深部高应力区岩爆烈度等级预测模型及应用

祁云; 白晨浩; 段宏飞; 代连朋; 李绪萍; 汪伟

doi:10.11858/gywlxb.20251103

深部高应力区岩爆烈度等级预测模型及应用

doi: 10.11858/gywlxb.20251103

祁云^{1, 2, 3,},
白晨浩^2,*, ,,
段宏飞⁴,
代连朋⁵,
李绪萍¹,
汪伟^{1, 2}

1.
内蒙古科技大学矿业与煤炭学院, 内蒙古包头　014010
2.
山西大同大学煤炭工程学院, 山西大同　037000
3.
中国职业安全健康协会《中国安全科学学报》编辑部, 北京　100011
4.
中山大学土木工程学院, 广东珠海　410012
5.
辽宁大学灾害岩体力学研究所, 辽宁沈阳　110036

基金项目: 国家自然科学基金（52174188，52464020）；内蒙古自然科学基金（2024LHMS05012）；山西省研究生实践创新项目（2024SJ378）；山西大同大学研究生实践创新项目（2024SJCX05）

详细信息

作者简介:
祁　云（1988－），男，博士，副教授，主要从事深部矿山动力灾害防治及应急技术研究. E-mail：qiyun_sx@163.com

通讯作者:
白晨浩（2001－），男，硕士研究生，主要从事深部矿山动力灾害防治及预警技术研究. E-mail：15248405464@163.com

中图分类号: X936; O521.9; O382
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出版历程
- 收稿日期: 2025-06-03
- 修回日期: 2025-08-08
- 网络出版日期: 2025-08-09

Prediction Model and Application of Rock Burst Tendency in Deep High Stress Areas

QI Yun^{1, 2, 3
,},
BAI Chenhao^{2,*
, ,},
DUAN Hongfei⁴,
DAI Lianpeng⁵,
LI Xuping¹,
WANG Wei^{1, 2}

1.
School of Mining and Coal, Inner Mongolia University of Science and Technology, Baotou 014010, Inner Mongolia, China
2.
College of Coal Engineering, Shanxi Datong University, Datong 037000, Shanxi, China
3.
Editorial Office of China Safety Science Journal, China Occupational Safety and Health Association, Beijing 100011, China
4.
School of Civil Engineering, Sun Yat-Sen University, Zhuhai 410012, Guangdong, China
5.
Institute of Disaster Rock Mechanics, Liaoning University, Shenyang 110036, Liaoning, China

摘要

摘要: 为确保深部高应力区岩土工程的施工安全，提升岩爆烈度等级预测的精准度，针对岩爆的突发性和复杂性，提出了一种基于鲸鱼优化算法（whale optimization algorithm，WOA）与极端梯度提升树（extreme gradient boosting，XGBoost）的组合岩爆烈度等级预测模型。首先，分析了影响岩爆烈度等级的主控因素，选取单轴抗压强度、最大切向应力、单轴抗拉强度、脆性系数、应力系数和弹性能量指数建立岩爆烈度等级预测指标体系，引入Pearson相关系数、链式方程多重插补法、合成少数类过采样技术（synthetic minority oversampling technique，SMOTE）和主成分分析法处理原始样本。其次，通过WOA优化XGBoost模型的最大迭代次数、树的最大深度和学习率，并采用准确率、精准度、召回率、F1分数和科恩卡帕系数综合评价所建模型的预测结果。最后，将该模型应用于秦岭终南山公路隧道和江边水电站引水系统预测岩爆烈度等级。结果表明：经WOA优化后XGBoost模型的最大迭代次数、树的最大深度和学习率分别为51、13和0.7325时效果最佳；基于WOA-XGBoost岩爆烈度等级预测模型得到的结果与实际等级的拟合度优于传统智能算法模型；通过将WOA-XGBoost模型应用于工程实践中，验证了该模型预测岩爆烈度等级具有较高的准确度和可靠性。
- 岩爆 /
- 鲸鱼优化算法（WOA） /
- 极端梯度提升树（XGBoost） /
- 链式方程多重插补法（MICE） /
- 合成少数类过采样技术（SMOTE）
Abstract: To ensure the construction safety of geotechnical engineering in deep high stress areas, a combined rock burst intensity prediction model based on whale optimization algorithm (WOA) and extreme gradient boosting (XGBoost) is proposed to address the suddenness and complexity of rock burst. Firstly, the main controlling factors that affect the intensity level of rock burst are analyzed, and the uniaxial compressive strength, maximum tangential stress, uniaxial tensile strength, brittleness coefficient, stress coefficient, and elastic energy index are selected to establish a prediction index system for rock burst intensity level. The original samples are processed using the Pearson correlation coefficient, multiple imputation by chained equations (MICE), synthetic minority oversampling technique (SMOTE), and principal component analysis (PCA). Secondly, the maximum number of iterations, maximum depth of the tree, and learning rate of the XGBoost model were optimized through WOA, and the prediction results of the model were comprehensively evaluated using accuracy, precision, recall, F1 score, and Cohen Kappa coefficient. Finally, the model was applied to predict the rock burst intensity level of the Qinlingzhongnanshan highway tunnel and the water diversion system for hydropower stations. Results show that the WOA-optimized XGBoost model achieves optimal performance when the maximum number of iterations, maximum tree depth, and learning rate are 51, 13, and 0.7325, respectively. Prediction results for rock burst intensity level using the WOA-XGBoost model outperform those of other intelligent algorithm models, verifying the model’s high accuracy and reliability in predicting rock burst intensity level.
- rock burst /
- whale optimization algorithm (WOA) /
- extreme gradient boosting (XGBoost) /
- multiple imputation by chained equations (MICE) /
- synthetic minority oversampling technique (SMOTE)

