基于WOA-XGBoost模型的胶结充填体强度预测

袁丛祥; 刘志祥; 杨小聪; 郭金峰; 万串串; 熊帅; 刘伟军

doi:10.11858/gywlxb.20230668

基于WOA-XGBoost模型的胶结充填体强度预测

doi: 10.11858/gywlxb.20230668

袁丛祥^1,,
刘志祥^1,*, ,,
杨小聪^{2, 3},
郭金峰⁴,
万串串^{2, 3},
熊帅¹,
刘伟军¹

1.
中南大学资源与安全工程学院, 湖南长沙　410083
2.
矿冶科技集团有限公司, 北京　102628
3.
国家金属矿绿色开采国际联合研究中心, 北京　102628
4.
中钢集团马鞍山矿山研究总院股份有限公司, 安徽马鞍山　243000

基金项目: 国家重点研发计划项目（2022YFC2904101）；国家自然科学基金（52374107，51974359）

详细信息

作者简介:
袁丛祥（1999－），男，硕士研究生，主要从事充填体与岩石力学研究. E-mail：225511036@csu.edu.cn

通讯作者:
刘志祥（1967－），男，博士，教授，主要从事采矿工程与岩石力学研究. E-mail：liulzx@csu.edu.cn

中图分类号: O346; TD853
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出版历程
- 收稿日期: 2023-05-22
- 修回日期: 2023-06-12
- 录用日期: 2023-07-14
- 网络出版日期: 2023-09-28
- 刊出日期: 2023-11-07

Strength Prediction of Cemented Paste Backfill Body Based on WOA-XGBoost Model

1.
School of Resources and Safety Engineering, Central South University, Changsha 410083, Hunan, China
2.
BGRIMM Technology Group, Beijing 102628, China
3.
National Center for International Joint Research on Green Mental Mining, Beijing 102628, China
4.
Sinosteel Maanshan General Institute of Mining Research Co. Ltd., Maanshan 243000, Anhui, China

摘要

摘要: 单轴抗压强度作为胶结充填体重要的力学性能指标，通常使用传统的力学试验来确定。使用鲸鱼优化算法（whale optimization algorithm，WOA）对极限梯度提升模型（XGBoost）进行优化，建立了WOA-XGBoost混合模型。以某铅锌矿充填料浆配比试验得到的80组数据作为数据库，选取固体质量分数、水泥占比、尾砂占比及养护天数作为输入参数，充填体试块抗压强度作为输出参数。为了与WOA-XGBoost模型进行比较，还构建了XGBoost、RF和WOA-RF模型。结果表明：WOA-XGBoost模型的决定系数为0.965 0，均方根误差为0.207 4，平均绝对误差为0.170 3；XGBoost模型的决定系数、均方根误差、平均绝对误差分别为0.897 1、0.408 4和0.246 7。可见，鲸鱼优化算法能够显著提高XGBoost模型的预测能力。相比XGBoost、RF和WOA-RF模型，WOA-XGBoost混合模型具有更高的预测精度。研究结果对于胶结充填材料的设计和配比优化具有重要意义。
- 胶结充填材料 /
- 单轴抗压强度 /
- 预测 /
- 极限梯度提升模型 /
- 鲸鱼优化算法
Abstract: The uniaxial compressive strength of cemented paste backfill (CPB), as an important indicator of their mechanical properties, is usually determined by traditional mechanical tests. In the proposed model, the whale optimization algorithm (WOA) with global optimization capacity was used to tune the hyperparameters of the extreme gradient boosting (XGBoost) model. Taking the 80 sets of data obtained from the filling slurry ratio test of a lead-zinc mine as the database, the solid mass fraction, cement content, tailings content as well as curing age, were selected as input variables and the uniaxial compressive strength of the filling body as an output variable. XGBoost, random forest (RF) and WOA-RF models were constructed to compare with the WOA-XGBoost model. The results indicates that the hybrid WOA-XGBoost model (Its determination coefficient is 0.965 0, the root mean square error is 0.207 4, and the mean absolute error is 0.170 3) performs rather better than the individual XGBoost model (Its determination coefficient is 0.897 1, the root mean square error is 0.408 4, and the mean absolute error is 0.246 7). Compared with other models, the WOA-XGBoost model exhibits the highest prediction accuracy, contributing to the design and ratio optimization of cemented paste backfill materials.
- cemented paste backfill /
- uniaxial compressive strength /
- prediction /
- extreme gradient boosting model /
- whale optimization algorithm

