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Evaluation strategy and mass balance for making decision about the amount of aluminum fluoride addition based on superheat degree
School of Information Science and Engineering, Central South University, Changsha 410083, China |
The purpose of aluminum fluoride (AlF3) addition is to adjust the superheat degree (SD) in the aluminum reduction process. Determining the appropriate amount of AlF3 to add has long been a challenging industrial issue as a result of its inherent complexity. Because of the decreasing number of experienced technicians, the manual addition of AlF3 is usually inexact, which easily leads to an unstable cell condition. In this paper, an evaluation strategy based on the SD for AlF3 addition is proposed. An extended naïve Bayesian classifier (ENBC) is designed to estimate the states of SD and its trends that represent the current and potential cell condition respectively, and then the process is graded by evaluating the estimated results based on fuzzy theory. The reduction process is divided into a few situations based on the evaluation grades, and mass balance is introduced to determine the amount of AlF3 addition in each situation. The results of experiments show that the proposed strategy is feasible, and the effectiveness of AlF3 addition is improved compared to the existing method. Moreover, automatic AlF3 addition is promising based on the proposed strategy.
References:
[1] |
I. Barbeito and R. Cao,
Smoothed stationary bootstrap bandwidth selection for density estimation with dependent data, Computational Statistics & Data Analysis, 104 (2016), 130-147.
doi: 10.1016/j.csda.2016.06.015. |
[2] |
K. Barbé, L. G. Fuentes, L. Barford and L. Lauwers,
A guaranteed blind and automatic probability density estimation of raw measurements, IEEE Transactions on Instrumentation & Measurement, 63 (2014), 2120-2128.
|
[3] |
Z. G. Chen, Y. G. Li, X. F. Chen and W. H. Gui,
Semantic Network Based on Intuitionistic Fuzzy Directed Hyper-Graphs and Application to Aluminum Electrolysis Cell Condition Identification, IEEE Access, 5 (2017), 20145-20156.
doi: 10.1109/ACCESS.2017.2752200. |
[4] |
Y. Chien,
Pattern classification and scene analysis, IEEE Transactions Automatic Control, 19 (1974), 462-463.
doi: 10.1109/TAC.1974.1100577. |
[5] |
K. S. Chuang, H. L. Tzeng and S. Chen,
Fuzzy c-means clustering with spatial information for image segmentation, Computerized Medical Imaging and Graphics, 30 (2006), 9-15.
doi: 10.1016/j.compmedimag.2005.10.001. |
[6] |
P. Desclaux,
AlF3 additions based on bath temperature measurements, Light Metals, (1987), 309-313.
|
[7] |
T. Drengstig, D. Ljungquist and B. A. Foss,
On the AlF3 and temperature control of an aluminum electrolysis cell, IEEE Transactions on Control Systems Technology, 6 (1998), 157-171.
|
[8] |
M. Dupuis and I. GéniSim,
Excess AlF3 concentration in bath control logic, National Conference on Advancements in Aluminium Electrolysis, Indian Institute of Metals, Angul, (2006), 309-313.
|
[9] |
P. M. Entner and G. A. Gudmundsson,
Further development of the temperature model, Light Metals, (1996), 445-449.
|
[10] |
W. Haupin and H. Kvande,
Mathematical model of fluoride evolution from Hall-Héroult Cells, Essential Readings in Light Metals, (2016), 903-909.
|
[11] |
Y. J. He, Y. Mao, W. L. Chen and Y. X. Chen,
Nonlinear metric learning with kernel density estimation, IEEE Transactions Knowledge and Data Engineering, 27 (2015), 1602-1614.
doi: 10.1109/TKDE.2014.2384522. |
[12] |
Y. L. He, R. Wang, S. Kwong and X. Z. Wang,
Bayesian classifiers based on probability density estimation and their applications to simultaneous fault diagnosis, Information Sciences, 259 (2014), 252-268.
