{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T01:26:05Z","timestamp":1767921965484,"version":"3.49.0"},"reference-count":21,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2017,9,1]],"date-time":"2017-09-01T00:00:00Z","timestamp":1504224000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61673055"],"award-info":[{"award-number":["61673055"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61333002"],"award-info":[{"award-number":["61333002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61673056"],"award-info":[{"award-number":["61673056"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The concentration of alumina in the electrolyte is of great significance during the production of aluminum. The amount of the alumina concentration may lead to unbalanced material distribution and low production efficiency and affect the stability of the aluminum reduction cell and current efficiency. The existing methods cannot meet the needs for online measurement because industrial aluminum electrolysis has the characteristics of high temperature, strong magnetic field, coupled parameters, and high nonlinearity. Currently, there are no sensors or equipment that can detect the alumina concentration on line. Most companies acquire the alumina concentration from the electrolyte samples which are analyzed through an X-ray fluorescence spectrometer. To solve the problem, the paper proposes a soft sensing model based on a kernel extreme learning machine algorithm that takes the kernel function into the extreme learning machine. K-fold cross validation is used to estimate the generalization error. The proposed soft sensing algorithm can detect alumina concentration by the electrical signals such as voltages and currents of the anode rods. The predicted results show that the proposed approach can give more accurate estimations of alumina concentration with faster learning speed compared with the other methods such as the basic ELM, BP, and SVM.<\/jats:p>","DOI":"10.3390\/s17092002","type":"journal-article","created":{"date-parts":[[2017,9,1]],"date-time":"2017-09-01T11:05:24Z","timestamp":1504263924000},"page":"2002","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Alumina Concentration Detection Based on the Kernel Extreme Learning Machine"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8010-6045","authenticated-orcid":false,"given":"Sen","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Automation & Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China"},{"name":"Key Laboratory of Knowledge Automation for Industrial Processes, Ministry of Education, Beijing 100083, China"}]},{"given":"Tao","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Automation & Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China"},{"name":"Key Laboratory of Knowledge Automation for Industrial Processes, Ministry of Education, Beijing 100083, China"}]},{"given":"Yixin","family":"Yin","sequence":"additional","affiliation":[{"name":"School of Automation & Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China"},{"name":"Key Laboratory of Knowledge Automation for Industrial Processes, Ministry of Education, Beijing 100083, China"}]},{"given":"Wendong","family":"Xiao","sequence":"additional","affiliation":[{"name":"School of Automation & Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China"},{"name":"Key Laboratory of Knowledge Automation for Industrial Processes, Ministry of Education, Beijing 100083, China"}]}],"member":"1968","published-online":{"date-parts":[[2017,9,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1023\/A:1009715923555","article-title":"Tutorial on Support Vector Machines for Pattern Recognition","volume":"2","author":"Burges","year":"1998","journal-title":"Data Min. Knowl. Discov."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1163\/092764411X571427","article-title":"Application research on neural network predictive control technology in Aluminum electrolysis process","volume":"8","author":"Li","year":"2011","journal-title":"Instrum. Tech. Sens."},{"key":"ref_3","first-page":"9","article-title":"Research of predicting alumina concentration based on orthogonal transformation","volume":"32","author":"Lin","year":"2010","journal-title":"J. Wuhan Inst. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Yan, G., and Liang, X. (2010, January 18\u201320). Predictive models of aluminum reduction cell based on LS-SVM. Proceedings of the 2010 International Conference on Digital Manufacturing and Automation (ICDMA), Changsha, China.","DOI":"10.1109\/ICDMA.2010.12"},{"key":"ref_5","first-page":"911","article-title":"Fuzzy expert control method based on on-line intelligent identification and its application","volume":"35","author":"Li","year":"2004","journal-title":"J. Cent. South Univ. Technol."