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摘要:
矿物浮选精矿品位是评估浮选效果的关键技术指标之一,其精确测定备受业内关注。然而,现有的辉钼矿浮选精矿品位在线检测方法检测精度不高且实施成本昂贵。为此,提出了一种基于粒子群优化随机森林算法(PSO−RF)的辉钼矿浮选精矿品位预测模型。该模型通过结合粒子群优化(PSO)算法与随机森林(RF)算法,有效提升了模型预测精度和泛化能力。首先通过辉钼矿浮选实验,分析了不同浮选药剂用量和磨矿细度对精矿品位的影响,并以此构建了多输入输出的随机森林预测模型;然后应用粒子群优化算法对随机森林模型进行参数优化,显著提升了模型的预测精度,在验证集上,RMSE值为
0.0369 ,MAE值为0.0245 ,R2值为0.9802 。相比随机森林模型(RF),PSO−RF模型R2提升了1.83%,RMSE值和MAE值分别降低了19.43%和16.95%。最后通过实验对PSO−RF模型进行了验证,预测值与实际值的最大相对误差在4.28%以内,表现出较高的预测精度和良好的泛化能力。同时,该模型还具备实时检测能力以及较低的实施成本,在工业生产中具有广阔的应用潜力。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) of0.0245 , 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.-
Key words:
- molybdenite /
- grade prediction /
- particle swarm optimization /
- random forest model
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表 1 实验数据集
Table 1. Dataset for the experiment
实验编号 X1/(g·t−1) X2/(g·t−1) X3/(g·t−1) X4/% 平均品位/% 1 80 30 0 65 1.18 2 100 30 0 65 1.22 3 120 30 0 65 1.28 4 140 30 0 65 1.66 …… …… …… …… …… …… 125 80 60 2000 60 1.49 126 100 60 2000 60 1.68 127 120 60 2000 60 1.79 128 140 60 2000 60 1.52 表 2 辉钼矿浮选精矿品位的方差分析
Table 2. Analysis of variance for the grade of molybdenite flotation concentrates
变异来源 平方和 自由度 均方 F值 P值 备注 模型 0.7238 13 0.0557 26.11 < 0.0001 显著 X1 0.0098 1 0.0098 4.58 0.0580 X2 0.0444 1 0.0444 20.82 0.0010 X3 0.0736 1 0.0736 34.51 0.0002 X4 0.2591 1 0.2591 121.47 < 0.0001 X1X2 0.0603 1 0.0603 28.27 0.0003 X1X3 0.0006 1 0.0006 0.2787 0.6091 X1X4 0.0030 1 0.0030 1.43 0.2594 X2X3 0.0947 1 0.0947 44.40 < 0.0001 X2X4 0.0542 1 0.0542 25.43 0.0005 X3X4 0.0751 1 0.0751 35.22 0.0001 X21 0.0274 1 0.0274 12.83 0.0050 X22 0.0533 1 0.0533 25.00 0.0005 X23 0.0246 1 0.0246 11.53 0.0068 失拟项 0.0124 5 0.0025 1.39 0.3628 不显著 残差 0.0089 5 0.0018 表 3 各模型在验证集上的预测效果
Table 3. Predictive performance of each model on the validation set
Model RMSE MAE R2 SVM 0.1785 0.1251 0.5298 LR 0.1763 0.1342 0.5793 KNN 0.1595 0.1187 0.6507 RF 0.0458 0.0295 0.9696 表 4 随机森林模型、PSO−RF模型在验证集上的预测性能指标统计
Table 4. Statistical performance metrics of the random forest model and PSO−RF model on the validation set
模型 RMSE MAE R2 优化时/s 最佳参数
组合 NMRRF 0.0458 0.0295 0.9626 − − − − PSO−RF 0.0369 0.0245 0.9802 21.34 58 38 32 -
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