doi: 10.1016/j.ins.2013.09.003. |
[13] |
Y. B. Huang, X. D. Qu and J. M. Zhou,
Coupled heat/mass balance model for analyzing correlation between excess AlF3 concentration and aluminum electrolyte temperature, Transactions of Nonferrous Metals Society of China, 19 (2009), 724-729.
|
[14] |
M. M. Hyland, E. C. Patterson, F. S. Mcfadden and B. J. Welch,
Aluminium fluoride consumption and control in smelting cells, Scand. J. Metall., 30 (2001), 404-414.
|
[15] |
H. J. Kim, S. N. MacEachern and Y. Jung, Bandwidth selection for kernel density estimation with a markov chain monte carlo sample, arXiv. Preprint. arXiv., 1607.08274 (2016), 1-16. |
[16] |
K. R. Kloetstra, S. Benninghoff, M. A. Stam and B. W. Toebes, Optimisation of Aluminium Fluoride Control at Aluminium Delfzijl, Proceedings of the 7th Australasian Aluminium Smelting Workshop, (2001), 506-514. |
[17] |
M. Köhler, A. Schindler and S. Sperlich,
A review and comparison of bandwidth selection methods for kernel regression, International Statistical Review, 82 (2014), 243-274.
doi: 10.1111/insr.12039. |
[18] |
S. Kolås,
Defining and verifying the 'correlation line' in aluminum electrolysis, JOM, 59 (2007), 55-60.
|
[19] |
S Kolås and T. Støre,
Bath temperature and AlF3 control of an aluminium electrolysis cell, Control and Engineering Practice, 17 (2009), 1035-1043.
|
[20] |
M. E. Maron and J. L. Kuhns,
On relevance, probabilistic indexing and information retrieval, Journal of the ACM, 7 (1960), 216-244.
doi: 10.1145/321033.321035. |
[21] |
A. Meghlaoui, Y. A. A. Farsi and N. H. Aljabri, Analytical and experimental study of fluoride evolution, Light Metals-Warrendale-Proceedings. TMS, 2001, 283-288. |
[22] |
A. R. Mugdadi and I. A. Ahmad,
A bandwidth selection for kernel density estimation of functions of random variables, Computational Statistics & Data Analysis, 47 (2004), 49-62.
doi: 10.1016/j.csda.2003.10.013. |
[23] |
R. J. Pak,
The influence function of the optimal bandwidth for kernel density estimation, Communications in Statistics, 46 (2017), 602-608.
doi: 10.1080/03610926.2014.1000501. |
[24] |
D. J. Salt,
Bath chemistry control system, Essential Readings in Light Metals, (2016), 798-803.
|
[25] |
A. T. Tabereaux, T. R. Alcorn and L Trembley,
Lithium-Modified Low Ratio Electrolyte Chemistry for Improved Performance in Modern Reduction Cells, Essential Readings in Light Metals, (2016), 83-88.
|
[26] |
J. Thonstand and S. Roselth,
Equilibrium between bath and side ledge in aluminum cells-Basic principles, Light Metals, (1983), 414-424.
|
[27] |
L. Y. Wang, W. H. Gui, K. L. Teo, R. C. Loxton and C. H. Yang,
Time delayed optimal control problems with multiple characteristic time points: Computation and industrial applications, Journal of Industrial & Management Optimization, 5 (2009), 705-718.
doi: 10.3934/jimo.2009.5.705. |
[28] |
X. Z. Wang, Y. L. He and D. D. Wang,
Non-naive bayesian classifiers for classification problems with continuous attributes, IEEE Transactions on Cybernetics, 44 (2013), 21-39.
doi: 10.1109/TCYB.2013.2245891. |
[29] |
M. J. Wilson, Practical considerations used in the development of a method for calculating aluminum fluoride additions based on cell temperatures, Light Metals (1992), 37-5-378. |
[30] |
J. Ye, H. Xu, E. Feng and Z. Xiu,
Optimization of a fed-batch bioreactor for 1, 3-propanediol production using hybrid nonlinear optimal control, Journal of Process Control, 24 (2014), 1556-1569.
