Health state diagnosis of aluminum electrolytic cells based on Adaboost-PSO-SVM

doi:10.11949/0438-1157.20231066

CIESC Journal ›› 2024, Vol. 75 ›› Issue (1): 354-365.DOI: 10.11949/0438-1157.20231066

• Process system engineering • Previous Articles Next Articles

Health state diagnosis of aluminum electrolytic cells based on Adaboost-PSO-SVM

Gang YIN¹(), Zhongyou QIAN¹, Wenqi CAO², Pengcheng QUAN², Hengquan XU², Feiya YAN³, Min WANG⁴, Yu XIANG⁵, Dongmei XIANG⁶, Jian LU³, Yuhai ZUO⁷, Wen HE⁸, Runting LU³

^1.State Key Laboratory of Coal Mine Disaster Dynamics and Control, College of Resource and Safety Engineering, Chongqing University, Chongqing 400044, China
^2.Aba Aluminium Factory, Aba 623001, Sichuan, China
^3.Guiyang Aluminium Magnesium Design & Research Institute Co. , Ltd. , Guiyang 550081, Guizhou, China
^4.Chongqing Qineng Electric Aluminum Co. , Ltd. , Chongqing 410420, China
^5.Communication NCO Academy, Army Engineering University of PLA, Chongqing 400353, China
^6.China Automobile Research Institute New Energy Technology Co. , Ltd. , Chongqing 400705, China
^7.Qinghai Haiyuan Green Wheel Manufacturing Co. , Ltd. , Xining 810000, Qinghai, China
^8.Bomei Qimingxing Aluminium Co. , Ltd. , Meishan 620010, Sichuan, China

Received:2023-10-16 Revised:2023-12-12 Online:2024-03-11 Published:2024-01-25
Contact: Gang YIN

基于Adaboost-PSO-SVM的铝电解槽健康状态诊断方法研究

尹刚¹(), 钱中友¹, 曹文琦², 全鹏程², 许亨权², 颜非亚³, 王民⁴, 向禹⁵, 向冬梅⁶, 卢剑³, 左玉海⁷, 何文⁸, 卢润廷³

^1.煤矿灾害动力学与控制全国重点实验室，重庆大学资源与安全学院，重庆 400044
^2.阿坝铝厂，四川阿坝 623001
^3.贵阳铝镁设计研究院有限公司，贵州贵阳 550081
^4.重庆旗能电铝有限公司，重庆 410420
^5.陆军工程大学通信士官学校，重庆 400353
^6.中汽院新能源科技有限公司，重庆 400705
^7.青海海源绿轮制造有限公司，青海西宁 810000
^8.眉山市博眉启明星铝业有限公司，四川眉山 620010

通讯作者: 尹刚
作者简介:尹刚（1964—），男，博士，教授，yk115@cqu.edu.cn
基金资助:
重庆英才·创新创业示范团队项目(CQYC202203091061);科技转化重大项目(H20201555);国家自然科学基金面上项目(62373069)

Abstract

Abstract:

In order to solve the problem of frequent failures of aluminum electrolytic cells in the aluminum electrolytic production process, a health state diagnosis model of aluminum electrolytic cells based on support vector machine (SVM) was proposed. The thickness of the wall, current efficiency and electrolytic temperature were taken as the comprehensive evaluation indexes of the health state of aluminum electrolytic cells, and the health state of aluminum electrolytic cells was divided into four grades: excellent, good, medium and poor. Considering that traditional support vector machine (SVM) can only be applied to binary classification problem, Adaboost algorithm is used to transform SVM binary classification problem into multi-classification problem to solve aluminum electrolytic cell health diagnosis problem, which fully considers the weight of submodels and strengthens the applicability of the model. The hyperparameters of the model were optimized by using PSO algorithm. The classification accuracy of the model was 94.70% and the Macro-F1 score was 0.9453 in the aluminum electrolytic cells. Compared with the Adaboost-SVM model without optimization algorithm and the PSO-SVM model without integrated algorithm, Adaboost-PSO-SVM improves classification accuracy by 8.34% and 4.93%, and Macro-F1 scores by 8.84% and 5.20%, respectively. Compared with the current mainstream machine learning algorithms DT and KNN, the classification accuracy is improved by 13.64% and 11.11%, respectively, and Macro-F1 scores are improved by 13.47% and 11.04%, respectively. The model provides a comprehensive assessment of the optimal maintenance period for aluminum electrolytic cells. This not only reduces the frequency of failures in aluminum electrolytic cells but also enhances the economic benefits of aluminum plants.

