A self-adaptive particle-tracking method for minerals processing

Abstract Modern analytical techniques used in the minerals processing industry can provide detailed characterization data at the particle level. However, process models that make full use of this information are currently not available, limiting the usefulness of these extensive datasets. This contribution addresses this issue. It presents a novel particle-based approach for process modelling capable of dealing with complete particle datasets and operating without human input. The method provides a probabilistic description for the behavior of individual particles in a given mineral separation unit, based on all measurable particle properties. It is applicable to any separation process that does not modify the physical dimensions of particles, i.e. it does not cover comminution. The method comprises a regularized logistic regression model with a probability adjustment step to accommodate geological variability. Even though this method supports any type of particle-level characterization data, its potential is illustrated here using data obtained by scanning electron microscope-based image analysis. Constructed cases demonstrate the efficiency of the method in recreating characteristic recovery trends for magnetic separation, hydrocyclone, and flotation units. In addition, the method was used successfully to reconstruct a real processing plant with three flotation and one magnetic separation circuits. Predicted results of compositions for all the intermediate and product streams correspond well with the results reported from the plant itself. The predicted masses of the products are much affected by the quality of sampling and still require improvement. The case study illustrates that the method proposed here provides a powerful tool to understand and optimize mineral separation processes – and thus increase the resource and energy efficiency of mining operations.

[1]  Jan D. Miller,et al.  Liberation-limited grade/recovery curves from X-ray micro CT analysis of feed material for the evaluation of separation efficiency , 2009 .

[2]  B. A. Wills,et al.  Mineral Processing Technology: An Introduction to the Practical Aspects of Ore Treatment and Mineral Recovery , 1988 .

[3]  Daniel Hodouin,et al.  Automatic Control in Mineral Processing Plants: an Overview. , 2009 .

[4]  Leo Breiman,et al.  Random Forests , 2001, Machine Learning.

[5]  M. Hekkert,et al.  Conceptualizing the Circular Economy: An Analysis of 114 Definitions , 2017 .

[6]  Pertti Lamberg,et al.  A TECHNIQUE FOR TRACKING MULTIPHASE MINERAL PARTICLES IN FLOTATION CIRCUITS , 2007 .

[7]  R. Ketcham,et al.  Acquisition, optimization and interpretation of X-ray computed tomographic imagery: applications to the geosciences , 2001 .

[8]  T. Oki,et al.  Experimental analysis of mineral liberation and stereological bias based on X-ray computed tomography and artificial binary particles , 2017 .

[9]  Tianqi Chen,et al.  XGBoost: A Scalable Tree Boosting System , 2016, KDD.

[10]  Robert Zimmermann,et al.  Recovery potential of flotation tailings assessed by spatial modelling of automated mineralogy data , 2017 .

[11]  J. Gaddum,et al.  Lognormal Distributions , 1945, Nature.

[12]  Marco Saerens,et al.  Adjusting the Outputs of a Classifier to New a Priori Probabilities: A Simple Procedure , 2002, Neural Computation.

[13]  Markus A. Reuter,et al.  Property-based modelling and simulation of mechanical separation processes using dynamic binning and neural networks , 2018 .

[14]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[15]  E. Cárdenas Particle tracking in geometallurgical testing for Leveäniemi Iron ore, Sweden , 2017 .

[16]  Hadley Wickham,et al.  ggplot2 - Elegant Graphics for Data Analysis (2nd Edition) , 2017 .

[17]  Markus A. Reuter,et al.  Statistical entropy analysis as tool for circular economy: Proof of concept by optimizing a lithium-ion battery waste sieving system , 2019, Journal of Cleaner Production.

[18]  Mark Cross,et al.  Modeling and Simulation of Mineral Processing Systems , 2003 .

[19]  Lorenzo Bruzzone,et al.  An Automatic Method for Subglacial Lake Detection in Ice Sheet Radar Sounder Data , 2019, IEEE Transactions on Geoscience and Remote Sensing.

