Research on Hard Rock Pillar Stability Prediction Based on SABO-LSSVM Model
Abstract
:1. Introduction
2. Materials and Methods
2.1. Pillar Dataset
2.2. Feature Correlation Analysis
2.3. Introduction of the LSSVM Model
2.4. Introduction of the Subtraction Average Optimization Algorithm
2.5. Oversampling Methods
3. Model Construction and Optimal Selection of Dataset Balancing Methods
3.1. Construction of Optimized Model
3.2. Workflow for Balancing Dataset
- (1)
- Preliminary oversampling using Smote. Similar to the individual Smote oversampling method, new sample points were constructed through linear interpolation between minority class samples until the imbalance between different classes was resolved.
- (2)
- Cleaning noise and boundary data using Tomek Links. Tomek Links pairs on class boundaries were identified and removed based on the minimum geometric distance principle to achieve a new balance.
4. Results and Discussion
4.1. Models Performance Comparison
4.2. Performance of Different Balancing Methods
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Zhao, G.Y.; Liu, J. Analysis of the pillar stability based on the Gaussian process for machine learning. J. Saf. Environ. 2017, 17, 1725–1729. [Google Scholar]
- Zhao, G.Y.; Liu, J.; Zhou, J. Recognition model of hard rock pillars state based on different discriminant criterions. J. Cent. South Univ. (Sci. Technol.) 2018, 49, 2813–2820. [Google Scholar]
- Zhu, W.C.; Dong, H.Y.; Liu, X.G.; Niu, L.L.; Dai, F.; Guan, K. Review of bearing and instability of multi-pillar in metal mines. J. Min. Strat. Control Eng. 2022, 4, 5–31. [Google Scholar]
- Peng, S.S. Ground Control Failures: A Pictorial View of Case Studies; Elsevier: Philadelphia, PA, USA, 2007. [Google Scholar]
- Brady, B.H.; Brown, E.T. Rock Mechanics: For Underground Mining; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2006. [Google Scholar]
- Deng, J.; Yue, Z.; Tham, L.; Zhu, H. Pillar design by combining finite element methods, neural networks and reliability: A case study of the Feng Huangshan copper mine, China. Int. J. Rock Mech. Min. Sci. 2003, 40, 585–599. [Google Scholar] [CrossRef]
- Martin, C.; Maybee, W. The strength of hard-rock pillars. Int. J. Rock Mech. Min. Sci. 2000, 37, 1239–1246. [Google Scholar] [CrossRef]
- Wilson, A.H. The stability of underground workings in the soft rocks of the coal measures. Int. J. Min. Eng. 1983, 1, 91–187. [Google Scholar] [CrossRef]
- Salamon, M.; Munro, A. A study of the strength of coal pillars. J. South. Afr. Inst. Min. Metall. 1967, 68, 55–67. [Google Scholar]
- Krauland, N.; Soder, P. Determining pillar strength-from pillar failure observation. E&MJ-Eng. Min. J. 1987, 188, 34–40. [Google Scholar]
- Potvin, Y.; Hudyma, M.; Miller, H. Rib pillar design in open stope mining. In CIM Bulletin; Canadian Institute of Mining, Metallurgy and Petroleum: Montreal, QC, Canada, 1988; p. 74. [Google Scholar]
- Lunder, P.; Pakalnis, R. Determination of the strength of hard-rock mine pillars. In CIM Bulletin; Canadian Institute of Mining, Metallurgy and Petroleum: Montreal, QC, Canada, 1997; Volume 90, pp. 51–55. [Google Scholar]
- Ghasemi, E.; Shahriar, K.; Sharifzadeh, M.; Hashemolhosseini, H. Quantifying the uncertainty of pillar safety factor by montecarlo simulation-a case study. Arch. Min. Sci. 2010, 55, 623–635. [Google Scholar]
- Yu, P.P.; Zhao, G.Y.; Zhou, L. Stability determination of underground mine pillars based on quantitative theory II. J. Saf. Environ. 2014, 14, 45–49. [Google Scholar] [CrossRef]
- Esterhuizen, G.; Dolinar, D.; Ellenberger, J. Pillar strength in underground stone mines in the United States. Int. J. Rock Mech. Min. Sci. 2011, 48, 42–50. [Google Scholar] [CrossRef]
- Zhen, Z.D.; Liu, M.Y.; Zhu, W.H. Estimation of pillar strength and stability evaluation. J. Wuhan Univ. Technol. 1993, 3, 59–67. [Google Scholar]