|
[31] |
J. Yi, D. Huang, S. Fu and T. Li,
Optimized relative transformation matrix using bacterial foraging algorithm for process fault detection, IEEE Transactions on Industrial Electronics, 63 (2016), 2595-2605.
doi: 10.1109/TIE.2016.2515057. |
[32] |
W. C. Yue, X. F. Chen, W. H. Gui and H. L. Zhang,
A knowledge reasoning Fuzzy-Bayesian network for root cause analysis of abnormal aluminum electrolysis cell condition, Fronters of Chemical Science and Engineering, 11 (2017), 414-428.
doi: 10.1007/s11705-017-1663-x. |
[33] |
S. P. Zeng and F. W. Cui,
Dynamic decision model for amount of AlF3 addition in industrial aluminum electrolysis, International Conference on Mechatronics, Robotics and Automation, (2015), 307-318.
|
[34] |
S. P. Zeng, S. S. Wang and Y. X. Qu,
Control of temperature and aluminum fluoride concentration based on model prediction in aluminum electrolysis, Advances in Materials Science & Engineering, (2014), 1-5.
|
[35] |
E. Zenteno, Z. A. Khan, M. Isaksson and P. Handel,
Finding structural information about RF power amplifiers using an orthogonal nonparametric kernel smoothing estimator, IEEE Transactions on Vehicular Technology, 65 (2016), 2883-2889.
doi: 10.1109/TVT.2015.2434497. |
[36] |
S. Q. Zhan, M. Li, J. M. Zhou and Y. W. Zhou,
CFD simulation of dissolution process of alumina in an aluminum reduction cell with two-particle phase population balance model, Applied Thermal Engineering, 73 (2014), 805-818.
doi: 10.1016/j.applthermaleng.2014.08.040. |
show all references
References:
[1] |
I. Barbeito and R. Cao,
Smoothed stationary bootstrap bandwidth selection for density estimation with dependent data, Computational Statistics & Data Analysis, 104 (2016), 130-147.
doi: 10.1016/j.csda.2016.06.015. |
[2] |
K. Barbé, L. G. Fuentes, L. Barford and L. Lauwers,
A guaranteed blind and automatic probability density estimation of raw measurements, IEEE Transactions on Instrumentation & Measurement, 63 (2014), 2120-2128.
|
[3] |
Z. G. Chen, Y. G. Li, X. F. Chen and W. H. Gui,
Semantic Network Based on Intuitionistic Fuzzy Directed Hyper-Graphs and Application to Aluminum Electrolysis Cell Condition Identification, IEEE Access, 5 (2017), 20145-20156.
doi: 10.1109/ACCESS.2017.2752200. |
[4] |
Y. Chien,
Pattern classification and scene analysis, IEEE Transactions Automatic Control, 19 (1974), 462-463.
doi: 10.1109/TAC.1974.1100577. |
[5] |
K. S. Chuang, H. L. Tzeng and S. Chen,
Fuzzy c-means clustering with spatial information for image segmentation, Computerized Medical Imaging and Graphics, 30 (2006), 9-15.
doi: 10.1016/j.compmedimag.2005.10.001. |
[6] |
P. Desclaux,
AlF3 additions based on bath temperature measurements, Light Metals, (1987), 309-313.
|
[7] |
T. Drengstig, D. Ljungquist and B. A. Foss,
On the AlF3 and temperature control of an aluminum electrolysis cell, IEEE Transactions on Control Systems Technology, 6 (1998), 157-171.
|
[8] |
M. Dupuis and I. GéniSim,
Excess AlF3 concentration in bath control logic, National Conference on Advancements in Aluminium Electrolysis, Indian Institute of Metals, Angul, (2006), 309-313.
|
[9] |
P. M. Entner and G. A. Gudmundsson,
Further development of the temperature model, Light Metals, (1996), 445-449.
