Robust HPGR model calibration using genetic algorithms V. Hasanzadeh a , A. Farzanegan b,⇑ a School of Mining, University College of Engineering, University of Tehran, P.O. Box 11155-4563, Tehran, Iran b Department of Mining, Faculty of Engineering, University of Kashan, Kashan, Iran article info Article history: Received 19 July 2010 Accepted 8 December 2010 Available online 7 January 2011 Keywords: Comminution High pressure grinding rolls Modeling and simulation Genetic algorithms abstract Mathematical modeling and simulation techniques are widely used to design and optimize comminution circuits in mineral processing plants. However, circuit performance predictions are prone to errors due to inaccurate calibration of models used in simulations. To address this problem, the authors applied a method based on genetic algorithms (GA) for estimation of HPGR (high pressure grinding rolls) model parameters. In this research, a simulation algorithm was developed and implemented in MATLAB™ based on published HPGR models to test and demonstrate GA application for model calibration. The GA toolbox of MATLAB was used to obtain the optimal values of HPGR model parameters. The authors successfully validated simulator predictions against HPGR data sets at laboratory and industrial scales. The results indicate that GA is a robust and powerful search method to find the best values of HPGR model param- eters that lead to more reliable simulation predictions. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction Comminution circuits have the highest level of energy con- sumption in mineral processing plants. Therefore, improving de- sign and operation of comminution devices to optimize performance and energy consumption are always an important part of manufacturers and process engineers’ researches. HPGR is the result of basic changes in roller crushers due to Schönert (1986). Subsequently, the comminution mechanism was changed in the new crusher due to its high pressures (Schönert, 1979, 1986). The high throughput of HPGR units and their low specific energy consumption made them increasingly suitable for use in comminution circuits. With respect to modeling of high pressure grinding rolls, the most considerable works were done by Morrell and co-workers (Morrell et al., 1997; Daniel and Morrell, 2004). Recently, Torres and Casali (2009), following the work done by Morrell and Daniel, developed a new method for modeling of HPGR. In the model pre- sented by Daniel and Morrell, outputs of drop-weight apparatus are used for ore characterization and their model is fitted to labo- ratory data through limiting the number of model parameters. In next step, the obtained model parameters are kept constant and used in a scale-up procedure to predict the performance of full- scale units. But in Torres and Casali new method, established func- tional expressions of breakage and selection functions are used for this purpose and also there is no scale-up procedure involved. In HPGR units, comminution mechanism basically differs from that of media mills due to the high pressure applied on particles. For this reason, the breakage and selection functions obtained using media mills such as a ball mill or a rod mill and other devices can- not be used for simulation of HPGR units. As a solution, these parameters can be estimated simultaneously by fitting the mea- sured data with corresponding models. Considering a normalizable breakage function and only the first two terms of the logarithmic polynomial expression used to define selection function, there will be totally six parameters which must be back calculated from ac- tual HPGR data sets in order to determine breakage function and selection functions. A programming environment equipped with powerful search tools for function optimization is a prerequisite for model fitting purposes. In a previous paper, successful application of genetic algorithm search method to optimize comminution circuits was reported by Farzanegan and Vahidipour (2009). Therefore, MATLAB environment and also its genetic algorithms toolbox were selected for implementation of HPGR simulation model, optimal calibration of model parameters and finally prediction of HPGR product size distribution in an open circuit. 2. Description of HPGR model Authors programmed the HPGR mathematical model explained by Torres and Casali (2009) as the main part of simulator structure. This model includes a set of equations that is based on ore charac- teristics, equipment dimensions and operating conditions. Given the required input, the model is able to predict throughput, power consumption and particle size distribution of HPGR product. 0892-6875/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.mineng.2010.12.004 ⇑ Corresponding author. Tel.: +98 361 5912450; fax: +98 361 5559930. E-mail addresses: a.farzanegan@kashanu.ac.ir, a.farzanegan@gmail.com (A. Farzanegan). Minerals Engineering 24 (2011) 424–432 Contents lists available at ScienceDirect Minerals Engineering journal homepage: www.elsevier.com/locate/mineng