“System Identification of a Non-Uniformly Sampled Multi-Rate System in Aluminium Electrolysis Cells”

Authors: Håkon Viumdal, Saba Mylvaganam and David Di Ruscio,
Affiliation: Telemark Technological R&D Centre (Tel-Tek) and Telemark University College
Reference: 2014, Vol 35, No 3, pp. 127-146.

Keywords: Height measurements, aluminium electrolysis, system identification

Abstract: Standard system identification algorithms are usually designed to generate mathematical models with equidistant sampling instants, that are equal for both input variables and output variables. Unfortunately, real industrial data sets are often disrupted by missing samples, variations of sampling rates in the different variables (also known as multi-rate systems), and intermittent measurements. In industries with varying events based maintenance or manual operational measures, intermittent measurements are performed leading to uneven sampling rates. Such is the case with aluminium smelters, where in addition the materials fed into the cell create even more irregularity in sampling. Both measurements and feeding are mostly manually controlled. A simplified simulation of the metal level in an aluminium electrolysis cell is performed based on mass balance considerations. System identification methods based on Prediction Error Methods (PEM) such as Ordinary Least Squares (OLS), and the sub-space method combined Deterministic and Stochastic system identification and Realization (DSR), and its variants are applied to the model of a single electrolysis cell as found in the aluminium smelters. Aliasing phenomena due to large sampling intervals can be crucial in avoiding unsuitable models, but with knowledge about the system dynamics, it is easier to optimize the sampling performance, and hence achieve successful models. The results based on the simulation studies of molten aluminium height in the cells using the various algorithms give results which tally well with the synthetic data sets used. System identification on a smaller data set from a real plant is also implemented in this work. Finally, some concrete suggestions are made for using these models in the smelters.