|
[10] |
W. Haupin and H. Kvande,
Mathematical model of fluoride evolution from Hall-Héroult Cells, Essential Readings in Light Metals, (2016), 903-909.
|
[11] |
Y. J. He, Y. Mao, W. L. Chen and Y. X. Chen,
Nonlinear metric learning with kernel density estimation, IEEE Transactions Knowledge and Data Engineering, 27 (2015), 1602-1614.
doi: 10.1109/TKDE.2014.2384522. |
[12] |
Y. L. He, R. Wang, S. Kwong and X. Z. Wang,
Bayesian classifiers based on probability density estimation and their applications to simultaneous fault diagnosis, Information Sciences, 259 (2014), 252-268.
doi: 10.1016/j.ins.2013.09.003. |
[13] |
Y. B. Huang, X. D. Qu and J. M. Zhou,
Coupled heat/mass balance model for analyzing correlation between excess AlF3 concentration and aluminum electrolyte temperature, Transactions of Nonferrous Metals Society of China, 19 (2009), 724-729.
|
[14] |
M. M. Hyland, E. C. Patterson, F. S. Mcfadden and B. J. Welch,
Aluminium fluoride consumption and control in smelting cells, Scand. J. Metall., 30 (2001), 404-414.
|
[15] |
H. J. Kim, S. N. MacEachern and Y. Jung, Bandwidth selection for kernel density estimation with a markov chain monte carlo sample, arXiv. Preprint. arXiv., 1607.08274 (2016), 1-16. |
[16] |
K. R. Kloetstra, S. Benninghoff, M. A. Stam and B. W. Toebes, Optimisation of Aluminium Fluoride Control at Aluminium Delfzijl, Proceedings of the 7th Australasian Aluminium Smelting Workshop, (2001), 506-514. |
[17] |
M. Köhler, A. Schindler and S. Sperlich,
A review and comparison of bandwidth selection methods for kernel regression, International Statistical Review, 82 (2014), 243-274.
doi: 10.1111/insr.12039. |
[18] |
S. Kolås,
Defining and verifying the 'correlation line' in aluminum electrolysis, JOM, 59 (2007), 55-60.
|
[19] |
S Kolås and T. Støre,
Bath temperature and AlF3 control of an aluminium electrolysis cell, Control and Engineering Practice, 17 (2009), 1035-1043.
|
[20] |
M. E. Maron and J. L. Kuhns,
On relevance, probabilistic indexing and information retrieval, Journal of the ACM, 7 (1960), 216-244.
doi: 10.1145/321033.321035. |
[21] |
A. Meghlaoui, Y. A. A. Farsi and N. H. Aljabri, Analytical and experimental study of fluoride evolution, Light Metals-Warrendale-Proceedings. TMS, 2001, 283-288. |
[22] |
A. R. Mugdadi and I. A. Ahmad,
A bandwidth selection for kernel density estimation of functions of random variables, Computational Statistics & Data Analysis, 47 (2004), 49-62.
doi: 10.1016/j.csda.2003.10.013. |
[23] |
R. J. Pak,
The influence function of the optimal bandwidth for kernel density estimation, Communications in Statistics, 46 (2017), 602-608.
doi: 10.1080/03610926.2014.1000501. |
[24] |
D. J. Salt,
Bath chemistry control system, Essential Readings in Light Metals, (2016), 798-803.
|
[25] |
A. T. Tabereaux, T. R. Alcorn and L Trembley,
Lithium-Modified Low Ratio Electrolyte Chemistry for Improved Performance in Modern Reduction Cells, Essential Readings in Light Metals, (2016), 83-88.
|
[26] |
J. Thonstand and S. Roselth,
Equilibrium between bath and side ledge in aluminum cells-Basic principles, Light Metals, (1983), 414-424.
|
[27] |
L. Y. Wang, W. H. Gui, K. L. Teo, R. C. Loxton and C. H. Yang,
Time delayed optimal control problems with multiple characteristic time points: Computation and industrial applications, Journal of Industrial & Management Optimization, 5 (2009), 705-718.
