Global sensitivity analyses of a neural networks model for a flotation circuit

Main Article Content

Manuel Saldaña
Luis Ayala
David Torres
Norman Toro


Modeling of flotation processes is complex due to the large number of variables involved and the lack of knowledge on the impact of operational parameters on the response(s), and given this problem, machine learning algorithms emerge as an alternative interesting when modeling dynamic processes. In this work, different artificial neural network (ANN) architectures for modeling the mineral concentrate in a rougher-cleaner-scavenger (RCS) circuit based on the main process variables are generated (variables as the recovery of the rougher, cleaner and scavenger cells, along with disaggregated variables). Analysis of the global sensitivity was performed to study the importance of the individual and joint perfor­mances of the stages of the flotation circuit, reflected by sensitivity indicators that allow to infer the impact that the stages and operational parameters produce on the dependent variables (mineral concentrate in rougher, cleaner and scavenger cells, in addition to the global concentration in the RCS circuit). It should be noted that the ANN is a useful tool for modeling dynamic systems such as flotation, while sensitivity analysis shows that the operation of the three threads turns out to be crucial for the subsequent evaluation of the circuit, while the Unbundled variables that most interact with the overall recovery are gas flow rate, bubble and particle diameters, bubble velocity, particle density, and surface tension.

Article Details

Chemical Engineering - General


Toro N, Jeldres RI, Órdenes JA, Robles P, Navarra A. Manganese Nodules in Chile, an Alternative for the Production of Co and Mn in the Future—A Review. Minerals. 2020;10(8):674.

Toro N, Robles P, Jeldres RI. Seabed mineral resources, an alternative for the future of renewable energy: A critical review. Ore Geol Rev. 2020;126:103699.

Pérez K, Toro N, Saldaña M, Salinas-Rodríguez E, Robles P, Torres D, Jeldres RI. Statistical Study for Leaching of Covellite in a Chloride Media. Metals (Basel). 2020;10(4):477.

Rodríguez M, Ayala L, Robles P, Sepúlveda R, Torres D, Carrillo-Pedroza FR, Jeldres RI, Toro N. Leaching chalcopyrite with an imidazolium-based ionic liquid and bromide. Metals (Basel). 2020;10(2):1-13.

Toro N, Pérez K, Saldaña M, Jeldres RI, Jeldres M, Cánovas M. Dissolution of pure chalcopyrite with manganese nodules and waste water. J Mater Res Technol. 2020;9(1):798-805.

Torres D, Pérez K, Trigueros E, I. Jeldres R, Salinas-Rodríguez E, Robles P, Toro N. Reducing-Effect of Chloride for the Dissolution of Black Copper. Metals (Basel). 2020;10(1):123.

Torres D, Ayala L, Jeldres RI, Cerecedo-Sáenz E, Salinas-Rodríguez E, Robles P, Toro N. Leaching Chalcopyrite with High MnO2 and Chloride Concentrations. Metals (Basel). 2020;10(1):107.

Agorhom EA, Lem JP, Skinner W, Zanin M. Challenges and opportunities in the recovery/rejection of trace elements in copper flotation-a review. Miner Eng. 2015;78:45-57.

Lucay F, Cisternas LA, Gálvez ED. Global sensitivity analysis for identifying critical process design decisions. Chem Eng Res Des. 2015;103:74-83.

Castellón CI, Piceros EC, Toro N, Robles P, López-Valdivieso A, Jeldres RI. Depression of pyrite in seawater flotation by guar gum. Metals (Basel). 2020;10(2).

Lucay F, Mellado ME, Cisternas LA, Gálvez ED. Sensitivity analysis of separation circuits. Int J Miner Process. 2012;110-111:30-45.

Sepúlveda FD, Lucay F, González JF, Cisternas LA, Gálvez ED. A methodology for the conceptual design of flotation circuits by combining group contribution, local/global sensitivity analysis, and reverse simulation. Int J Miner Process. 2017;164:56-66.

Mendez DA, Gálvez ED, Cisternas LA. State of the art in the conceptual design of flotation circuits. Int J Miner Process. 2009;90(1-4):1-15.

Sepúlveda FD, Cisternas LA, Elorza MA, Gálvez ED. A methodology for the conceptual design of concentration circuits: Group contribution method. Comput Chem Eng. 2014;63:173-183.

Conejeros V, Pérez K, Jeldres RI, Castillo J, Hernández P, Toro N. Novel treatment for mixed copper ores: Leaching ammonia – Precipitation – Flotation (L.A.P.F.). Miner Eng. 2020;149:106242.

Sepúlveda FD, Cisternas LA, Gálvez ED. The use of global sensitivity analysis for improving processes: Applications to mineral processing. Comput Chem Eng. 2014;66:221-232.

Saltelli A, Tarantola S, Campolongo F, Ratto M. Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models (Google EBook).; 2004.

Liu S. Global Sensitivity Analysis: The Primer by Andrea Saltelli, Marco Ratto, Terry Andres, Francesca Campolongo, Jessica Cariboni, Debora Gatelli, Michaela Saisana, Stefano Tarantola. Vol 76.; 2008.

Salinas-Rodriguez E, Flores-Badillo J, Hernandez-Avila J, Cerecedo-Saenz E, Gutierrez-Amador M del P, Jeldres RI, Toro N. Assessment of silica recovery from metallurgical mining waste, by means of column flotation. Metals (Basel). 2020;10(1):1-12.

Schlesinger M, King M, Sole K, Davenport W. Extractive Metallurgy of Copper. Fifth Edit.; 2011.

