Grey-box Recursive Parameter Identification of a Nonlinear Dynamic Model for Mineral Flotation
Abstract: This study presents a grey-box recursive identification technique to estimate key parameters in a mineral flotation process across two scenarios. The method is applied to a nonlinear physics-based dynamic model validated at a laboratory scale, allowing real-time updates of two model parameters, n and C, in response to changing conditions. The proposed approach effectively adapts to process variability and allows for continuous adjustments based on operational fluctuations, resulting in a significantly improved estimation of concentrate grade - one key performance indicator. In Scenario 1, parameters n and C achieved fit metrics of 97.99 and 96.86, respectively, with concentrate grade estimations improving from 75.1 to 98.69 using recursive identification. In Scenario 2, the fit metrics for n and C were 96.27 and 95.48, respectively, with the concentrate grade estimations increasing from 96.27 to 99.45 with recursive identification. The results demonstrate the effectiveness of the proposed grey-box recursive identification method in accurately estimating parameters and predicting concentrate grade in a mineral flotation process.
- M. Runge, K. Flaßkamp, and C. Büskens, “Model predictive control with online nonlinear parameter identification for a robotic system,” in 2020 7th International Conference on Control, Decision and Information Technologies (CoDIT), vol. 1, pp. 312–318, 2020.
- P. Quintanilla, S. J. Neethling, D. Navia, and P. R. Brito-Parada, “A dynamic flotation model for predictive control incorporating froth physics. Part I: Model development,” Minerals Engineering, vol. 173, p. 107192, 2021.
- P. Quintanilla, S. J. Neethling, D. Mesa, D. Navia, and P. R. Brito-Parada, “A dynamic flotation model for predictive control incorporating froth physics. part ii: Model calibration and validation,” Minerals Engineering, vol. 173, p. 107190, 2021.
- P. Quintanilla, D. Navia, S. J. Neethling, and P. R. Brito-Parada, “Economic model predictive control for a rougher froth flotation cell using physics-based models,” Minerals Engineering, vol. 196, p. 108050, 5 2023.
- L. Ljung and T. Söderström, Theory and Practice of Recursive Identification. MIT press, 1983.
- C. Pan, Y. Xi, and Y. Hu, “Grey-box parameter identification for drive-train system of large-scale wind turbine,” in 2019 Chinese Control Conference (CCC), pp. 1512–1519, IEEE, 2019.
- T. Wigren, “Recursive prediction error identification using the nonlinear wiener model,” Automatica, vol. 29, no. 4, pp. 1011–1025, 1993.
- P. C. Young, “Real-time updating in flood forecasting and warning,” Flood Risk Science and Management, pp. 163–195, 2010.
- T. P. Bohlin, Practical Grey-Box Process Identification: Theory and Applications. Springer Science & Business Media, 2006.
- D. Mesa, P. Quintanilla, and F. Reyes, “Bubble Analyser - An open-source software for bubble size measurement using image analysis,” Minerals Engineering, vol. 180, 2022.
- K. Hadler, C. D. Smith, and J. J. Cilliers, “Recovery vs. mass pull: The link to air recovery,” Minerals Engineering, vol. 23, no. 11-13, pp. 994–1002, 2010.
- S. J. Neethling, “Simple approximations for estimating froth recovery,” International Journal of Mineral Processing, vol. 89, no. 1-4, pp. 44–52, 2008.
- S. J. Neethling and P. R. Brito-Parada, “Predicting flotation behaviour – The interaction between froth stability and performance,” Minerals Engineering, vol. 120, pp. 60–65, 2018.
- S. J. Neethling and J. J. Cilliers, “The entrainment factor in froth flotation: Model for particle size and other operating parameter effects,” International Journal of Mineral Processing, vol. 93, pp. 141–148, 10 2009.
- S. J. Neethling and J. J. Cilliers, “Modelling flotation froths,” International Journal of Mineral Processing, vol. 72, no. 1-4, pp. 267–287, 2003.
- J. R. Magnus and H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics. John Wiley & Sons, 2019.
- Cambridge University Press, 2012.
- Prentice-Hall, 1999.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.