- Liu, X.Z.; Zhai, D.Y. Reliability design of mine pillars. Chin. J. Rock Mech. Eng. 2000, 1, 85–88. [Google Scholar]
- Ghasemi, E.; Ataei, M.; Shahriar, K. An intelligent approach to predict pillar sizing in designing room and pillar coal mines. Int. J. Rock Mech. Min. Sci. 2014, 65, 86–95. [Google Scholar] [CrossRef]
- Yao, G.H.; Wu, A.X.; Wang, Y.M.; Xia, H.C. Stability analysis of stope retention pillars in broken rock conditions. J. Univ. Sci. Technol. Beijing 2011, 33, 400–405. [Google Scholar]
- Wang, C.; Guo, J.P.; Wang, L.G. Recognition of goaf risk based on support vector machines method. J. Chongqing Univ. 2015, 38, 85–90. [Google Scholar]
- Xie, X.; Jiang, W.; Guo, J. Research on rockburst prediction classification based on GA-XGB model. IEEE Access 2021, 9, 83993–84020. [Google Scholar] [CrossRef]
- Zhou, J.; Li, X.; Shi, X.Z. Long-term prediction model of rockburst in underground openings using heuristic algorithms and support vector machines. Saf. Sci. 2012, 50, 629–644. [Google Scholar] [CrossRef]
- Han, L.; Liu, D.-S.; Li, G.-J.; Wang, Y.-T. BP neural network forecast of blasting muck pile form of high bench cast blasting based on Weibull model. J. China Coal Soc. 2013, 38, 1947–1952. [Google Scholar]
- Sun, W.B.; Liu, X.L.; Tan, Z.L.; Li, Y.; Zhao, X.S. Parameter optimization of BP-neural network based on the forecast of cast blasting. J. China Coal Soc. 2012, 37, 59–64. [Google Scholar]
- Zhou, J.; Li, X.B.; Shi, X.Z.; Wei, W.; Wu, B.B. Predicting pillar stability for underground mine using Fisher discriminant analysis and SVM methods. Trans. Nonferr. Met. Soc. China 2011, 21, 2734–2743. [Google Scholar] [CrossRef]
- Lunder, P.J. Hard Rock Pillar Strength Estimation an Applied Empirical Approach. Ph.D. Thesis, University of British Columbia, Vancouver, BC, Canada, 1994. [Google Scholar]
- Walton, G.; Sinha, S. Improved empirical hard rock pillar strength predictions using unconfined compressive strength as a proxy for brittleness. Int. J. Rock Mech. Min. Sci. 2021, 148, 104934. [Google Scholar] [CrossRef]
- Ji, Y.Y. Research on Train Delay Prediction Method Based on Feature Selection and Machine Learning. Master’s Thesis, Beijing Jiaotong University, Beijing, China, 2020. [Google Scholar]
- Zhang, H. Correlation Mining Based Cross-media Retrieval. Ph.D. Thesis, Zhejiang University, Hangzhou, China, 2007. [Google Scholar]
- Edelmann, D.; Móri, T.F.; Székely, G.J. On relationships between the Pearson and the distance correlation coefficients. Stat. Probab. Lett. 2021, 169, 6. [Google Scholar] [CrossRef]
- Xu, H.H.; Deng, Y. Dependent Evidence Combination Based on Shearman Coefficient and Pearson Coefficient. IEEE Access 2017, 6, 11634–11640. [Google Scholar] [CrossRef]
- Song, Y.; Niu, W.; Wang, Y.; Xie, X.; Yang, S. A Novel Method for Energy Consumption Prediction of Underwater Gliders Using Optimal LSSVM with PSO Algorithm. In Proceedings of the Global Oceans 2020: Singapore–U.S. Gulf Coast, Biloxi, MS, USA, 5–30 October 2020; pp. 1–5. [Google Scholar]
- Trojovský, P.; Dehghani, M. Subtraction-average-based optimizer: A new swarm-inspired metaheuristic algorithm for solving optimization problems. Biomimetics 2023, 8, 149. [Google Scholar] [CrossRef] [PubMed]
- Lv, H.; Wang, L.; Zhu, Y.Z.; Du, W.L.; Liu, N.; Yang, D.H.; Ceng, B.Y. Harmonic Prediction of Power Grid Based on Improved SABO-BP Algorithm. Guangdong Electr. Power 2024, 37, 56–65. [Google Scholar]
- Tang, L.Z.; Wang, X.; Xu, Q.J. Rockburst prediction based on oversampling and objective weighting method. J. Tsinghua Univ. (Sci. Technol.) 2021, 61, 543–555. [Google Scholar]
- Chawla, N.V.; Bowyer, K.W.; Hall, L.O.; Kegelmeyer, W.P. SMOTE: Synthetic minority over-sampling technique. J. Artif. Intell. Res. 2002, 16, 321–357. [Google Scholar] [CrossRef]