Key words: electrolysis, algorithm, health state, prediction, experimental validation

摘要：

针对铝电解槽在铝电解生产过程中故障频发的问题，提出了一种基于支持向量机（support vector machine， SVM）的铝电解槽健康状态诊断模型，考虑传统的支持向量机只能适用于二分类问题，采用自适应推进算法（adaptive boosting， Adaboost）将支持向量机的二分类问题转化为多分类问题用于求解铝电解槽健康状态诊断问题，充分考虑了子模型的权重，强化了模型的适用性。并利用粒子群优化算法（particle swarm optimization，PSO）对其超参数寻优，提高模型的预测精度。实验结果表明，提出的铝电解槽健康状态诊断模型的准确率和Macro-F1分数分别达到94.70%和0.9453，相较于其他传统模型均有显著提升。

关键词: 电解, 算法, 健康状态, 预测, 实验验证

CLC Number:

TF 821

Gang YIN, Zhongyou QIAN, Wenqi CAO, Pengcheng QUAN, Hengquan XU, Feiya YAN, Min WANG, Yu XIANG, Dongmei XIANG, Jian LU, Yuhai ZUO, Wen HE, Runting LU. Health state diagnosis of aluminum electrolytic cells based on Adaboost-PSO-SVM[J]. CIESC Journal, 2024, 75(1): 354-365.

尹刚, 钱中友, 曹文琦, 全鹏程, 许亨权, 颜非亚, 王民, 向禹, 向冬梅, 卢剑, 左玉海, 何文, 卢润廷. 基于Adaboost-PSO-SVM的铝电解槽健康状态诊断方法研究[J]. 化工学报, 2024, 75(1): 354-365.

Figures/Tables 19

Fig.1 Execution process of the Adaboost algorithm

Table 1 Criteria for judging the health state of aluminum electrolytic cells

类别	指标范围			健康状态等级
类别	炉帮厚度d/cm	电流效率	电解温度T/℃	健康状态等级
1	d≥12	94%~100%	950<T<965	优
2	10≤d<12	92%~94%	935<T≤950	良
3	8≤d<10	85%~92%	965≤T＜975	中
4	d<8	70%~85%	T≤935 or T≥975	差

Table 2 The Pearson correlation coefficient for the health state parameters of aluminum electrolytic cells

参数	槽电压	分子比	铝水平	电解质水平	氧化铝浓度	出铝量	氟化盐含量	效应系数
电解温度	0.94	0.92	0.91	0.89	0.85	0.83	0.79	0.74
电流效率	0.92	0.91	0.89	0.88	0.82	0.96	0.85	0.78
炉帮厚度	0.96	0.89	0.92	0.91	0.92	0.79	0.88	0.83

Fig.2 Adaboost-PSO-SVM health state diagnosis model for aluminum electrolytic cells

Table 3 State labels and sample distribution

样本数	训练集样本数	测试集样本数	状态	标签
820	738	82	优	1
620	558	62	良	2
730	657	73	中	3
470	423	47	差	4

Table 4 Experimental data acquisition information

参数	数值
数据获取时间	2020年10月至2022年9月
电解槽数量	15（201^#~215^#槽）
特征数量	8
实验样本数	2640
训练集/测试集占比	9∶1

Fig.3 PSO optimized SVM parameter flow chart

Table 5 SVM model parameters

超参数	最优值
C	156.688
g	1.278

Fig.4 Relationship between the number and accuracy of Adaboost weak classifiers

Fig.5 Adaboost-PSO-SVM model diagnosis results

Fig.6 Adaboost-SVM model diagnosis results

Fig.7 PSO-SVM model diagnosis results

Fig.8 Comparison of performance between single model and fusion model

Fig.9 KNN model diagnosis results

Fig.10 DT model diagnosis results

Fig.11 Performance comparison between Adaboost-PSO-SVM and traditional classification algorithms