PDF PDF (946 Kb)        DOI: 10.4173/mic.2014.3.1

DOI forward links to this article:
[1] Yuxuan Shen, Zidong Wang, Bo Shen and Fuad E. Alsaadi (2020), doi:10.1049/iet-cta.2019.0085
[2] Binish Fatimah and Shiv Dutt Joshi (2021), doi:10.1007/s11265-020-01619-x
[3] Erlend Torje Berg Lundby, Adil Rasheed, Jan Tommy Gravdahl and Ivar Johan Halvorsen (2021), doi:10.1016/j.jprocont.2021.06.005
[4] Yuxuan Shen, Zidong Wang, Hongli Dong, Fuad E. Alsaadi and Hongjian Liu (2021), doi:10.1002/rnc.5884
[5] Yuxuan Shen, Zidong Wang, Hongjian Liu, Hongli Dong and Xiaojian Yi (2022), doi:10.1002/rnc.6128
[6] Qi Li, Yufu Zhi, Hailong Tan and Weiguo Sheng (2022), doi:10.1016/j.isatra.2022.07.023
[7] Jiarui Cui, Zhijing Li, Xiangquan Li, Bo Liu, Qing Li, Qun Yan, Ruoyu Huang, Hui Lu and Bin Cao (2022), doi:10.3390/app122312403
[8] Yuxuan Shen, Zidong Wang, Hongli Dong, Guoping Lu and Fawaz E. Alsaadi (2023), doi:10.1109/TNSE.2022.3229889
[9] Zhaowei Qi and Jinling Liang (2024), doi:10.1007/978-981-97-3951-6_17
[1] Bojarevics, V. and Pericleous, K. (2006). Comparison of MHD models for aluminium reduction cells, In TMS annual meeting and exhibition. pages 347--352.
[2] Bojarevics, V. and Pericleous, K. (2009). Solutions for the metal-bath interface in aluminium electrolysis cells, In TMS annual meeting and exhibition, volume1. pages 569--574.
[3] DiRuscio, D. (1996). Combined Deterministic and Stochastic System Identification and Realization: DSR - A Subspace Approach Based on Observations, Modeling, Identification and Control. 17(3):193--230. doi:10.4173/mic.1996.3.3
[4] DiRuscio, D. (1997). A Three Dimensional DSR Algorithm, Technical report, Telemark University College, Faculty of Technology, 1997.
[5] DiRuscio, D. (2000). Subspace system identification of multiple time series and different sampling rates, Unpublished report. pages 1--18.
[6] DiRuscio, D. (2001). Model Predictive Control and Optimization, Technical report, Telemark University College, Faculty of Technology, 2001. Lecture Notes.
[7] Ding, F., Qiu, L., and Chen, T. (2009). Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems, Automatica. 45(2):324 -- 332. doi:10.1016/j.automatica.2008.08.007
[8] Draper, N. and Smith, H. (1998). Applied regression analysis, Wiley series in probability and mathematical statistics. Applied probability and statistics. Wiley, 3rd edition.
[9] Golub, G.H. and Loan, C. F.V. (1996). Matrix Computations, The John Hopkins University Press, 3rd edition.
[10] Grjotheim, K. (1993). Introduction to Aluminium Electrolysis: Understanding the Hall-Heroult Process, Aluminium-Verlag. http://www.beuth.de/en/publication/introduction-to-aluminium-electrolysis/143079846.
[11] Kranc, G. (1957). Input-output analysis of multirate feedback systems, Automatic Control, IRE Transactions on. 3(1):21--28. doi:10.1109/TAC.1957.1104783
[12] Kurenkov, A., Thess, A., Zikanov, O., Segatz, M., Droste, C., and Vogelsang, D. (2004). Stability of aluminium reduction cells with mean flow, Magnetohydrodynamics. 40(2):203--212.
[13] Li, D., Shah, S., Chen, T., and Patwardhan, R. (1999). System identification and long-range predictive control of multi-rate systems, In American Control Conference. Proceedings of the 1999, volume1. pages 336--340 vol.1. doi:10.1109/ACC.1999.782796
[14] Li, D., Shah, S., Chen, T., and Qi, K. (2003). Application of dual-rate modeling to CCR octane quality inferential control, Control Systems Technology, IEEE Transactions on. 11(1):43--51. doi:10.1109/TCST.2002.806433
[15] Li, W., Shah, S.L., and Xiao, D. (2008). Kalman filters in non-uniformly sampled multirate systems: For FDI and beyond, Automatica. 44(1):199 -- 208. doi:10.1016/j.automatica.2007.05.009
[16] Ljung, L. (1999). System Identification -Theory for the User, Prentice Hall, 2nd edition.
[17] Lu, W. and GrantFisher, D. (1989). Least-squares output estimation with multirate sampling, Automatic Control, IEEE Transactions on. 34(6):669--672. doi:10.1109/9.24247
[18] Shannon, C. (1949). Communication in the presence of noise, Proceedings of the IRE. 37(1):10--21. doi:10.1109/JRPROC.1949.232969
[19] Shannon, C. (1998). Communication in the presence of noise, Proceedings of the IEEE. 86(2):447--457. doi:10.1109/JPROC.1998.659497
[20] Sheng, J., Chen, T., and Shah, S.L. (2002). Generalized predictive control for non-uniformly sampled systems, Journal of Process Control. 12(8):875 -- 885. doi:10.1016/S0959-1524(02)00009-4
[21] Viumdal, H. and Mylvaganam, S. (2010). Beyond the dip stick: Level measurements in aluminum electrolysis, JOM. 62(11):18--25. doi:10.1007/s11837-010-0161-0
[22] Viumdal, H., Yan, R., Liane, M., Moxnes, B., and Mylvaganam, S. (2010). Multi sensor data fusion for aluminium cell health monitoring and control, In TMS annual meeting and exhibition supplemental proceedings, volume3. pages 149--159. ISBN Number 978-0-87339-753-7.
[23] Wang, J., Chen, T., and Huang, B. (2004). Multirate sampled-data systems: computing fast-rate models, Journal of Process Control. 14(1):79 -- 88. ewbloc doi:10.1016/S0959-1524(03)00033-7

  title={{System Identification of a Non-Uniformly Sampled Multi-Rate System in Aluminium Electrolysis Cells}},
  author={Viumdal, Håkon and Mylvaganam, Saba and Di Ruscio, David},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}