# 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
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##### References:
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
Values of characteristic parameters over two months
(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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