Abstract:
Mineral flotation concentrate grade is one of the crucial technical indicators for evaluating flotation efficiency, and its measurement accuracy plays a significant guiding role in optimizing production processes, adjusting operations, and controlling product quality. For many years, the accurate real−time measurement of flotation concentrate grade has been a key research focus within the mining industry. However, current online detection methods for molybdenite flotation concentrate grades generally exhibit notable shortcomings, such as inadequate measurement accuracy, high equipment costs, and complex maintenance procedures, severely limiting their widespread implementation in industrial production. Therefore, developing an online detection method characterized by high accuracy, low implementation cost, and ease of industrial deployment has significant practical importance. To overcome these limitations, this study proposed a molybdenite flotation concentrate grade prediction model based on a Particle Swarm Optimization–Random Forest (PSO−RF) algorithm. The objective of this study was to address the accuracy and cost issues inherent to existing detection approaches and to provide a more economical and efficient predictive tool suitable for industrial practice. The proposed PSO−RF model effectively combined the global optimization capability of the particle swarm optimization (PSO) algorithm and the superior ability of random forest (RF) models in handling complex data, significantly enhancing the model’s predictive accuracy and generalization performance. Initially, flotation experiments involving molybdenite were conducted to systematically investigate the influence of critical flotation parameters, including reagent dosage and grinding fineness, on the concentrate grade. Based on the experimental data obtained from these trials, a multi−input and multi−output random forest prediction model was constructed. Subsequently, considering that the prediction performance of random forest models is sensitive to hyperparameter selection (specifically, n_estimators, max_depth, and random_state), the particle swarm optimization algorithm was employed to globally optimize these critical hyperparameters. This optimization approach effectively overcame the limitations of traditional manual hyperparameter tuning, substantially improving model prediction performance and stability. In the model validation stage, the optimized PSO−RF model currently exhibits excellent predictive performance. Specifically, on the validation dataset, the PSO−RF model achieves a root mean square error (RMSE) of
0.0369, mean absolute error (MAE) of
0.0245, and a coefficient of determination (
R²) of 0.980 2. Compared to the unoptimized random forest model, the proposed model improves the
R² value by 1.83%, reduces the RMSE by 19.43%, and decreases the MAE by 16.95%. Furthermore, additional experimental validation confirms that the maximum relative error between predicted and actual measured concentrate grades is consistently below 4.28%, demonstrating high prediction accuracy and strong generalization capability. In conclusion, the PSO−RF prediction model proposed in this study effectively addresses the existing deficiencies of conventional online detection methods. This model not only realizes accurate real−time prediction of flotation concentrate grades but also features lower implementation costs and ease of industrial application. Consequently, the proposed PSO−RF model demonstrates substantial potential for practical application and economic value in industrial molybdenite flotation processes.