doi: 10.3934/jimo.2009.5.705. |
[28] |
X. Z. Wang, Y. L. He and D. D. Wang,
Non-naive bayesian classifiers for classification problems with continuous attributes, IEEE Transactions on Cybernetics, 44 (2013), 21-39.
doi: 10.1109/TCYB.2013.2245891. |
[29] |
M. J. Wilson, Practical considerations used in the development of a method for calculating aluminum fluoride additions based on cell temperatures, Light Metals (1992), 37-5-378. |
[30] |
J. Ye, H. Xu, E. Feng and Z. Xiu,
Optimization of a fed-batch bioreactor for 1, 3-propanediol production using hybrid nonlinear optimal control, Journal of Process Control, 24 (2014), 1556-1569.
|
[31] |
J. Yi, D. Huang, S. Fu and T. Li,
Optimized relative transformation matrix using bacterial foraging algorithm for process fault detection, IEEE Transactions on Industrial Electronics, 63 (2016), 2595-2605.
doi: 10.1109/TIE.2016.2515057. |
[32] |
W. C. Yue, X. F. Chen, W. H. Gui and H. L. Zhang,
A knowledge reasoning Fuzzy-Bayesian network for root cause analysis of abnormal aluminum electrolysis cell condition, Fronters of Chemical Science and Engineering, 11 (2017), 414-428.
doi: 10.1007/s11705-017-1663-x. |
[33] |
S. P. Zeng and F. W. Cui,
Dynamic decision model for amount of AlF3 addition in industrial aluminum electrolysis, International Conference on Mechatronics, Robotics and Automation, (2015), 307-318.
|
[34] |
S. P. Zeng, S. S. Wang and Y. X. Qu,
Control of temperature and aluminum fluoride concentration based on model prediction in aluminum electrolysis, Advances in Materials Science & Engineering, (2014), 1-5.
|
[35] |
E. Zenteno, Z. A. Khan, M. Isaksson and P. Handel,
Finding structural information about RF power amplifiers using an orthogonal nonparametric kernel smoothing estimator, IEEE Transactions on Vehicular Technology, 65 (2016), 2883-2889.
doi: 10.1109/TVT.2015.2434497. |
[36] |
S. Q. Zhan, M. Li, J. M. Zhou and Y. W. Zhou,
CFD simulation of dissolution process of alumina in an aluminum reduction cell with two-particle phase population balance model, Applied Thermal Engineering, 73 (2014), 805-818.
doi: 10.1016/j.applthermaleng.2014.08.040. |

















Parameter | Ab. | Value | Role analysis |
Aluminum level | AL | 20-23 cm | The height of the molten aluminum. A higher AL leads to greater heat loss, and vice versa. A suitable AL can stabilize the cell voltage. |
Molecular ratio | MR | 2.64-3.0 | This affects the dissolution of the alumina in the electrolyte, with a higher MR leading to a lower SD, and vice versa. |
Electrolyte level | EL | 23-28 cm | This stabilize the thermal balance of the cell. Thus, the thermal balance is robust with a suitable EL. |
Waving | WA | 0-20 mv | A strong low-frequency noise may be due to insufficient energy intake for the cell. |
Vibration | VI | 0-50 mv | VI is an indicator of the stability of the cell. A greater VI is more likely for a cold cell. |
Under/over number ratio | UO | 0.75-1 | The UO is the ratio between the under and over feeding times. A smaller UO is more likely for a cold cell, and vice versa. |
Tapping amount | TA | 2.9-3.05 ton | The TA has a great influence on the energy balance. A greater TA is more likely for a hot cell, and vice versa. |