Fig.12 Adaboost-SSA-SVM model diagnosis results

Fig.13 Adaboost-GWO-SVM model diagnosis results

Fig.14 Performance comparison of different optimization algorithms

References 41

1	傅长宏. 电解槽槽况综合分析评价手段[J]. 世界有色金属, 2012(11): 36-39.
	Fu C H. Comprehensive analysis and evaluation means of electrolytic cell condition[J]. World Nonferrous Metals, 2012(11): 36-39.
2	Pass J M, Zheng Y, Wead W B, et al. Classification of cell states for aluminum electrolysis based on data[J]. Computer Engineering & Applications, 2015, 180(3): H946-H955.
3	邓少松. 基于阳极电流分布的铝电解槽异常诊断[D]. 北京: 北方工业大学, 2017.
	Deng S S. The abnormal diagnosis of aluminum reduction cell based on anode current[D]. Beijing: North China University of Technology, 2017.
4	张旖芮, 阳春华, 朱红求. 基于数据的铝电解槽况分类[J]. 计算机工程与应用, 2015, 51(11): 233-237.
	Zhang Y R, Yang C H, Zhu H Q. Classification of cell states for aluminum electrolysis based on data[J]. Computer Engineering and Applications, 2015, 51(11): 233-237.
5	侯婕, 田学法, 孔淑麒. 基于LSTM的铝电解槽况预测[J]. 轻金属, 2021(1): 33-37, 62.
	Hou J, Tian X F, Kong S Q. Prediction of aluminum pot conditions based on LSTM[J]. Light Metals, 2021(1): 33-37, 62.
6	曹丹阳, 孔淑麒, 高磊. 基于高斯混合模型的铝电解槽况聚类研究[J]. 轻金属, 2020(2): 26-30.
	Cao D Y, Kong S Q, Gao L. Research on state clustering of aluminum electrolytic cell based on Gaussian mixture model[J]. Light Metals, 2020(2): 26-30.
7	韦业辉. 基于火眼图像的铝电解槽况诊断及过热度识别研究[D]. 南宁: 广西大学, 2022.
	Wei Y H. Research on status diagnosis and superheat degree identification of aluminum reduction cell based on fire eye image[D].Nanning: Guangxi University, 2022.
8	陈祖国, 李勇刚, 卢明, 等. 基于贝叶斯概率语义网的铝电解槽况知识表示模型与约简方法[J]. 控制与决策, 2020, 35(7): 1569-1583.
	Chen Z G, Li Y G, Lu M, et al. Aluminum electrolysis cell condition knowledge representation model and reduction method based on Bayesian probability semantic network[J]. Control and Decision, 2020, 35(7): 1569-1583.
9	李界家, 高天浩, 纪昕洋. 基于布谷鸟-支持向量机和深度学习的铝电解异常状态诊断方法[J]. 轻金属, 2019(10): 32-40.
	Li J J, Gao T H, Ji X Y. Aluminum electrolysis abnormal state diagnosis method based on cuckoo support vector machine and deep learning[J]. Light Metals, 2019(10): 32-40.
10	崔桂梅, 薛法远, 刘丕亮. 基于槽况分类的铝电解电流效率预测研究[J]. 计算机仿真, 2017, 34(1): 288-291, 387.
	Cui G M, Xue F Y, Liu P L. Prediction modelof the current efficiency for aluminum electrolysis process based on status classification[J]. Computer Simulation, 2017, 34(1): 288-291, 387.
11	于世福, 陈兆娜. 基于主元分析的铝电解槽故障诊断[J]. 电子世界, 2019(22): 174-175.
	Yu S F, Chen Z N. Fault diagnosis of aluminum reduction cell based on principal component analysis[J]. Electronics World, 2019(22): 174-175.
12	刘志元. 基于多元统计方法的电解铝生产流程监测及故障诊断策略的研究[J]. 轻金属, 2018(7): 58-61.
	Liu Z Y. Research on process monitoring and fault diagnosis strategy of aluminum production based on multiple statistical methods[J]. Light Metals, 2018(7): 58-61.
13	Wang B J, Zhang X L, Xing S, et al. Sparse representation theory for support vector machine kernel function selection and its application in high-speed bearing fault diagnosis[J]. ISA Transactions, 2021, 118: 207-218.
