Hybrid modeling of an industrial grinding-classification process

• Phenomenological model combined with statistical learning is proposed for grinding-classification of bauxite.
• A nonlinear breakage rate function is proposed.
• Operating conditions, ball characteristic and ore properties are considered in the models.
• The models are simple to use yet effective, as is shown by the validation and application results.

An industrial grinding-classification process of diasporic bauxite is modeled based on the integration of phenomenological and statistical learning methods. The breakage characteristics of the ore and running status of the whole process are first investigated by laboratory testing and process sampling, respectively. Based on the population balance model (PBM) framework, the breakage distribution function is estimated from laboratory test data. The breakage rates are back-calculated directly from the industrial data, where a nonlinear breakage rate function is proposed for coarse particles. They are then correlated to the operating variables (including the water flow rate and feed flow rate), ball characteristics and material properties using the least squares support vector machine (LSSVM) method so that the model is suitable to various grinding conditions. Material transportation through the mill was treated as two equal smaller fully mixed reactors followed by a large one. The particle size distribution (PSD) of the mill product is then predicted by sequentially solving the reactors in series, considering the nonlinear breakage kinetics. A spiral classifier model is obtained with the Rosin–Rammer curve, where the bypass, real classification effect and operating conditions are included. The simulation results of the whole process by using the sequential module approach (SMA) demonstrate reasonable agreement between the predicted and measured industrial process data. The models are finally applied to the process for the prediction of particle size indices and to provide valuable information for the operation and further optimization of the process.

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