope of cell resistance. Figure 11(c) is on prediction result obtained by the LMSRCKF algorithm for the accumulated slope of cell resistance.)
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Figure 12.  The absolute errors between actual value and prediction value obtained by the three algorithms for the accumulated slope of cell resistance
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Figure 13.  The relative error between actual value and prediction value obtained by the three algorithms for the accumulated slope of cell resistance
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Figure 14.  Membership functions of three input variables
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Figure 15.  The image of defuzzification after fused fuzzy variable $CA$ and fused fuzzy variable $CB$
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Figure 16.  The image of defuzzification after adjusting the results on the convergence of fuzzy variable $CA$ and fuzzy variable $CB$
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Table 1.  The corresponding similarity to each curve in Figure 5
Curve typesSimilarity
Red curve 0.9419
Green curve 0.9526
Blue curve 0.9661
Turquoise curve 0.9628
Carmine curve 0.9587
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Curve typesSimilarity
Red curve 0.9419
Green curve 0.9526
Blue curve 0.9661
Turquoise curve 0.9628
Carmine curve 0.9587
Table 2.  The corresponding similarity to each curve in Figure 7
Curve typesSimilarity
Red curve 0.9278
Green curve 0.9152
Blue curve 0.9472
Turquoise curve 0.9324
Carmine curve 0.9461
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Curve typesSimilarity
Red curve 0.9278
Green curve 0.9152
Blue curve 0.9472
Turquoise curve 0.9324
Carmine curve 0.9461
Table 3.  Mean accuracy and time advance of three similarity search methods
Time advance ($min$) DPMD Minkowski distance Euclidean distance
Mean accuracy Mean accuracy Mean accuracy
$0 \sim 40$ 55.4% 47.9% 45.9%
$5 \sim 40$ 51.1% 42.3% 38.5%
$10 \sim 40$ 46.8% 38.3% 35.6%
$15 \sim 40$ 43.9% 32.6% 31.2%
$20 \sim 40$ 40.4% 26.1% 25.6%
$25 \sim 40$ 38.4% 21.4% 22.1%
$30 \sim 40$ 36.5% 15.2% 18.3%
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Time advance ($min$) DPMD Minkowski distance Euclidean distance
Mean accuracy Mean accuracy Mean accuracy
$0 \sim 40$ 55.4% 47.9% 45.9%
$5 \sim 40$ 51.1% 42.3% 38.5%
$10 \sim 40$ 46.8% 38.3% 35.6%
$15 \sim 40$ 43.9% 32.6% 31.2%
$20 \sim 40$ 40.4% 26.1% 25.6%
$25 \sim 40$ 38.4% 21.4% 22.1%
$30 \sim 40$ 36.5% 15.2% 18.3%
Table 4.  Mean accuracy and time advance of three prediction algorithms
Time advance ($min$) LMSRCKF SRCKF EKF
Mean accuracy Mean accuracy Mean accuracy
$0 \sim 40$ 75.6% 57.1% 51.6%
$5 \sim 40$ 72.3% 51.2% 45.3%
$10 \sim 40$ 68.8% 44.7% 40.2%
$15 \sim 40$ 62.9% 35.3% 32.7%
$20 \sim 40$ 59.8% 31.2% 28.6%
$25 \sim 40$ 55.4% 25.7% 23.4%
$30 \sim 40$ 51.2% 19.3% 17.6%
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Time advance ($min$) LMSRCKF SRCKF EKF
Mean accuracy Mean accuracy Mean accuracy
$0 \sim 40$ 75.6% 57.1% 51.6%
$5 \sim 40$ 72.3% 51.2% 45.3%
$10 \sim 40$ 68.8% 44.7% 40.2%
$15 \sim 40$ 62.9% 35.3% 32.7%
$20 \sim 40$ 59.8% 31.2% 28.6%
$25 \sim 40$ 55.4% 25.7% 23.4%
$30 \sim 40$ 51.2% 19.3% 17.6%
Table 5.  The result statistics of AE-predicting using the fused results of fuzzy variable $CA$ and fuzzy variable $CB$
Results of AE-predicting of the fused CA and CB
Mean accuracy Time advance (min)
93.3% 0 ~ 40
91.5% 5 ~ 40
89.2% 10 ~ 40
88.6% 15 ~ 40
85.1% 20 ~ 40
83.9% 25 ~ 40
80.2% 30 ~ 40
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Results of AE-predicting of the fused CA and CB
Mean accuracy Time advance (min)
93.3% 0 ~ 40
91.5% 5 ~ 40
89.2% 10 ~ 40
88.6% 15 ~ 40
85.1% 20 ~ 40
83.9% 25 ~ 40
80.2% 30 ~ 40
Table 6.  Result statistics of AE-occurring and AE-predicting obtained using the CTFM algorithm
Project names cell numbers
201$\sharp$ 202$\sharp$ 203$\sharp$ 204$\sharp$ 205$\sharp$ 206$\sharp$ 207$\sharp$ 208$\sharp$
Total number of occurring AE 34 41 37 41 29 35 38 47
Total number of successful AE-predicting 32 39 36 41 27 34 36 45
Total number of AE-predicting 35 41 39 45 30 35 39 51
Total number of underreporting 2 2 1 2 2 1 2 2
Total number of underreporting 3 2 3 4 3 1 3 6
Mean accuracy 94.1% 95.1% 97.3% 95.3% 93.1% 97.1% 94.7% 95.7%
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Project names cell numbers
201$\sharp$ 202$\sharp$ 203$\sharp$ 204$\sharp$ 205$\sharp$ 206$\sharp$ 207$\sharp$ 208$\sharp$
Total number of occurring AE 34 41 37 41 29 35 38 47
Total number of successful AE-predicting 32 39 36 41 27 34 36 45
Total number of AE-predicting 35 41 39 45 30 35 39 51
Total number of underreporting 2 2 1 2 2 1 2 2
Total number of underreporting 3 2 3 4 3 1 3 6
Mean accuracy 94.1% 95.1% 97.3% 95.3% 93.1% 97.1% 94.7% 95.7%
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