},{"key":"ref_6","first-page":"883","article-title":"Application of gray GM (1, 1) model to alumina concentration estimation in aluminum electrolysis","volume":"29","author":"Zhang","year":"2008","journal-title":"Chin. J. Sci. Instrum."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1007\/s00521-007-0139-1","article-title":"Multi-stage extreme learning machine for fault diagnosis on hydraulic tube tester","volume":"17","author":"Hu","year":"2008","journal-title":"Neural Comput. Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.1007\/s00521-011-0522-9","article-title":"Leukocyte image segmentation by visual attention and extreme learning machine","volume":"21","author":"Pan","year":"2012","journal-title":"Neural Comput. Appl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.neucom.2013.03.059","article-title":"Real-time fault diagnosis for gas turbine generator systems using extreme learning machine","volume":"128","author":"Wang","year":"2014","journal-title":"Neurocomputing"},{"key":"ref_10","unstructured":"Huang, G.-B., Zhou, H., Ding, X., and Zhang, R. (2016). Extreme learning machine for regression and multi-class classification. IEEE Trans. Syst. Man Cybern. Part B."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"7978","DOI":"10.1016\/j.ijleo.2016.05.108","article-title":"Illumination Correction of Dyeing Products Based on Grey-Edge and Kernel Extreme Learning Machine","volume":"127","author":"Zhou","year":"2016","journal-title":"Optik Int. J. Light Electron Opt."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/j.apenergy.2016.12.130","article-title":"Electricity Price Forecasting by a Hybrid Model, Combining Wavelet Transform, ARMA and Kernel-based Extreme Learning Machine Methods","volume":"190","author":"Zhang","year":"2017","journal-title":"Appl. Energy"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1109\/TNN.2003.809401","article-title":"Learning capability and storage capacity of two hidden-layer feed forward networks","volume":"12","author":"Huang","year":"2003","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_14","first-page":"16","article-title":"Extreme Learning Machine with Randomly Assigned RBF Kernels","volume":"11","author":"Huang","year":"2005","journal-title":"Int. J. Inf. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1016\/j.neucom.2005.12.126","article-title":"Extreme learning machine: Theory and Applications","volume":"70","author":"Huang","year":"2006","journal-title":"Neurocomputing"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3066","DOI":"10.1016\/j.neucom.2009.03.016","article-title":"Partial lanczos extreme learning machine for single-output regression problems","volume":"72","author":"Tang","year":"2009","journal-title":"Neurocomputing"},{"key":"ref_17","first-page":"1","article-title":"Cross-person activity recognition using reduced kernel extreme learning machine","volume":"53","author":"Deng","year":"2014","journal-title":"Neural Netw. Off. J. Int. Neural Netw. Soc."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/j.neucom.2013.09.072","article-title":"Multiple kernel extreme learning machine","volume":"149","author":"Liu","year":"2015","journal-title":"Neurocomputing"},{"key":"ref_19","unstructured":"Fr\u00e9nay, B., and Verleysen, M. (2010, January 28\u201330). Using SVMs with Randomized Feature Spaces: An Extreme Learning Approach. Proceedings of the European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning, Bruges, Belgium."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2526","DOI":"10.1016\/j.neucom.2010.11.037","article-title":"Parameter-insensitive kernel in extreme learning for non-linear support vector regression","volume":"74","author":"Verleysen","year":"2011","journal-title":"Neurocomputing"},{"key":"ref_21","unstructured":"Cheng, J.X., Zhang, Q., Wu, X., and Qi, K.R. (2014, January 29\u201330). An Application of Minimum Penalty Coefficient K-fold Cross Validation\u2013Support Vector Machine in the Regression Analysis of Railway Monthly Freight Volume. Proceedings of the International Conference on Advanced Computer Science and Engineering, Guangzhou, China."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/9\/2002\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:43:55Z","timestamp":1760208235000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/9\/2002"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,1]]},"references-count":21,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2017,9]]}},"alternative-id":["s17092002"],"URL":"https:\/\/doi.org\/10.3390\/s17092002","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9,1]]}}}