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图 1 尾砂粒级组成曲线

Figure 1. Particle size distribution curve of the tailings

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图 2 试块测试过程示意图

Figure 2. Schematic diagram of the test process

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图 3 WOA优化XGBoost模型流程

Figure 3. XGBoost optimization process with WOA

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图 4 WOA-XGBoost预测模型不同种群大小的适应度变化曲线

Figure 4. Fitness value versus iteration curves of the WOA-XGBoost model with different population sizes

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图 5 模型训练集和测试集的预测值与实测值的对比

Figure 5. Comparison of the predicted and actual values of the WOA-XGBoost model

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图 6 模型的性能评价参数的对比

Figure 6. Comparison of performance metrics with mentioned models

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图 7 模型的单轴抗压强度预测能力对比

Figure 7. Comparison of the compressive strength predictive ability of the developed methods

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图 8 各输入参数的重要性得分

Figure 8. Importance scores of the input parameters

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表 1 分级尾砂的物理性质和粒径分布

Table 1. Physical property and particle size distribution of classified tailings

Physical property				Particle size distribution/μm
Loose bulk density/(g·cm⁻³)	Loose porosity/%	Density/(g·cm⁻³)	Specific gravity	D₁₀	D₅₀	D₆₀	D₉₀
1.81	46.99	3.36	3.42	2.210	38.237	56.355	163.321

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表 2 尾砂化学成分（阳离子）

Table 2. Chemical components of the tailings (cations) %

Mg	Al	K	Ca	Fe	Mn	Ti	Cu	Zn	Pb	Rest
1.230	2.680	0.430	16.700	12.600	0.770	0.120	0.020	0.150	0.010	<0.003

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表 3 尾砂胶结充填体强度测试结果

Table 3. Test results for unconfined compressive strength of cemented paste backfill

Group	Mass fraction of solid/%	Cement proportion	Tailings proportion	σ_c/MPa
Group	Mass fraction of solid/%	Cement proportion	Tailings proportion	7 d	14 d	28 d	60 d	90 d
A₁	72	0.20	0.80	1.84	2.88	3.00	4.44	4.67
A₂	72	0.11	0.89	0.85	1.35	2.06	2.15	2.23
A₃	72	0.09	0.91	0.78	1.07	1.15	1.20	1.50
A₄	72	0.08	0.92	0.55	0.91	1.01	1.08	1.13
B₁	70	0.20	0.80	1.61	2.58	2.76	4.23	4.48
B₂	70	0.11	0.89	0.71	1.15	1.28	1.34	1.52
B₃	70	0.09	0.91	0.62	1.05	1.12	1.17	1.25
B₄	70	0.08	0.92	0.43	0.70	0.75	0.78	0.94
C₁	68	0.20	0.80	1.34	2.52	2.65	2.66	3.00
C₂	68	0.11	0.89	0.56	0.90	0.99	1.06	1.20
C₃	68	0.09	0.91	0.48	0.66	0.73	0.85	1.06
C₄	68	0.08	0.92	0.33	0.55	0.70	0.74	0.92
D₁	65	0.20	0.80	0.79	1.27	1.31	2.16	2.58
D₂	65	0.11	0.89	0.37	0.60	0.83	0.86	0.91
D₃	65	0.09	0.91	0.30	0.53	0.58	0.65	0.71
D₄	65	0.08	0.92	0.27	0.44	0.49	0.62	0.68

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表 4 WOA-XGBoost预测模型的性能参数

Table 4. Performance metrics of the proposed WOA-XGBoost model

Swarm size	Training set			Test set
Swarm size	R²	δ_RMSE	δ_MAE	R²	δ_RMSE	δ_MAE
25	0.999 7	0.016 8	0.012 4	0.931 0	0.283 4	0.192 6
50	0.999 6	0.020 9	0.016 4	0.926 7	0.269 0	0.190 1
75	0.999 5	0.021 1	0.016 4	0.917 9	0.344 0	0.355 4
100	0.999 7	0.016 1	0.013 3	0.964 2	0.214 3	0.183 8
125	0.999 8	0.014 3	0.010 9	0.965 0	0.207 4	0.170 3
150	0.999 7	0.018 4	0.014 8	0.917 1	0.147 0	0.123 2

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