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Frontiers of Earth Science

ISSN 2095-0195

ISSN 2095-0209(Online)

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Front. Earth Sci.    2024, Vol. 18 Issue (2) : 400-411    https://doi.org/10.1007/s11707-024-1101-6
Machine learning methods for predicting the uniaxial compressive strength of the rocks: a comparative study
Tao WEN1,2,3(), Decheng LI1, Yankun WANG1,3, Mingyi HU1,3, Ruixuan TANG1,3
1. School of Geosciences, Yangtze University, Wuhan 430100, China
2. Badong National Observation and Research Station of Geohazards, China University of Geosciences, Wuhan 430074, China
3. Jiacha County Branch of Hubei Yangtze University Technology Development Co., Ltd, Shannan 856499, China
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Abstract

The uniaxial compressive strength (UCS) of rocks is a critical index for evaluating the mechanical properties and construction of an engineering rock mass classification system. The most commonly used method for determining the UCS in laboratory settings is expensive and time-consuming. For this reason, UCS can be estimated using an indirect determination method based on several simple laboratory tests, including point-load strength, rock density, longitudinal wave velocity, Brazilian tensile strength, Schmidt hardness, and shore hardness. In this study, six data sets of indices for different rock types were utilized to predict the UCS using three nonlinear combination models, namely back propagation (BP), particle swarm optimization (PSO), and least squares support vector machine (LSSVM). Moreover, the best prediction model was examined and selected based on four performance prediction indices. The results reveal that the PSO–LSSVM model was more successful than the other two models due to its higher performance capacity. The ratios of the predicted UCS to the measured UCS for the six data sets were 0.954, 0.982, 0.9911, 0.9956, 0.9995, and 0.993, respectively. The results were more reasonable when the predicted ratio was close to a value of approximately 1.
Keywords uniaxial compressive strength      particle swarm optimization      least squares support vector machine      prediction model      prediction performance     
Corresponding Author(s): Tao WEN   
Online First Date: 05 June 2024    Issue Date: 19 July 2024
 Cite this article:   
Tao WEN,Decheng LI,Yankun WANG, et al. Machine learning methods for predicting the uniaxial compressive strength of the rocks: a comparative study[J]. Front. Earth Sci., 2024, 18(2): 400-411.
 URL:  
https://academic.hep.com.cn/fesci/EN/10.1007/s11707-024-1101-6
https://academic.hep.com.cn/fesci/EN/Y2024/V18/I2/400
References Prediction models Input parameters Output parameters Samples
Mohamad et al. (2015) PSO-ANN BTS, Is(50), Vp, DD UCS 40
Momeni et al. (2015b) PSO-ANN Rn, Vp, Is(50), DD UCS 66
Jahed Armaghani et al. (2016) ICA-ANN Rn, Vp, Is(50) UCS 108
Jahed Armaghani et al. (2016) NLMR, ANN, ANFIS Rn, Vp, Is(50) UCS 124
Li and Tan (2016) MLR, LSSVM TS, Vp, Is(50),DD UCS 24
Mohamad et al. (2018) PSO-BP Vp, Is(50), DD, MC,Id2 UCS 38
Abdi et al. (2020) PSO-ANN Rn, Vp, DD UCS 60
Aladejare (2020) Several empirical equations Is(50), ne, DD, BPI, SHH UCS 60
Li et al. (2020) GMDH Rn, Vp, DD UCS 86
Teymen and Mengüç (2020) SRA, MRA, ANN, ANFIS, GEP BTS, Vp, Is(50),DD, SHH, SSH UCS 93
Gowida et al. (2021) ANN, ANFIS, SVM ROP, GPM, SPP, RPM, T, WOB UCS 1771
Zhang et al. (2022) GA-SEL Vp, Is(50), BPI, Rn UCS 166
Liu et al. (2022) XGBoost Rn, Vp, Is(50) UCS 108
Skentou et al. (2023) ANN-LM, ANN-PSO, ANN-ICA Rn, Vp, ne UCS 274
Tab.1  Some of existing studies in field of rock strength prediction
Fig.1  The flow chart of the PSO-BP model.
Fig.2  The flow chart of the PSO-LSSVM model.
Fig.3  Key differences of the three models.
Fig.4  Relationships between different parameters and the measured UCS for different rock types from different places: (a) Is(50); (b) Vp; (c) BTS; (d) SHH; (e) SSH; (f) density.
Fig.5  Measured value and predicted value of the UCS for testing data at different rock types: (a) shale; (b) sandstone; (c) volcanic rock; (d) slightly weathered granite; (e) different rock types from different places; (f) granite with different weathered degrees.
Types R2 RMSE VAF MAE
BP PSO-BP PSO-LSSVM BP PSO-BP PSO-LSSVM BP PSO-BP PSO-LSSVM BP PSO-BP PSO-LSSVM
1 0.92 0.95 0.96 21.33 7.88 8.70 93.85 93.09 85.74 7.33 0.54 2.67
2 0.94 0.97 0.96 42.00 17.82 5.82 77.52 93.04 95.26 6.21 0.80 0.71
3 0.76 0.82 0.67 80.07 63.51 4.64 36.10 73.23 95.22 16.45 11.85 0.47
4 0.39 0.49 0.83 48.40 40.55 3.46 74.78 67.00 95.66 3.70 3.62 0.16
5 0.81 0.95 0.97 86.82 46.70 35.95 97.85 94.47 98.57 4.54 0.96 0.45
6 0.77 0.64 0.79 110.06 139.12 99.63 30.80 38.00 33.82 9.28 9.59 6.37
Tab.2  The error analysis of the predicted results for the three models
Fig.6  Measured UCS and predicted UCS for training data and validation data at different rock types: (a) shale; (b) sandstone; (c) volcanic rock; (d) slightly weathered granite; (e) different rock types from different places; (f) granite with different weathered degrees.
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