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

Zuguo Chen; Yonggang Li; Xiaofang Chen; Chunhua Yang; Weihua Gui

doi:10.3934/jimo.2018060

Article Contents

2019, Volume 15, Issue 2: 595-618. Doi: 10.3934/jimo.2018060

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

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

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

Received: October 2017

Revised: December 2017

Early access: April 2018

Published: January 2019

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).

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Abstract

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:

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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. 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. 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 types	Similarity
Red curve	0.9419
Green curve	0.9526
Blue curve	0.9661
Turquoise curve	0.9628
Carmine curve	0.9587

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Table 2. The corresponding similarity to each curve in Figure 7

Curve types	Similarity
Red curve	0.9278
Green curve	0.9152
Blue curve	0.9472
Turquoise curve	0.9324
Carmine curve	0.9461

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Table 3. Mean accuracy and time advance of three similarity search methods

Time advance ($min$)	DPMD	Minkowski distance	Euclidean distance
Time advance ($min$)	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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Table 4. Mean accuracy and time advance of three prediction algorithms

Time advance ($min$)	LMSRCKF	SRCKF	EKF
Time advance ($min$)	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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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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Table 6. Result statistics of AE-occurring and AE-predicting obtained using the CTFM algorithm

Project names	cell numbers
Project names	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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