Skip to main content

Advertisement

SpringerLink
Log in

Prediction of Uniaxial Compressive Strength of Rock Via Genetic Algorithm—Selective Ensemble Learning

  • Original Paper
  • Published:
Natural Resources Research Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6

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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Briševac, Z., Hrženjak, P., & Buljan, R. (2016). Modeli za procjenu jednoosne tlačne čvrstoće i modula elastičnosti. Građevinar, 68(1), 19–28.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Chen, B., Hong, J., & Wang, Y. (1997). The problem of finding optimal subset of features. Chinese Journal of Computers, 2, 133–138.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Jing, 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Sharma, L. K., Vishal, V., & Singh, T. N. (2017). Developing novel models using neural networks and fuzzy systems for the prediction of strength of rocks from key geomechanical properties. Measurement, 102, 158–169.

    Article  Google Scholar 

  • Sun, Y., Li, G., & Zhang, J. (2020). Developing hybrid machine learning models for estimating the unconfined compressive strength of jet grouting composite: A comparative study. Applied Sciences, 10(5), 1612.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Xu, J. W., & Yang, Y. (2018). A survey of ensemble learning approaches. Journal of Yunnan University, 40(6), 1082–1092.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Zhang, P., Yin, Z. Y., Jin, 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.

    Article  Google Scholar 

  • Zhou, Z.-H., Wu, J., & Tang, W. (2002). Ensembling neural networks: Many could be better than all. Artificial Intelligence, 137(1–2), 239–263.

    Article  Google Scholar 

Download references

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

  1. Faculty of Land Resources Engineering, Kunming University of Science and Technology, Kunming, 650093, Yunnan, China

    Huajin Zhang, Shunchuan Wu & Zhongxin Zhang

  2. School of Civil and Resources Engineering, University of Science and Technology Beijing, Beijing, 100083, China

    Shunchuan Wu

Authors
  1. Huajin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shunchuan Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhongxin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shunchuan Wu.

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

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11053-022-10065-4

Keywords

Search

Navigation