Abstract
Reasonable and effective determination of uniaxial compressive strength (UCS) is critical for rock mass engineering stability research, design, and construction. To estimate the UCS of rock simply, conveniently, and accurately, a selective ensemble learning technology is introduced here based on modern artificial intelligence research, and a prediction method of the UCS of rock via genetic algorithm—selective ensemble learning (GA–SEL) is proposed. Based on a UCS data set, a batch of different base learners was firstly trained independently with the data sample and the algorithm parameter perturbation method. Then, the optimal base learner subset was searched using GA. Further, the GA–SEL model was constructed by fusing the base learners in that subset. According to the 161 data set collected, the prediction performance of the GA–SEL model was evaluated by four evaluation indices, then two empirical regression models and seven common machine learning models were compared with it. The results of the GA–SEL model agreed with the measured data very well, showing that the model had the best prediction and generalization ability, it was more stable and accurate than the empirical methods and common machine learning models. Because it only needs seven high-quality base learners, the GA–SEL model also has better operation efficiency compared to other ensemble learning models. Therefore, this method could be used as an effective method to predict the UCS of rock and serve for rock engineering problems.
Similar content being viewed by others
References
Aladejare, A. E., Alofe, E. D., Onifade, M., Lawal, A. I., Ozoji, T. M., & Zhang, Z. X. (2021). Empirical estimation of uniaxial compressive strength of rock: Database of simple, multiple, and artificial intelligence-based regressions. Geotechnical and Geological Engineering, 39(6), 4427–4455.
Armaghani, D. J., Amin, M. F. M., Yagiz, S., Faradonbeh, R. S., & Abdullah, R. A. (2016a). Prediction of the uniaxial compressive strength of sandstone using various modeling techniques. International Journal of Rock Mechanics and Mining Sciences, 85, 174–186.
Armaghani, D. J., Mohamad, E. T., Momeni, E., Monjezi, M., & Narayanasamy, M. S. (2016b). Prediction of the strength and elasticity modulus of granite through an expert artificial neural network. Arabian Journal of Geosciences, 9(1), 1–16.
Armaghani, D. J., Safari, V., Fahimifar, A., Mohd Amin, M. F., Monjezi, M., & Mohammadi, M. A. (2018). Uniaxial compressive strength prediction through a new technique based on gene expression programming. Neural Computing and Applications, 30(11), 3523–3532.
ASTM, (American Society of Testing and Materials). (2002). Standard test method for unconfined compressive strength of intact rock core specimens, D2938-95 (R2). https://doi.org/10.1520/D2938-95.
Azimian, A., Ajalloeian, R., & Fatehi, L. (2014). An empirical correlation of uniaxial compressive strength with P-wave velocity and point load strength index on marly rocks using statistical method. Geotechnical and Geological Engineering, 32(1), 205–214.
Barzegar, R., Sattarpour, M., Deo, R., Fijani, E., & Adamowski, J. (2020). An ensemble tree-based machine learning model for predicting the uniaxial compressive strength of travertine rocks. Neural Computing and Applications, 32(13), 9065–9080.
Beiki, M., Majdi, A., & Givshad, A. D. (2013). Application of genetic programming to predict the uniaxial compressive strength and elastic modulus of carbonate rocks. International Journal of Rock Mechanics and Mining Sciences, 1997(63), 159–169.
Briševac, Z., Hrženjak, P., & Buljan, R. (2016). Modeli za procjenu jednoosne tlačne čvrstoće i modula elastičnosti. Građevinar, 68(1), 19–28.
Briševac, Z., Pollak, D., Maričić, A., & Vlahek, A. (2021). Modulus of elasticity for grain-supported carbonates—determination and estimation for preliminary engineering purposes. Applied Sciences, 11(13), 6148.
Ceryan, N. (2014). Application of support vector machines and relevance vector machines in predicting uniaxial compressive strength of volcanic rocks. Journal of African Earth Sciences, 100, 634–644.
Chen, B., Hong, J., & Wang, Y. (1997). The problem of finding optimal subset of features. Chinese Journal of Computers, 2, 133–138.
Deere, D. U., & Miller, R. P. (1966). Engineering classification and index properties for intact rock. Illinois Univ At Urbana Dept Of Civil Engineering.
Ebdali, M., Khorasani, E., & Salehin, S. (2020). A comparative study of various hybrid neural networks and regression analysis to predict unconfined compressive strength of travertine. Innovative Infrastructure Solutions, 5(3), 1–14.
Fattahi, H. (2017). Applying soft computing methods to predict the uniaxial compressive strength of rocks from schmidt hammer rebound values. Computational Geosciences, 21(4), 665.
Ghasemi, E., Kalhori, H., Bagherpour, R., & Yagiz, S. (2018). Model tree approach for predicting uniaxial compressive strength and Young’s modulus of carbonate rocks. Bulletin of Engineering Geology and the Environment, 77(1), 331–343.
İnce, İ, Bozdağ, A., Fener, M., & Kahraman, S. (2019). Estimation of uniaxial compressive strength of pyroclastic rocks (Cappadocia, Turkey) by gene expression programming. Arabian Journal of Geosciences, 12(24), 1–13.