[20]  W. Petruk,et al.  Applied Mineralogy in the Mining Industry , 2000 .

[21]  R. Tolosana-Delgado,et al.  Monitoring gravitational and particle shape settling effects on MLA sampling preparation , 2015 .

[22]  K. Gerald van den Boogaart,et al.  Analyzing Compositional Data with R , 2013 .

[23]  Daniel S. Wilks,et al.  Extending logistic regression to provide full‐probability‐distribution MOS forecasts , 2009 .

[24]  A Ralph Henderson,et al.  The bootstrap: a technique for data-driven statistics. Using computer-intensive analyses to explore experimental data. , 2005, Clinica chimica acta; international journal of clinical chemistry.

[25]  K. G. Boogaart,et al.  Multidimensional characterization of separation processes – Part 1: Introducing kernel methods and entropy in the context of mineral processing using SEM-based image analysis , 2019, Minerals Engineering.

[26]  Antonio J. Plaza,et al.  Spectral–Spatial Classification of Hyperspectral Data Using Local and Global Probabilities for Mixed Pixel Characterization , 2014, IEEE Transactions on Geoscience and Remote Sensing.

[27]  J. A. Brod,et al.  THE KAMAFUGITE-CARBONATITE ASSOCIATION IN THE ALTO PARANAÍBA IGNEOUS PROVINCE (APIP) SOUTHEASTERN BRAZIL , 2000 .

[28]  Délzio De Lima Machado Júnior,et al.  Geologia e aspectos metalogeneticos do complexo alcalino-carbonatitico de Catalão II (GO) , 1991 .

[29]  Norman O. Lotter,et al.  Modern Process Mineralogy: An integrated multi-disciplined approach to flowsheeting , 2011 .

[30]  R. D. Pascoe,et al.  QEMSCAN analysis as a tool for improved understanding of gravity separator performance , 2007 .

[31]  D. Sandmann Method development in automated mineralogy , 2015 .

[32]  G. Keppel,et al.  Design and Analysis: A Researcher's Handbook , 1976 .

[33]  Trevor Hastie,et al.  Statistical Learning with Sparsity: The Lasso and Generalizations , 2015 .

[34]  S. Birtel,et al.  Constraining the Economic Potential of By-Product Recovery by Using a Geometallurgical Approach: The Example of Rare Earth Element Recovery at Catalão I, Brazil , 2019 .

[35]  Lidia Auret,et al.  Machine learning applications in minerals processing: A review , 2019, Minerals Engineering.

[36]  D. Cox The Regression Analysis of Binary Sequences , 1958 .

[37]  A. Welsh,et al.  Generalized additive modelling and zero inflated count data , 2002 .

[38]  Timothy A. Warner,et al.  Implementation of machine-learning classification in remote sensing: an applied review , 2018 .

[39]  J. Gutzmer,et al.  Volume quantification in interphase voxels of ore minerals using 3D imaging , 2019 .

[40]  Brian D. Ripley,et al.  Pattern Recognition and Neural Networks , 1996 .

[41]  Rolf Fandrich,et al.  Modern SEM based mineral liberation analysis , 2007 .

[42]  M. Vasconcelos,et al.  Spatial Prediction of Fire Ignition Probabilities: Comparing Logistic Regression and Neural Networks , 2001 .

[43]  Trevor Hastie,et al.  Regularization Paths for Generalized Linear Models via Coordinate Descent. , 2010, Journal of statistical software.

[44]  An appraisal of partition curves for coal-cleaning processes , 1986 .

[45]  M. Frenzel,et al.  The geometallurgical assessment of by-products—geochemical proxies for the complex mineralogical deportment of indium at Neves-Corvo, Portugal , 2018, Mineralium Deposita.

[46]  E. Olson,et al.  Particle Shape Factors and Their Use in Image Analysis – Part 1 : Theory , 2013 .