14	Mathur A, Foody G M. Multiclass and binary SVM classification: implications for training and classification users[J]. IEEE Geoscience and Remote Sensing Letters, 2008, 5(2): 241-245.
15	吴海燕, 陈晓磊, 范国轩. 一种自适应核SMOTE-SVM算法用于不平衡数据分类[J]. 北京化工大学学报(自然科学版), 2023, 50(2): 97-104.
	Wu H Y, Chen X L, Fan G X. An adaptive kernel SMOTE- SVM algorithm for imbalanced data classification[J]. Journal of Beijing University of Chemical Technology (Natural Science Edition), 2023, 50(2): 97-104.
16	王众, 鲁淑霞. 不平衡数据分类问题的基于间隔放大损失的支持向量机[J]. 重庆邮电大学学报(自然科学版), 2023, 35(1): 70-78.
	Wang Z, Lu S X. Support vector machine with margin magnification loss for imbalanced data classification problems[J]. Journal of Chongqing University of Posts and Telecommunications (Natural Science Edition), 2023, 35(1): 70-78.
17	鲁淑霞, 周谧, 金钊. 非均衡加权随机梯度下降SVM在线算法[J]. 计算机科学与探索, 2017, 11(10): 1662-1671.
	Lu S X, Zhou M, Jin Z. Imbalanced weighted stochastic gradient descent online algorithm for SVM[J]. Journal of Frontiers of Computer Science and Technology, 2017, 11(10): 1662-1671.
18	尹刚, 李伊惠, 何飞, 等. 基于KPCA和SVM的铝电解槽漏槽事故预警方法[J]. 化工学报, 2023, 74(8): 3419-3428.
	Yin G, Li Y H, He F, et al. Early warning method of aluminum reduction cell leakage accident based on KPCA and SVM[J]. CIESC Journal, 2023, 74(8): 3419-3428.
19	孙同敏. 基于DBN-SVM的航空发动机健康状态评估方法[J]. 控制工程, 2021, 28(6): 1163-1170.
	Sun T M. Research on aero engine health state assessment using DBN and SVM[J]. Control Engineering of China, 2021, 28(6): 1163-1170.
20	王萍, 范凌峰, 程泽. 基于健康特征参数的锂离子电池SOH和RUL联合估计方法[J]. 中国电机工程学报, 2022, 42(4): 1523-1534.
	Wang P, Fan L F, Cheng Z. A joint state of health and remaining useful life estimation approach for lithium-ion batteries based on health factor parameter[J]. Proceedings of the CSEE, 2022, 42(4): 1523-1534.
21	叶远波, 李端超, 谢民, 等. 基于SSA-SVM的继电保护装置状态评估方法研究[J]. 电力系统保护与控制, 2022, 50(8): 171-178.
	Ye Y B, Li D C, Xie M, et al. A state evaluation method for a relay protection device based on SSA-SVM[J]. Power System Protection and Control, 2022, 50(8): 171-178.
22	魏永合, 王明华. 基于EEMD和SVM的滚动轴承退化状态识别[J]. 计算机集成制造系统, 2015, 21(9): 2475-2483.
	Wei Y H, Wang M H. Degradation state recognition of rolling bearing based on EEMD and SVM[J]. Computer Integrated Manufacturing Systems, 2015, 21(9): 2475-2483.
23	Li R, Li W R, Zhang H N, et al. On-line estimation method of lithium-ion battery health status based on PSO-SVM[J]. Frontiers in Energy Research, 2021, 9: 693249.
24	Lan Y F, Zhang Y Q, Lin W W. Diagnosis algorithms for indirect bridge health monitoring via an optimized AdaBoost-linear SVM[J]. Engineering Structures, 2023, 275: 115239.
25	姚宏亮. 基于组合加权朴素贝叶斯的铝电解槽健康度评价方法及系统[D]. 长沙: 中南大学, 2022.
	Yao H L. Aluminum electrolytic cell health evaluation method and system based on combinatorial weighted naive Bayes[D]. Changsha: Central South University, 2022.
26	Zhou W, Shi J Y, Yin G, et al. Optimal control for aluminum electrolysis process using adaptive dynamic programming[J]. IEEE Access, 2020, 8: 220374-220383.
27	尹刚, 陈根, 何文, 等. 基于SDAE和随机森林的铝电解槽阳极效应预测方法研究[J]. 稀有金属, 2021, 45(4): 428-436.