HTML全文

图 1 SMOTE算法原理

Figure 1. SMOTE principle

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图 2 XGBoost算法流程

Figure 2. XGBoost algorithm flow

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图 3 各变量分布情况

Figure 3. Distribution of variables

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图 4 6个评价指标间的相关性

Figure 4. Correlation among the 6 evaluation indicators

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图 5 原始样本异常值分布

Figure 5. Distribution of outliers in the original sample

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图 6 原始数据与插补数据的对比

Figure 6. Comparison between original data and imputed data

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图 7 异常值处理后样本与平衡后样本对比

Figure 7. Comparison between samples after outlier processing and balanced samples

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图 8 平衡后样本分布

Figure 8. Sample distribution after equilibrium

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图 9 方差累计贡献率

Figure 9. Cumulative contribution rate of variances

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图 10 PCA处理后样本的分布情况

Figure 10. Distribution of samples after PCA treatment

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图 11 WOA-XGBoost预测模型流程

Figure 11. Flow of WOA-XGBoost prediction model

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图 12 3种优化算法的适应度迭代曲线

Figure 12. Fitness iteration curves for 3 optimization algorithms

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图 13 各预测模型的评价指标对比

Figure 13. Comparison of evaluation indicators of each prediction model

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图 14 各模型的ROC曲线

Figure 14. ROC curves of each model

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图 15 各模型预测结果

Figure 15. Prediction results of each model

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图 16 各模型岩爆混淆矩阵结果

Figure 16. Results of rock burst confusion matrix for each model

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表 1 岩爆烈度等级分类标准

Table 1. Criteria for classification of rock burst intensity levels

Rock burst level	σ_c/MPa	σ_θ/MPa	σ_t/MPa	σ_c/σ_t	σ_θ/σ_c	W_et
No rock burst (Ⅰ)	<80	<24	<5	>40.0	<0.3	<2.0
Minor rock burst (Ⅱ)	80−120	24−60	5−7	26.7−40.0	0.3−0.5	2.0−4.0
Moderate rock burst (Ⅲ)	120−180	60−126	7−9	14.5−26.7	0.5−0.7	4.0−6.0
Strong rock burst (Ⅳ)	>180	126−200	9−30	<14.5	>0.7	>6.0

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表 2 国内外部分岩爆工程案例数据^[19–22]

Table 2. Partial domestic and international rock burst engineering case data set^[19–22]

Serial No.	σ_θ/MPa	σ_c/MPa	σ_t/MPa	σ_c/σ_t	σ_θ/σ_c	W_et	Rock burst level
1	22.40	91.20	5.99	15.23	0.25	2.60	Ⅰ
2	12.60	41.70	3.15	13.24	0.30	1.70	Ⅰ
…	…	…	…	…	…	…	…
105	110.35	167.19	87.53	1.91	0.66	6.83	Ⅳ
106	26.06	118.46	19.61	6.04	0.22	2.89	Ⅱ

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表 3 变量的基本信息

Table 3. Basic information of variables

Statistic	σ_θ/MPa	σ_c/MPa	σ_t/MPa	σ_θ/σ_c	σ_c/σ_t	W_et
Average	60.20	141.75	13.76	0.43	17.74	5.11
Standard deviation	31.97	55.12	15.55	0.23	13.22	2.05
Minimum value	7.50	29.45	1.50	0.05	1.91	0.70
Maximum value	132.60	306.58	87.53	1.40	80.00	10.57
25% percentile (Q₁)	34.24	115.45	5.20	0.29	9.79	3.80
50% percentile (Q₂)	57.92	140.00	8.30	0.40	14.90	5.00
75% percentile (Q₃)	89.53	169.52	13.73	0.54	21.75	6.50
Median	57.92	140.00	8.30	0.40	14.90	5.00
Mode	105.00	115.00	8.30	0.38	17.50	5.00

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表 4 部分标准化数据

Table 4. Partial standardized data

Serial No.	σ_θ/MPa	σ_c/MPa	σ_t/MPa	σ_c/σ_t	σ_θ/σ_c	W_et	Rock burst level
1	0.12	0.22	0.05	0.15	0.17	0.19	Ⅰ
2	0.04	0.04	0.02	0.19	0.15	0.10	Ⅰ
…	…	…	…	…	…	…	…
105	0.82	0.50	1.00	0.45	0	0.62	Ⅳ
106	0.15	0.32	0.21	0.13	0.05	0.22	Ⅱ

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表 5 各指标缺失情况及剩余样本量

Table 5. Missing conditions of each indicator and remaining sample size

Statistic	Missing quantity	Remaining sample size
σ_θ	0	106
σ_c	10	96
σ_t	11	95
σ_θ/σ_c	3	103
σ_c/σ_t	4	102
W_et	1	105

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表 6 特征提取后部分样本数据

Table 6. Partial sample data after feature extraction

Serial No.	σ_θ	σ_c	σ_t	Rock burst level
1	−1.12	−0.57	−0.17	Ⅰ
2	−1.51	−1.40	−0.44	Ⅰ
3	0.24	1.69	0.22	Ⅲ
…	…	…	…	…
167	1.46	2.46	−0.73	Ⅳ
168	2.12	−0.96	−1.72	Ⅳ

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表 7 XGBoost超参数的初始值和预定的搜索范围

Table 7. Initial values of XGBoost hyperparameters and predetermined search scope

Parameter	Parameter meaning	Range	Initial value
Num_iters	Maximum number of iterations	[10, 100]	30
Max_depth	Maximum depth of tree	[1, 18]	6
Eta	Learning rate	[0, 1]	0.3

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表 8 模型各等级预测情况

Table 8. Prediction of each level of the model

Rock burst level	Actual quantity	Predicted quantity
Rock burst level	Actual quantity	WOA-XGBoost	DBO-XGBoost	SSA-XGBoost	RF	BPNN	SVM
Ⅰ	8	7	7	6	6	6	5
Ⅱ	8	7	7	7	7	6	7
Ⅲ	8	8	6	7	6	7	7
Ⅳ	8	8	8	7	7	6	6
Total	32	30	28	27	26	25	25

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表 9 原始及特征提取后岩爆工程实例样本

Table 9. Sample examples of rock burst engineering after original and feature extraction

Engineering name	Serial No.	σ_θ/MPa	σ_c/MPa	σ_t/MPa	σ_c/σ_t	σ_θ/σ_c	W_et	F₁	F₂	Rock burst level
Qinlingzhongnanshan highway tunnel	1	43.1	122.0	5.38	22.68	0.35	3.31	−0.83	−0.25	Ⅱ
	2	62.8	120.0	6.45	18.60	0.52	4.16	0.38	0.40	Ⅲ
	3	54.2	134.0	9.09	14.74	0.4	7.08	1.35	−0.70	Ⅲ
	4	79.1	124.0	8.64	14.35	0.64	7.74	2.20	0.75	Ⅳ
	5	70.3	128.5	8.73	14.72	0.55	6.43	1.70	0.08	Ⅲ
	6	56.1	132.0	9.44	13.98	0.43	7.44	1.57	−0.52	Ⅲ
	7	56.2	119.0	7.21	16.50	0.47	5.52	0.59	0.29	Ⅲ
	8	87.5	121.0	8.73	13.86	0.72	9.05	2.73	1.29	Ⅳ
Water diversion system for hydropower stations	9	19.4	106.3	2.76	38.52	0.18	2.03	−3.35	0.25	Ⅰ
	10	9.7	88.5	2.16	40.97	0.11	1.77	−4.28	0.96	Ⅰ
	11	34.9	151.7	7.47	20.31	0.23	3.17	−0.23	−2.37	Ⅱ
	12	33.9	117.5	4.23	27.77	0.29	2.37	−1.81	−0.17	Ⅱ

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