Calisaya DA, López-Valdivieso A, de la Cruz MH, Gálvez EE, Cisternas LA. A strategy for the identification of optimal flotation circuits. Miner Eng. 2016;96-97:157-167.

Clift R, Grace JR, Weber ME. Bubbles, Drops and Particles. Mineola, NY, USA: Academic Press; 1985.

Karimi M, Akdogan G, Bradshaw SM. A computational fluid dynamics model for the flotation rate constant, Part I: Model development. Miner Eng. 2014;69:214-222.

Schubert H, Bischofberger C. On the hydrodynamics of flotation machines. Int J Miner Process. 1978;5(2):131-142.

Jones RL, Horsley RR. Viscosity modifiers in the mining industry. Miner Process Extr Metall Rev. 1999;20(1):215-223.

Hassanzadeh A, Azizi A, Kouachi S, Karimi M, Celik MS. Estimation of flotation rate constant and particle-bubble interactions considering key hydrodynamic parameters and their interrelations. Miner Eng. 2019;141:105836.

Mehrotra SP, Kapur PC. The effects of aeration rate, particle size and pulp density on the flotation rate distributions. Powder Technol. 1974;9(5-6):213-219.

Runge KC, Tabosa E, Crosbie R, Mcmaster JK. Eff ect of Flotation Feed Density on the Operation of a Flotation Cell. In: Eleventh Mill Operators’ Conference. Hobart, Tasmania; 2012:29-31.

Wills BA, Finch JA. Froth Flotation. In: Wills’ Mineral Processing Technology. Elsevier; 2016:265-380.

Vilinska A. Frothing Phenomena in Phosphate Gangue Flotation from Magnetite Fines with Fatty Acid based Collector and MIBC Frother. Open Miner Process J. 2013;6(1):1-12.

Grosan C, Abraham A. Intelligent Systems. Vol 17. First Ed. (Grosan C, Abraham A, eds.). Berlin, Heidelberg, Germany: Springer Berlin Heidelberg; 2011.

Alpaydin E. Introduction to Machine Learning. In: Introduction to Machine Learning. ; 2014:105-128.

Simeone O. A Very Brief Introduction to Machine Learning with Applications to Communication Systems. IEEE Trans Cogn Commun Netw. 2018;4(4):648-664.

Harrington P. Machine Learning in Action. Vol 37.; 2012.

Schmidhuber J. Deep Learning in neural networks: An overview. Neural Networks. 2015;61:85-117.

Alom MZ, Taha TM, Yakopcic C, Westberg S, Sidike P, Nasrin MS, Hasan M, Van Essen BC, Awwal AAS, Asari VK. A state-of-the-art survey on deep learning theory and architectures. Electron. 2019;8(3).

Shrestha A, Mahmood A. Review of deep learning algorithms and architectures. IEEE Access. 2019;7:53040-53065.

Hawkin S. Neural Networks and Learning Machines. Third Edit.; 2008.

Wu Y chen, Feng J wen. Development and Application of Artificial Neural Network. Wirel Pers Commun. 2018;102(2):1645-1656.

Keras SIG. About Keras. Keras Spec Interes Gr. 2020.

Python Software Foundation. Python 3.7.0. 2019.

Monad H, Naud C, Makowski D. Uncertainty and Sensitivity Analysis for Crop Models.; 2006.

Devore J. Probability & Statistics for Engineering and the Sciences. 8th ed. (Julet M, ed.). Boston, MA, USA: Cengage Learning; 2010.

Montgomery DC, Runger GC. Applied Statistics and Probalisty for Engineers.; 2014.

Toro N, Saldaña M, Gálvez E, Cánovas M, Trigueros E, Castillo J, Hernández PC. Optimization of Parameters for the Dissolution of Mn from Manganese Nodules with the Use of Tailings in An Acid Medium. Minerals. 2019;9(7):387.

Saldaña M, Toro N, Castillo J, Hernández P, Navarra A. Optimization of the Heap Leaching Process through Changes in Modes of Operation and Discrete Event Simulation. Minerals. 2019;9(7):421.

Meagher C, Dimitrakopoulos R, Avis D. Optimized open pit mine design, pushbacks and the gap problem—a review. J Min Sci. 2014;50(3):508-526.

Macfarlane AS, Williams TP. Optimizing value on a copper mine by adopting a geometallurgical solution. J South African Inst Min Metall. 2014;114(11):929-936.

Seguel F, Soto I, Krommenacker N, Maldonado M, Becerra Yoma N. Optimizing flotation bank performance through froth depth profiling: Revisited. Miner Eng. 2015;77:179-184.

Massinaei M, Falaghi H, Izadi H. Optimisation of metallurgical performance of industrial flotation column using neural network and gravitational search algorithm. Can Metall Q. 2013;52(2):115-122.

Saldaña M, Gálvez E, Jeldres RI, Díaz C, Robles P, Sinha MK, Toro N. Optimization of Cu and Mn Dissolution from Black Coppers by Means of an Agglomerate and Curing Pretreatment. Metals (Basel). 2020;10(5):657.

Saldaña M, González J, Jeldres R, Villegas Á, Castillo J, Quezada G, Toro N. A Stochastic Model Approach for Copper Heap Leaching through Bayesian Networks. Metals (Basel). 2019;9(11):1198.

Saldaña M, González J, Pérez-Rey I, Jeldres M, Toro N. Applying Statistical Analysis and Machine Learning for Modeling the UCS from P-Wave Velocity, Density and Porosity on Dry Travertine. Appl Sci. 2020;10(13):4565.

McCoy JT, Auret L. Machine learning applications in minerals processing: A review. Miner Eng. 2019;132:95-109.

Most read articles by the same author(s)