	Yin G, Chen G, He W, et al. A method for anode effect prediction of aluminium electrolysis cell based on SDAE and random forest[J]. Chinese Journal of Rare Metals, 2021, 45(4): 428-436.
28	尹刚, 陈根, 何文, 等. 基于深度学习的300 kA铝电解槽阳极效应预测[J]. 中国有色金属学报, 2021, 31(1): 161-170.
	Yin G, Chen G, He W, et al. Anode effect prediction of 300 kA aluminium electrolysis cell based on deep learning[J]. The Chinese Journal of Nonferrous Metals, 2021, 31(1): 161-170.
29	尹刚, 向冬梅, 王民, 等. 基于数据驱动的铝电解槽剩余寿命预测方法研究[J]. 稀有金属, 2023, 47(2): 273-280.
	Yin G, Xiang D M, Wang M, et al. Prediction method of remaining life of aluminum reduction cell based on data drive[J]. Chinese Journal of Rare Metals, 2023, 47(2): 273-280.
30	Zhou W, Zheng F J, Yin G, et al. YOLOTrashCan: a deep learning marine debris detection network[J]. IEEE Transactions on Instrumentation and Measurement, 2023, 72: 1-12.
31	Rätsch G, Onoda T, Müller K R. Soft margins for AdaBoost[J]. Machine Learning, 2001, 42(3): 287-320.
32	汤卫雄, 程云章, 张天逸, 等. 基于脑电非线性特征和AdaBoost算法的诱导期麻醉深度检测[J]. 中国医学物理学杂志, 2023, 40(5): 616-621.
	Tang W X, Cheng Y Z, Zhang T Y, et al. Monitoring depth of anesthesia during induction using EEG nonlinear characteristics combined with AdaBoost algorithm[J]. Chinese Journal of Medical Physics, 2023, 40(5): 616-621.
33	鲁淑霞, 张振莲, 翟俊海. 代价敏感惩罚AdaBoost算法的非平衡数据分类[J]. 南京航空航天大学学报, 2023, 55(2): 339-346.
	Lu S X, Zhang Z L, Zhai J H. Imbalanced data classification based on cost sensitivity penalized AdaBoost algorithm[J]. Journal of Nanjing University of Aeronautics & Astronautics, 2023, 55(2): 339-346.
34	Merler S, Caprile B, Furlanello C. Parallelizing AdaBoost by weights dynamics[J]. Computational Statistics & Data Analysis, 2007, 51(5): 2487-2498.
35	Cortes C, Vapnik V. Support-vector networks[J]. Machine Learning, 1995, 20(3): 273-297.
36	Wang D S, Tan D P, Liu L. Particle swarm optimization algorithm: an overview[J]. Soft Computing, 2018, 22(2): 387-408.
37	曾振双, 贺昕兴. 500 kA石墨化阴极电解槽数学管控模型研究及生产实践[J]. 金属材料与冶金工程, 2023, 51(4): 33-37.
	Zeng Z S, He X X. Research on mathematical control model and production practice of 500 kA graphitized cathode electrolytic cell[J]. Metal Materials and Metallurgy Engineering, 2023, 51(4): 33-37.
38	兰海波, 靳开强, 杜青松. 320 kA预焙铝电解槽电流效率的影响因素及提高方法[J]. 四川有色金属, 2022(1): 36-39.
	Lan H B, Jin K Q, Du Q S. Influencing factors and improving methods of current efficiency of 320 kA prebaked aluminum reduction cell[J]. Sichuan Nonferrous Metals, 2022(1): 36-39.
39	邱竹贤. 预焙槽练铝[M]. 北京: 冶金工业出版社, 2006.
	Qiu Z X. Prebaked Aluminium[J]. Beijing: Metallurgical Industry Press, 2006.
40	Yu K, Liu L, Li J Y, et al. Multi-source causal feature selection[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2020, 42(9): 2240-2256.
41	Cervantes J, Garcia-Lamont F, Rodríguez-Mazahua L, et al. A comprehensive survey on support vector machine classification: applications, challenges and trends[J]. Neurocomputing, 2020, 408: 189-215.

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Health state diagnosis of aluminum electrolytic cells based on Adaboost-PSO-SVM

基于Adaboost-PSO-SVM的铝电解槽健康状态诊断方法研究

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