# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2018169

## 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

*Corresponding author: Xiaofang Chen (e-mail: xiaofangchen@csu.edu.cn)

Received  June 2018 Revised  August 2018 Published  October 2018

Fund Project: This project was supported by the National Natural Science Foundation of China (61773405, 61533020, 61621062 and 61725306); and the innovation project of Central South University (502390003)

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.

Citation: Weichao Yue, Weihua Gui, Xiaofang Chen, Zhaohui Zeng, Yongfang Xie. Evaluation strategy and mass balance for making decision about the amount of aluminum fluoride addition based on superheat degree. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2018169
##### References:
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Kvande, Mathematical model of fluoride evolution from Hall-Héroult Cells, Essential Readings in Light Metals, (2016), 903-909. Google Scholar [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. Google Scholar [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. Google Scholar [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. Google Scholar [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. Google Scholar [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.Google Scholar [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.Google Scholar [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. Google Scholar [18] S. Kolås, Defining and verifying the 'correlation line' in aluminum electrolysis, JOM, 59 (2007), 55-60. Google Scholar [19] S Kolås and T. Støre, Bath temperature and AlF3 control of an aluminium electrolysis cell, Control and Engineering Practice, 17 (2009), 1035-1043. Google Scholar [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. Google Scholar [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.Google Scholar [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. Google Scholar [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. Google Scholar [24] D. J. Salt, Bath chemistry control system, Essential Readings in Light Metals, (2016), 798-803. Google Scholar [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. Google Scholar [26] J. Thonstand and S. Roselth, Equilibrium between bath and side ledge in aluminum cells-Basic principles, Light Metals, (1983), 414-424. Google Scholar [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. Google Scholar [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. Google Scholar [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.Google Scholar [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. Google Scholar [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. Google Scholar [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. Google Scholar [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. Google Scholar [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. Google Scholar [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. Google Scholar [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. Google Scholar