- Chen, X.C. Research on Algorithm and Application of Deep Learning Based on Convolutional Neural Network. Master’s Thesis, Zhejiang Gongshang University, Hangzhou, China, 2014. [Google Scholar]
- Zhang, L.; Cui, Y.; Liu, J.; Jiang, Y.; Wu, J.P. Application of Machine Learning in Cyberspace Security Research. Chin. J. Comput. 2018, 41, 1943–1975. [Google Scholar]
- Goldberg, D.E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning; Addison-Wesley Longman Publishing: Boston, MA, USA, 1989. [Google Scholar]
- Kohavi, R. A study of cross-validation and bootstrap for accuracy estimation and model selection. In Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI), Montreal, QC, Canada, 20–25 August 1995; pp. 1137–1145. [Google Scholar]
- Qiao, W.B.; Huang, K.; Azimi, M.; Han, S. A Novel Hybrid Prediction Model for Hourly Gas Consumption in Supply Side Based on Improved Whale Optimization Algorithm and Relevance Vector Machine. IEEE Access 2019, 7, 88218–88230. [Google Scholar] [CrossRef]
- Xiang, L.; Deng, Z.Q.; Hu, A.J. Forecasting Short-Term Wind Speed Based on IEWT-LSSVM model Optimized by Bird Swarm Algorithm. IEEE Access 2019, 7, 59333–59345. [Google Scholar] [CrossRef]
- Ding, X.G.; Ye, S.Y.; Gao, Z.J. Development and applications of grain size analysis technique. Glob. Geol. 2005, 24, 203–207. [Google Scholar]
- Jiang, J.Y. Research on Classification of Imbalanced Data Sets Based on Maximize F1-Measure Learning. Master’s Thesis, Harbin Institute of Technology, Harbin, China, 2017. [Google Scholar]
- Opitz, J.; Burst, S. Macro f1 and macro f1. arXiv 2019, arXiv:1911.03347. [Google Scholar]
W | H | K | Cpav | UCS | σ | σp | |
---|---|---|---|---|---|---|---|
M-1 | √ | √ | √ | √ | √ | √ | √ |
M-2 | √ | √ | √ | √ | √ | √ | |
M-3 | √ | √ | √ | √ | √ | ||
M-4 | √ | √ | √ | √ | |||
M-5 | √ | √ | √ |
Model | Hyperparameter | Range of Values |
---|---|---|
LSSVM SVM | γ | {2−8, 2−6, 2−4, 2−2, 20, 22, 24, 26, 28} |
σ | ||
ELM | n | {10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000} |
SABO-LSSVM | LSSVM | SVM | ELM | SF | Average | |
---|---|---|---|---|---|---|
M-1 | 84.74 | 71.43 | 47.62 | 70.95 | 49.38 | 64.82 |
M-2 | 85.33 | 61.90 | 47.62 | 71.94 | 49.38 | 63.23 |
M-3 | 85.58 | 71.43 | 52.38 | 68.10 | / | 69.37 |
M-4 | 83.04 | 61.90 | 52.38 | 60.00 | / | 64.33 |
M-5 | 80.04 | 57.14 | 57.14 | 63.81 | / | 64.53 |
Average | 83.75 | 64.76 | 51.43 | 66.96 | 49.38 |
SABO | PSO | GWO | GA | KOA | WOA | Average | |
---|---|---|---|---|---|---|---|
M-1 | 84.74 | 82.93 | 81.93 | 73.28 | 78.92 | 79.30 | 80.18 |
M-2 | 85.33 | 83.46 | 83.53 | 73.82 | 79.29 | 79.52 | 80.82 |
M-3 | 85.58 | 84.28 | 83.52 | 74.73 | 79.72 | 79.57 | 81.23 |
M-4 | 83.04 | 83.18 | 83.23 | 73.66 | 76.62 | 76.09 | 79.30 |
M-5 | 80.04 | 80.87 | 80.53 | 73.83 | 75.93 | 73.48 | 77.45 |
Average | 83.75 | 82.94 | 82.55 | 73.86 | 78.10 | 77.59 |
Predicted Value | ||||
---|---|---|---|---|
Positive | Negative | |||
True value | Positive | TP | FN | TPR |
Negative | FP | TN | TNR | |
PPV | FPR | ACC |
Index | Formula | Significance |
---|---|---|
Accuracy (ACC) | Proportion of correctly predicted samples among all predictions | |
Precision (PPV) | Proportion of correctly predicted positive samples among positive predictions | |
False-positive rate (FPR) | Proportion of incorrectly predicted negative samples among negative predictions | |
Recall (TPR) | The ratio that is accurately predicted in an actual positive example | |
Specificity (TNR) | The ratio that is accurately predicted in an actual negative example | |
F1 score | The harmonic mean of precision and recall | |
Micro F1 | Calculate F1 score using precision and recall based on the overall sample set without distinguishing between classes | |
Macro F1 | For class distinction, calculate average precision and recall for each class separately to compute F1 score |
Model (Sampling Method) | Accuracy | Micro F1 | Macro F1 | