Prediction for Rock Compressive Strength Based on Ensemble Learning and Bayesian Optimization
-
摘要: 岩石抗压强度是评估岩体工程稳定性的重要力学参数，传统统计回归方法对于岩石抗压强度预测存在一定的局限性.为此，提出了一种利用简单岩石力学参数实现岩石抗压强度智能预测的方法，首先收集了620组含不同类型岩石的三轴试验数据，然后分别采用随机森林(Random Forest，RF)、极限梯度提升树(XGBoost，XGB)和轻量梯度提升机(LightGBM，LGB)3种主流的集成学习算法建立了岩石抗压强度预测模型，使用贝叶斯优化算法在模型训练过程中进行超参数优化，最后利用决定系数(R2)、平均绝对百分比误差(MAPE)和均方根误差(RMSE)对优化后模型的泛化能力进行了综合评估和对比分析.此外，利用LGB模型对输入特征进行重要性分析，以评估不同输入特征对模型泛化性能的影响重要程度.研究结果表明：所建立的3种模型对岩石抗压强度均取得了较好的预测结果，其中LGB模型泛化性能优于另外两种模型(R2=0.978，RMSE=5.58，MAPE=9.70%)，且运行耗时相对最少.弹性模量(E)、围压(σ3)和密度(ρ)对模型的泛化性能影响较大，泊松比(v)影响较小.提出的预测模型对于岩石抗压强度预测有良好的适用性，为机器学习与岩土工程的结合提供了新的思路.Abstract: Rock compressive strength is an important mechanical parameter to evaluate the stability of rock mass engineering. The traditional statistical regression method has some limitations on the prediction of rock compressive strength. To this end, in this paper it proposes a method for intelligent prediction of rock compressive strength using simple rock mechanics parameters. Firstly, 620 sets of triaxial test data containing different types of rocks were collected and preprocessed. Then, three main stream ensemble learning algorithms, Random forest, XGBoost and LightGBM, were used to establish a rock compressive strength prediction model, and Bayesian optimization algorithm was used to optimize the hyperparameters during model training. Finally, the coefficient of determination (R2), mean absolute percentage error (MAPE) and root mean square error (RMSE) were used to evaluate and compare the generalization ability of the optimized model. In addition, the importance of input features was analyzed by LGB model, to evaluate the importance of input features on the generalization ability of the model. The results show that the three models have achieved good prediction results for rock compressive strength. And the generalization ability of the LGB model is slightly better than that of the other two models (R2 = 0.978, RMSE=5.58, MAPE=9.70%), and the running time is relatively minimum. Elastic modulus (E), confining pressure (σ3) and density (ρ) have great influence on generalization ability of model, while Poisson's ratio(v)has little influence. The prediction model has good applicability to rock strength prediction, and provides a new idea for the combination of machine learning and geotechnical engineering.
-
Key words:
- rock strength /
- ensemble learning /
- Bayesian optimization /
- random forest /
- XGBoost /
- LightGBM /
- engineering geology
-
图 2 不同模型下的预测值与实测值对比
Fig. 2. Comparison between predicted values and measured values under different models
表 1 基于贝叶斯优化后的3种模型最优超参数和运行耗时
Table 1. Optimal super parameters and running time of three models based on Bayesian optimization
模型 超参数名称 最优取值 运行耗时(s) Random Forest n_estimators 915 13.625 max_depth 13 max_features 7 min_samples_split 2 min_samples_leaf 1 LightGBM n_estimators 615 5.383 max_depth 17 gamma 26.251 lambda 0.849 alpha 24.513 num_leaves 82 learning_rate 0.201 XGBoost n_estimators 985 24.558 max_depth 3 gamma 25.802 lambda 2.881 alpha 8.830 learning_rate 0.185 
下载: 导出CSV
表 2 预测模型评价指标
Table 2. Evaluation index of prediction model
评价指标 计算公式 评判标准 决定系数 $ {R}^{2}=1-\frac{{\sum\limits _{i=1}^{n}\left({y}_{i}-{\widehat{y}}_{i}\right)}^{2}}{{\sum \limits_{i=1}^{n}\left({y}_{i}-{\stackrel{-}{y}}_{i}\right)}^{2}} $ R2数值越大，模型性能越好 均方根误差 $ \mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\frac{1}{n}\times {\sum \limits_{i=1}^{n}\left({y}_{i}-{\widehat{y}}_{i}\right)}^{2}} $ RMSE数值越小，模型性能越好 平均绝对百分比误差 $ \mathrm{M}\mathrm{A}\mathrm{P}\mathrm{E}=\sum\limits _{i=1}^{n}\left|\frac{{y}_{i}-{\widehat{y}}_{i}}{{y}_{i}}\right|\times \frac{100\mathrm{\%}}{n} $ MAPE数值越小，模型性能越好 注：式中，n为预测样本的数量，$ {\stackrel{-}{y}}_{i} $和ŷi分别表示实测值yi的平均值和预测值.
下载: 导出CSV
-
Aladejare, A. E., 2020. Evaluation of Empirical Estimation of Uniaxial Compressive Strength of Rock Using Measurements from Index and Physical Tests. Journal of Rock Mechanics and Geotechnical Engineering, 12(2): 256-268. https://doi.org/10.1016/j.jrmge.2019.08.001 Arjmandpour, J., Hosseinitoudeshki, V., 2013. Estimation of Tensile Strength of Limestone from Some of Its Physical Properties via Simple Regression. Journal of Novel Applied Sciences, 2: 1041-1044. Bieniawski, Z. T., 1974. Estimating the Strength of Rock Materials. Journal of the South African Institute of Mining and Metallurgy, 74(8): 312-320. http://saimm.org.za/Journal/v074n08p312.pdf Breiman, L., 2001. Random Forests. Machine Learning, 45: 5-32. doi: 10.1023/A:1010933404324 Cargill, J. S., Shakoor, A., 1990. Evaluation of Empirical Methods for Measuring the Uniaxial Compressive Strength of Rock. International Journal of Rock Mechanics and Mining Sciences, 27(6): 495-503. doi:https://doi.org/ 10.1016/0148-9062(90)91001-N Chen, T., Guestrin, C., 2016. XGBoost: A Scalable Tree Boosting System. Proceedings of the 22nd ACM Sigkdd International Conference on Knowledge Discovery and Data Mining, San Francisco, 785-794. https://doi.org/10.1145/2939672.2939785 Çobanoğlu, İ., Çelik, S. B., 2008. Estimation of Uniaxial Compressive Strength from Point Load Strength, Schmidt Hardness and P-Wave Velocity. Bulletin of Engineering Geology and the Environment, 67: 491-498. doi: 10.1007/s10064-008-0158-x Cui, J. X., Yang, B., 2018. Survey on Bayesian Optimization Methodology and Applications. Journal of Software, 29(10): 3068-3090 (in Chinese with English abstract). http://www.researchgate.net/publication/330103291_Survey_on_Bayesian_Optimization_Methodology_and_Applications Culshaw, M. G., 2015. The ISRM Suggested Methods for Rock Characterization, Testing and Monitoring: 2007‒2014. Bulletin of Engineering Geology and the Environment, 74: 1499-1500. https://doi.org/10.1007/978-3-319-007713-0 Edelbro, C., 2003. Rock Mass Strength: A Review. Department of Civil Engineering Division of Rock Mechanics, Beijing. Gokceoglu, C., 2002. A Fuzzy Triangular Chart to Predict the Uniaxial Compressive Strength of the Ankara Agglomerates from Their Petrographic Composition. Engineering Geology, 66: 39-51. https://doi.org/10.1016/S0013-7952(02)00023-6 Goudie, A. S., 2006. The Schmidt Hammer in Geomorphological Research. Progress in Physical Geography, 30: 703-718. doi:https://doi.org/ 10.1177/0309133306071954 Grima, M. A., Babuška, R., 1999. Fuzzy Model for the Prediction of Unconfined Compressive Strength of Rock Samples. International Journal of Rock Mechanics and Mining Sciences, 36: 339-349. doi:https://doi.org/ 10.1016/S0148-9062(99)00007-8 Guo, Z. Z., Yin, K. L., Fu, S., et al., 2019. Evaluation of Landslide Susceptibility Based on GIS and WOE-BP Model. Earth Science, 44(12): 4299-4312 (in Chinese with English abstract). http://www.researchgate.net/publication/324390254_Evaluation_of_Landslide_Susceptibility_Based_on_GIS_and_WOE-BP_Model He, M., 2019. Deep Convolutional Neural Network for Fast Determination of the Rock Strength Parameters Using Drilling Data. International Journal of Rock Mechanics and Mining Sciences, 123: 104084. https://doi.org/10.1016/j.ijrmms.2019.104084 Huang, F. M., Cao, Y., Fan, X. M., et al., 2021. Effects of Different Landslide Boundaries and Their Spatial Shapes on the Uncertainty of Landslide Susceptibility Prediction. Chinese Journal of Rock Mechanics and Engineering, 40(S02): 3227-3240 (in Chinese with English abstract). Huang, F. M., Chen, B., Mao, D. X., et al., 2023. Landslide Susceptibility Prediction Modeling and Interpretability Based on Self-Screening Deep Learning Model. Earth Science, 48(5): 1696-1710 (in Chinese with English abstract). Huang, X. H., Li, Z. H., Deng, T., et al., 2022. Uranium Potential Evaluation of the Zhuguangshan Granitic Pluton in South China Based on Machine Learning. Earth Science, 1-23 (in Chinese with English abstract). Jahed Armaghani, D., 2016. Application of Several Non- Linear Prediction Tools for Estimating Uniaxial Compressive Strength of Granitic Rocks and Comparison of Their Performances. Engineering with Computers, 32: 189-206. doi: 10.1007/s00366-015-0410-5 Ke, G., 2017. Light GBM: A Highly Efficient Gradient Boosting Decision Tree. Advances in Neural Information Processing Systems, New Orleans, 30. Li, S., Chen, J., Liu, C., et al., 2021. Mineral Prospectivity Prediction via Convolutional Neural Networks Based on Geological Big Data. Journal of Earth Science, 32(2): 327-347. https://doi.org/10.1007/s12583-020-1365-z Li, W., Tan, Z. Y., 2016. Comparison on Rock Strength Prediction Models Based on MLR and LS-SVM. Mining Research and Development, 36(11): 36-40 (in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTotal-KYYK201611008.htm Li, W. B., Fan, X. M., Huang, F. M., et al., 2021. Uncertainties of Landslide Susceptibility Modeling under Different Environmental Factor Connections and Prediction Models. Earth Science, 46(10): 3777-3795 (in Chinese with English abstract). http://www.sciencedirect.com/science/article/pii/S0341816221001090 Li, Y. R., Zhang, Y. L., Wang, J. C., 2022. Survey on Bayesian Optimization Methods for Hyper-Parameter Tuning. Computer Science, 49(S01): 86-92 (in Chinese with English abstract). Mahmoodzadeh, A., 2022. Machine Learning Techniques to Predict Rock Strength Parameters. Rock Mechanics and Rock Engineering, 55: 1721-1741. doi: 10.1007/s00603-021-02747-x Miah, M. I., 2020. Machine Learning Approach to Model Rock Strength: Prediction and Variable Selection with Aid of Log Data. Rock Mechanics and Rock Engineering, 53: 4691-4715. doi: 10.1007/s00603-020-02184-2 Mohamad, E. T., 2018. Rock Strength Estimation: A PSO-Based BP Approach. Neural Computing and Applications, 30: 1635-1646. doi: 10.1007/s00521-016-2728-3 Sagi, O., Rokach, L., 2018. Ensemble Learning: A Survey. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 8: e1249. https://doi.org/10.1002/widm.1249 Sarkar, K., 2010. Estimation of Strength Parameters of Rock Using Artificial Neural Networks. Bulletin of Engineering Geology and the Environment, 69: 599-606. doi: 10.1007/s10064-010-0301-3 Singh, T., 2012. Correlation between Point Load Index and Uniaxial Compressive Strength for Different Rock Types. Rock Mechanics and Rock Engineering, 45: 259-264. doi: 10.1007/s00603-011-0192-z Tang, Z. L., Xu, Q. J., 2020. Rockburst Prediction Based on Nine Machine Learning Algorithms. Chinese Journal of Rock Mechanics and Engineering, 39(4): 773-781 (in Chinese with English abstract). Wang, M., Wan, W., 2019. A New Empirical Formula for Evaluating Uniaxial Compressive Strength Using the Schmidt Hammer Test. International Journal of Rock Mechanics and Mining Sciences, 123: 104094. https://doi.org/10.1016/j.ijrmms.2019.104094 Wang, R., 2020. Application of Ultrasonic-Rebound Method in Fast Prediction of Rock Strength. Geotechnical and Geological Engineering, 38: 5915-5924. doi: 10.1007/s10706-020-01402-6 Yang, K., Yuan, L., Qi, L. G., et al., 2013. Establishing Predictive Model for Rock Uniaxial Compressive Strength of No. 11-2 Coal Seam Roof in Huainan Mining Area. Chinese Journal of Rock Mechanics and Engineering, 32(10): 1991-1998 (in Chinese with English abstract). http://www.researchgate.net/publication/287704654_Establishing_predictive_model_for_rock_uniaxial_compressive_strength_of_No11-2coal_seam_roof_in_Huainan_mining_area Zhang, C. L., Zhang, C. P., Xu, J., 2015. Comparison Test of Rock Point Load Strength and Uniaxial Compressive Strength. Chinese Journal of Underground Space and Engineering, 11(S2): 447-451 (in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTotal-BASE2015S2014.htm Zhang, W. G., He, Y. W., Wang, L. Q., et al., 2023. Machine Learning Solution for Landslide Susceptibility Based on Hydrographic Division: Case Study of Fengjie County in Chongqing. Earth Science, 48(5): 2024-2038 (in Chinese with English abstract). Zhang, W. G., Li, H. R., Wu, C. Z., et al., 2021a. Stability Assessment of Underground Entry-Type Excavations Using Data-Driven RF and KNN Methods. Journal of Hunan University (Natural Sciences), 48(3): 164-172 (in Chinese with English abstract). Zhang, W. G., Tang, L. B., Chen, F. Y., et al., 2021b. Prediction for TBM Penetration Rate Using Four Hyperparameter Optimization Methods and Random Forest Model. Journal of Basic Science and Engineering, 29(5): 1186-1200 (in Chinese with English abstract). doi: 10.1007/978-981-16-6835-7_8 Zhou, Z. H., 2016. Machine Learning. Tsinghua University Press, Beijing, 173(in Chinese). Zhou, Z. H., 2021. Ensemble Learning, Machine Learning. Springer, Berlin, 181-210. 崔佳旭, 杨博, 2018. 贝叶斯优化方法和应用综述. 软件学报, 29(10): 3068-3090. https://www.cnki.com.cn/Article/CJFDTOTAL-RJXB201810011.htm 郭子正, 殷坤龙, 付圣, 等, 2019. 基于GIS与WOE-BP模型的滑坡易发性评价. 地球科学, 44(12): 4299-4312. doi: 10.3799/dqkx.2018.555 黄发明, 曹昱, 范宣梅, 等, 2021. 不同滑坡边界及其空间形状对滑坡易发性预测不确定性的影响规律. 岩石力学与工程学报, 40(S02): 3227-3240. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2021S2023.htm 黄发明, 陈彬, 毛达雄, 等, 2023. 基于自筛选深度学习的滑坡易发性预测建模及其可解释性. 地球科学, 48(5): 1696-1710. https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX202305003.htm 黄鑫怀, 李增华, 邓腾, 等, 2022. 基于机器学习的华南诸广山花岗岩体铀矿潜力评价. 地球科学, 1-23. 李文, 谭卓英, 2016. 基于MLR与LS-SVM的岩石强度预测模型比较. 矿业研究与开发, 36(11): 36-40. https://www.cnki.com.cn/Article/CJFDTOTAL-KYYK201611008.htm 李文彬, 范宣梅, 黄发明, 等, 2021. 不同环境因子联接和预测模型的滑坡易发性建模不确定性. 地球科学, 46(10): 3777-3795. doi: 10.3799/dqkx.2021.042 李亚茹, 张宇来, 王佳晨, 2022. 面向超参数估计的贝叶斯优化方法综述. 计算机科学, 49(S01): 86-92. https://www.cnki.com.cn/Article/CJFDTOTAL-JSJA2022S1013.htm 汤志立, 徐千军, 2020. 基于9种机器学习算法的岩爆预测研究. 岩石力学与工程学报, 39(4): 773-781. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX202004011.htm 杨科, 袁亮, 祁连光, 等, 2013. 淮南矿区11-2煤顶板岩石单轴抗压强度预测模型构建. 岩石力学与工程学报, 32(10): 1991-1998. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201310005.htm 张春玲, 张传鹏, 徐静, 2015. 岩石点荷载强度与单轴抗压强度的对比试验. 地下空间与工程学报, 11(S2): 447-451. https://www.cnki.com.cn/Article/CJFDTOTAL-BASE2015S2014.htm 仉文岗, 何昱苇, 王鲁琦, 等, 2023. 基于水系分区的滑坡易发性机器学习分析方法——以重庆市奉节县为例. 地球科学: 48(5): 2024-2038. https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX202305028.htm 仉文岗, 李红蕊, 巫崇智, 等, 2021a. 基于RF和KNN的地下采场开挖稳定性评估. 湖南大学学报(自然科学版), 48(3): 164-172. https://www.cnki.com.cn/Article/CJFDTOTAL-HNDX202103017.htm 仉文岗, 唐理斌, 陈福勇, 等, 2021b. 基于4种超参数优化算法及随机森林模型预测TBM掘进速度. 应用基础与工程科学学报, 29(5): 1186-1200. https://www.cnki.com.cn/Article/CJFDTOTAL-YJGX202105009.htm 周志华, 2016. 机器学习. 北京: 清华大学出版社, 173. -
点击查看大图
图(3) / 表(2)
计量
- 文章访问数: 1050
- HTML全文浏览量: 680
- PDF下载量: 120
- 被引次数: 0