ISRM, (International Society for Rock Mechanics). (2007). In: Ulusay, R. & Hudson, J. A. (Eds.), The complete ISRM suggested methods for rock characterization, testing and monitoring: 1974–2006. ISRM Turkish National Group, Ankara.
Iyare, U. C., Blake, O. O., & Ramsook, R. (2021). Estimating the uniaxial compressive strength of Argillites using Brazilian tensile strength, ultrasonic wave velocities, and elastic properties. Rock Mechanics and Rock Engineering, 54(4), 2067–2078.
Jalali, S. H., Heidari, M., & Mohseni, H. (2017). Comparison of models for estimating uniaxial compressive strength of some sedimentary rocks from Qom Formation. Environmental Earth Sciences, 76(22), 1–15.
**g, H., Nikafshan Rad, H., Hasanipanah, M., Jahed Armaghani, D., & Qasem, S. N. (2021). Design and implementation of a new tuned hybrid intelligent model to predict the uniaxial compressive strength of the rock using SFS-ANFIS. Engineering with Computers, 37(4), 2717–2734.
Karaman, K., Cihangir, F., Ercikdi, B., Kesimal, A., & Demirel, S. (2015). Utilization of the Brazilian test for estimating the uniaxial compressive strength and shear strength parameters. Journal of the Southern African Institute of Mining and Metallurgy, 115(3), 185–192.
Kong, F., & Shang, J. (2018). A validation study for the estimation of uniaxial compressive strength based on index tests. Rock Mechanics and Rock Engineering, 51(7), 2289–2297.
Koo, T. K., & Li, M. Y. (2016). A guideline of selecting and reporting intraclass correlation coefficients for reliability research. Journal of Chiropractic Medicine, 15(2), 155–163.
Koolivand-Salooki, M., Esfandyari, M., Rabbani, E., Koulivand, M., & Azarmehr, A. (2017). Application of genetic programing technique for predicting uniaxial compressive strength using reservoir formation properties. Journal of Petroleum Science and Engineering, 159, 35–48.
Madhubabu, N., Singh, P. K., Kainthola, A., Mahanta, B., Tripathy, A., & Singh, T. N. (2016). Prediction of compressive strength and elastic modulus of carbonate rocks. Measurement, 88, 202–213.
Mahdiabadi, N., & Khanlari, G. (2019). Prediction of uniaxial compressive strength and modulus of elasticity in calcareous mudstones using neural networks, fuzzy systems, and regression analysis. Periodica Polytechnica Civil Engineering, 63(1), 104–114.
Mahmoodzadeh, A., Mohammadi, M., Ibrahim, H. H., Abdulhamid, S. N., Salim, S. G., Ali, H. F. H., & Majeed, M. K. (2021). Artificial intelligence forecasting models of uniaxial compressive strength. Transportation Geotechnics, 27, 100499.
Matin, S. S., Farahzadi, L., Makaremi, S., Chelgani, S. C., & Sattari, G. (2018). Variable selection and prediction of uniaxial compressive strength and modulus of elasticity by random forest. Applied Soft Computing, 70, 980–987.
Mishra, D. A., & Basu, A. (2013). Estimation of uniaxial compressive strength of rock materials by index tests using regression analysis and fuzzy inference system. Engineering Geology, 160, 54–68.
Mohamad, E. T., Armaghani, D. J., Momeni, E., & Abad, S. V. A. N. K. (2015). Prediction of the unconfined compressive strength of soft rocks: A PSO-based ANN approach. Bulletin of Engineering Geology and the Environment, 74(3), 745–757.
Mokhtari, M., & Behnia, M. (2019). Comparison of LLNF, ANN, and COA-ANN techniques in modeling the uniaxial compressive strength and static Young’s modulus of limestone of the Dalan formation. Natural Resources Research, 28(1), 223–239.
Momeni, E., Armaghani, D. J., Hajihassani, M., & Amin, M. F. M. (2015). Prediction of uniaxial compressive strength of rock samples using hybrid particle swarm optimization-based artificial neural networks. Measurement, 60, 50–63.
Monjezi, M., Khoshalan, H. A., & Razifard, M. (2012). A neuro-genetic network for predicting uniaxial compressive strength of rocks. Geotechnical and Geological Engineering, 30(4), 1053–1062.
Özöğür-Akyüz, S., Windeatt, T., & Smith, R. (2015). Pruning of error correcting output codes by optimization of accuracy–diversity trade off. Machine Learning, 101(1), 253–269.
Perrone, M. P., & Cooper, L. N. (1992). When networks disagree: Ensemble methods for hybrid neural networks. Brown Univ Providence Ri Inst for Brain and Neural Systems.
Rahman, T., & Sarkar, K. (2021). Lithological control on the estimation of uniaxial compressive strength by the P-wave velocity using supervised and unsupervised learning. Rock Mechanics and Rock Engineering, 54, 1–17.
