基于粒子群优化随机森林算法的辉钼矿浮选精矿品位预测模型

宛鹤, 杨亮亮, 屈娟萍, 江鹏. 基于粒子群优化随机森林算法的辉钼矿浮选精矿品位预测模型[J]. 矿产保护与利用, 2025, 45(3): 76-86. doi: 10.13779/j.cnki.issn1001-0076.2025.08.026
引用本文: 宛鹤, 杨亮亮, 屈娟萍, 江鹏. 基于粒子群优化随机森林算法的辉钼矿浮选精矿品位预测模型[J]. 矿产保护与利用, 2025, 45(3): 76-86. doi: 10.13779/j.cnki.issn1001-0076.2025.08.026
WAN He, YANG Liangliang, QU Juanping, JIANG Peng. A PSO−RF−Based Prediction Model for Molybdenite Flotation Concentrate Grade[J]. Conservation and Utilization of Mineral Resources, 2025, 45(3): 76-86. doi: 10.13779/j.cnki.issn1001-0076.2025.08.026
Citation: WAN He, YANG Liangliang, QU Juanping, JIANG Peng. A PSO−RF−Based Prediction Model for Molybdenite Flotation Concentrate Grade[J]. Conservation and Utilization of Mineral Resources, 2025, 45(3): 76-86. doi: 10.13779/j.cnki.issn1001-0076.2025.08.026

基于粒子群优化随机森林算法的辉钼矿浮选精矿品位预测模型

  • 基金项目: 国家自然科学基金面上项目(52274271)
详细信息
    作者简介: 宛鹤(1982—),男,辽宁锦州人,博士,教授,博士生导师,主要从事资源综合利用、浮选药剂、选矿智能化等方面研究,E-mail:wanhe@xauat.edu.cn
    通讯作者: 宛鹤, wanhe@xauat.edu.cn
  • 中图分类号: TD954;TD923

A PSO−RF−Based Prediction Model for Molybdenite Flotation Concentrate Grade

More Information
  • 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0.0369MAE值为0.0245R2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。

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  • 图 1  浮选实验流程

    Figure 1. 

    图 2  随机森林算法

    Figure 2. 

    图 3  粒子群优化随机森林算法流程

    Figure 3. 

    图 4  辉钼矿浮选精矿品位响应面

    Figure 4. 

    图 5  模型诊断结果

    Figure 5. 

    图 6  随机森林模型预测效果

    Figure 6. 

    图 7  PSO−RF模型预测效果

    Figure 7. 

    图 8  PSO−RF模型验证效果

    Figure 8. 

    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/%
    180300651.18
    2100300651.22
    3120300651.28
    4140300651.66
    ………………………………
    12580602000601.49
    126100602000601.68
    127120602000601.79
    128140602000601.52
    下载: 导出CSV

    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 P 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
    下载: 导出CSV

    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
    下载: 导出CSV

    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 NMR
    RF 0.0458 0.0295 0.9626
    PSO−RF 0.0369 0.0245 0.9802 21.34 58 38 32
    下载: 导出CSV
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出版历程
收稿日期:  2025-01-13
刊出日期:  2025-06-15

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