Electrolyte temperature | ET | 955-965℃ | This affects the entire operation condition of the cell. A higher temperature is more likely for a hot cell, and vice versa. |
Parameter | Ab. | Value | Role analysis |
Aluminum level | AL | 20-23 cm | The height of the molten aluminum. A higher AL leads to greater heat loss, and vice versa. A suitable AL can stabilize the cell voltage. |
Molecular ratio | MR | 2.64-3.0 | This affects the dissolution of the alumina in the electrolyte, with a higher MR leading to a lower SD, and vice versa. |
Electrolyte level | EL | 23-28 cm | This stabilize the thermal balance of the cell. Thus, the thermal balance is robust with a suitable EL. |
Waving | WA | 0-20 mv | A strong low-frequency noise may be due to insufficient energy intake for the cell. |
Vibration | VI | 0-50 mv | VI is an indicator of the stability of the cell. A greater VI is more likely for a cold cell. |
Under/over number ratio | UO | 0.75-1 | The UO is the ratio between the under and over feeding times. A smaller UO is more likely for a cold cell, and vice versa. |
Tapping amount | TA | 2.9-3.05 ton | The TA has a great influence on the energy balance. A greater TA is more likely for a hot cell, and vice versa. |
Electrolyte temperature | ET | 955-965℃ | This affects the entire operation condition of the cell. A higher temperature is more likely for a hot cell, and vice versa. |
Definitions for SD | Definitions for dSD | |||||
Label | Meaning | Membership | Label | Meaning | Membership | |
VL | Very low | | HN | High negative | | |
LL | Little low | | LN | Low negative | | |
N | Normal | | Z | zero | | |
LH | Little high | | LP | Low positive | | |
VH | Very high | | HP | High positive | |
Definitions for SD | Definitions for dSD | |||||
Label | Meaning | Membership | Label | Meaning | Membership | |
VL | Very low | | HN | High negative | | |
LL | Little low | | LN | Low negative | | |
N | Normal | | Z | zero | | |
LH | Little high | | LP | Low positive | | |
VH | Very high | | HP | High positive | |
Data set names | Number of instances | Accuracy rate | ||||
training | test | attributes | ENBC | NBC | ||
hline seeds | 135 | 75 | 7 | 0.9733 | 0.8933 | |
banknote | 1297 | 75 | 5 | 0.9467 | 0.8267 |
Data set names | Number of instances | Accuracy rate | ||||
training | test | attributes | ENBC | NBC | ||
hline seeds | 135 | 75 | 7 | 0.9733 | 0.8933 | |
banknote | 1297 | 75 | 5 | 0.9467 | 0.8267 |
Labels | Index | Parameters | |||||||
MR | EL (cm) | WA (mv) | VI (mv) | UO | TA kg | ET (℃) | AL (cm) | ||
VL | 1 | 3.05 | 33 | 537 | 799 | 0.76 | 3023 | 959 | 22.0 |
LL | 2 | 2.98 | 32 | 89 | 114 | 0.52 | 2988 | 960 | 23.0 |
N | 3 | 2.79 | 23 | 6 | 10 | 0.40 | 2811 | 974 | 25.5 |
LH | 4 | 2.87 | 31 | 2 | 6 | 1.18 | 2787 | 976 | 21.0 |
VH | 5 | 2.52 | 25 | 3 | 5 | 0.33 | 2896 | 985 | 24.0 |
Labels | Index | Parameters | |||||||
MR | EL (cm) | WA (mv) | VI (mv) | UO | TA kg | ET (℃) | AL (cm) | ||
VL | 1 | 3.05 | 33 | 537 | 799 | 0.76 | 3023 | 959 | 22.0 |
LL | 2 | 2.98 | 32 | 89 | 114 | 0.52 | 2988 | 960 | 23.0 |
N | 3 | 2.79 | 23 | 6 | 10 | 0.40 | 2811 | 974 | 25.5 |
LH | 4 | 2.87 | 31 | 2 | 6 | 1.18 | 2787 | 976 | 21.0 |
VH | 5 | 2.52 | 25 | 3 | 5 | 0.33 | 2896 | 985 | 24.0 |
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