Saldaña, M., González, J., Pérez-Rey, I., Jeldres, M., & Toro, N. (2020). Applying statistical analysis and machine learning for modeling the UCS from P-Wave velocity, density and porosity on dry travertine. Applied Sciences, 10(13), 4565.
Salehin, S. (2017). Investigation into engineering parameters of marls from Seydoon dam in Iran. Journal of Rock Mechanics and Geotechnical Engineering, 9(5), 912–923.
Sharma, L. K., Vishal, V., & Singh, T. N. (2017). Develo** novel models using neural networks and fuzzy systems for the prediction of strength of rocks from key geomechanical properties. Measurement, 102, 158–169.
Sun, Y., Li, G., & Zhang, J. (2020). Develo** hybrid machine learning models for estimating the unconfined compressive strength of jet grouting composite: A comparative study. Applied Sciences, 10(5), 1612.
Sun, Y., Li, G., Zhang, N., Chang, Q., Xu, J., & Zhang, J. (2021). Development of ensemble learning models to evaluate the strength of coal-grout materials. International Journal of Mining Science and Technology, 31(2), 153–162.
Torabi-Kaveh, M., Naseri, F., Saneie, S., & Sarshari, B. (2015). Application of artificial neural networks and multivariate statistics to predict UCS and E using physical properties of Asmari limestones. Arabian Journal of Geosciences, 8(5), 2889–2897.
Ulusay, R., Gokceoglu, C., & Sulukcu, S. (2001). Draft ISRM suggested method for determining block punch strength index (BPI). International Journal of Rock Mechanics and Mining Sciences, 8(38), 1113–1119.
Vafaie, H., & De J. K. (1993). Robust feature selection algorithms. In Proceedings of 1993 IEEE Conference on Tools with Al (Tai-93) (pp. 356–363).
Wang, H. L., & Yin, Z. Y. (2020). High performance prediction of soil compaction parameters using multi expression programming. Engineering Geology, 276, 105758.
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.
Wang, Z., Li, W., & Chen, J. (2021). Application of various nonlinear models to predict the uniaxial compressive strength of weakly cemented Jurassic rocks. Natural Resources Research, 31(1), 371–384.
Wen, L., Luo, Z. Q., Yang, S. J., Qin, Y. G., & Wang, W. (2019). Correlation of geo-mechanics parameters with uniaxial compressive strength and P-wave velocity on dolomitic limestone using a statistical method. Geotechnical and Geological Engineering, 37(2), 1079–1094.
Wu, Y., Ma, C., Tan, X., Yang, D., Tian, H., & Yang, J. (2019). A new evaluation method for the uniaxial compressive strength ahead of the tunnel face based on the driving data and specification parameters of TBM. Shock and Vibration. https://doi.org/10.1155/2019/5309480
Xu, C., Amar, M. N., Ghriga, M. A., Ouaer, H., Zhang, X., & Hasanipanah, M. (2020a). Evolving support vector regression using Grey Wolf optimization; forecasting the geomechanical properties of rock. Engineering with Computers. https://doi.org/10.1007/s00366-020-01131-7
Xu, H., Chen, C., Zheng, H., Luo, G., Yang, L., Wang, W., Wu, S., & Ding, J. (2020b). AGA-SVR-based selection of feature subsets and optimization of parameter in regional soil salinization monitoring. International Journal of Remote Sensing, 41(12), 4470–4495.
Xu, J. W., & Yang, Y. (2018). A survey of ensemble learning approaches. Journal of Yunnan University, 40(6), 1082–1092.
Yang, C., Yin, X., Hao, H., Yan, Y., & Wang, Z. B. (2014). Classifier ensemble with diversity: Effectiveness analysis and ensemble optimization. Acta Automatica Sinica, 40, 660–674.
Yin, J. H., Wong, R. H. C., Chau, K. T., Lai, D. T. W., & Zhao, G. S. (2017). Point load strength index of granitic irregular lumps: Size correction and correlation with uniaxial compressive strength. Tunnelling and Underground Space Technology, 70, 388–399.
Zhang, Y., Burer, S., Nick Street, W., Bennett, K. P., & Parrado-Hernández, E. (2006). Ensemble pruning via semi-definite programming. Journal of Machine Learning Research, 7(7), 1315–1338.
Zhang, P., Yin, Z. Y., **, Y. F., & Chan, T. H. T. (2020). A novel hybrid surrogate intelligent model for creep index prediction based on particle swarm optimization and random forest. Engineering Geology, 265, 105328.
Zhou, Z.-H., Wu, J., & Tang, W. (2002). Ensembling neural networks: Many could be better than all. Artificial Intelligence, 137(1–2), 239–263.
Acknowledgments
This work is supported by the National Natural Science Foundation of China (No. 51934003 and No. 51774020) and the Yunnan Innovation Team (No. 202105AE160023).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Rights and permissions
About this article
Cite this article
Zhang, H., Wu, S. & Zhang, Z. Prediction of Uniaxial Compressive Strength of Rock Via Genetic Algorithm—Selective Ensemble Learning. Nat Resour Res 31, 1721–1737 (2022). https://doi.org/10.1007/s11053-022-10065-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11053-022-10065-4