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. Google Scholar [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. Google Scholar [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. Google Scholar [4] Y. Chien, Pattern classification and scene analysis, IEEE Transactions Automatic Control, 19 (1974), 462-463. doi: 10.1109/TAC.1974.1100577. Google Scholar [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. Google Scholar [6] P. Desclaux, AlF3 additions based on bath temperature measurements, Light Metals, (1987), 309-313. Google Scholar [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. Google Scholar [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. Google Scholar [9] P. M. Entner and G. A. Gudmundsson, Further development of the temperature model, Light Metals, (1996), 445-449. Google Scholar [10] W. Haupin and H. Kvande, Mathematical model of fluoride evolution from Hall-Héroult Cells, Essential Readings in Light Metals, (2016), 903-909. Google Scholar [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. Google Scholar [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. Google Scholar [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. Google Scholar [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. Google Scholar [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.Google Scholar [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.Google Scholar [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. Google Scholar [18] S. Kolås, Defining and verifying the 'correlation line' in aluminum electrolysis, JOM, 59 (2007), 55-60. Google Scholar [19] S Kolås and T. Støre, Bath temperature and AlF3 control of an aluminium electrolysis cell, Control and Engineering Practice, 17 (2009), 1035-1043. Google Scholar [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. Google Scholar [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.Google Scholar [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. Google Scholar [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. Google Scholar [24] D. J. Salt, Bath chemistry control system, Essential Readings in Light Metals, (2016), 798-803. Google Scholar [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. Google Scholar [26] J. Thonstand and S. Roselth, Equilibrium between bath and side ledge in aluminum cells-Basic principles, Light Metals, (1983), 414-424. Google Scholar [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. Google Scholar [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. Google Scholar [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.Google Scholar [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. Google Scholar [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. Google Scholar [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. Google Scholar [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. Google Scholar [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. Google Scholar [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. Google Scholar [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. Google Scholar
Sketch of aluminum reduction cell
Sketch of binary phase diagram of NaF-AlF3
Internal and external environments of aluminum reduction process
Response of AlF3 addition with respect to relationship between electrolyte temperature and SD
Solution for amount decision concerning AlF3 addition
Naïve Bayes for SD state evaluation
Naïve Bayes classifier for dSD state estimation
(a) Fuzzy inference rules for evaluation and (b) evaluation grade based on SD and dSD
Changes with balance point variation
Classification results for NBC and ENBC with seeds data set
Classification results for NBC and ENBC with banknote data set
Classification result-based NBC and ENBC with data set of cell
The evaluation grades with the better AlF3 addition
Values of characteristic parameters over two months
Evaluation grades for cell condition
(a) Comparison between actual feeding times and those based on proposed strategy; (b) comparison between actual feeding times and those based on linear programming model; (c) Comparison between actual feeding times and those based on NBC and mass balance
Error comparison of feeding times based on proposed strategy and existing strategy
Eight characteristic parameters.
 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.
Fuzzy numbers definitions for SD and its trends.
 Definitions for SD Definitions for dSD Label Meaning Membership Label Meaning Membership VL Very low $\mu \left( VL \right)=P\left( VL\left| {{{\bf{x}}}_{i}} \right. \right)$ HN High negative $\mu \left( HN \right)=P\left( HN\left| \Delta {{{\bf{x}}}_{i}} \right. \right)$ LL Little low $\mu \left( LL \right)=P\left( LL\left| {{{\bf{x}}}_{i}} \right. \right)$ LN Low negative $\mu \left( LN \right)=P\left( LN\left| \Delta {{{\bf{x}}}_{i}} \right. \right)$ N Normal $\mu \left( N\right)=P\left( N\left| {{{\bf{x}}}_{i}} \right. \right)$ Z zero $\mu \left( N \right)=P\left( N\left| \Delta {{{\bf{x}}}_{i}} \right. \right)$ LH Little high $\mu \left( LP \right)=P\left( LP\left| {{{\bf{x}}}_{i}} \right. \right)$ LP Low positive $\mu \left( LH \right)=P\left( LH\left| \Delta {{{\bf{x}}}_{i}} \right. \right)$ VH Very high $\mu \left( LH \right)=P\left( LH\left| {{{\bf{x}}}_{i}} \right. \right)$ HP High positive $\mu \left( HP \right)=P\left( HP\left| \Delta {{{\bf{x}}}_{i}} \right. \right)$
 Definitions for SD Definitions for dSD Label Meaning Membership Label Meaning Membership VL Very low $\mu \left( VL \right)=P\left( VL\left| {{{\bf{x}}}_{i}} \right. \right)$ HN High negative $\mu \left( HN \right)=P\left( HN\left| \Delta {{{\bf{x}}}_{i}} \right. \right)$ LL Little low $\mu \left( LL \right)=P\left( LL\left| {{{\bf{x}}}_{i}} \right. \right)$ LN Low negative $\mu \left( LN \right)=P\left( LN\left| \Delta {{{\bf{x}}}_{i}} \right. \right)$ N Normal $\mu \left( N\right)=P\left( N\left| {{{\bf{x}}}_{i}} \right. \right)$ Z zero $\mu \left( N \right)=P\left( N\left| \Delta {{{\bf{x}}}_{i}} \right. \right)$ LH Little high $\mu \left( LP \right)=P\left( LP\left| {{{\bf{x}}}_{i}} \right. \right)$ LP Low positive $\mu \left( LH \right)=P\left( LH\left| \Delta {{{\bf{x}}}_{i}} \right. \right)$ VH Very high $\mu \left( LH \right)=P\left( LH\left| {{{\bf{x}}}_{i}} \right. \right)$ HP High positive $\mu \left( HP \right)=P\left( HP\left| \Delta {{{\bf{x}}}_{i}} \right. \right)$
Detailed statistical results.
 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 for each data group.
 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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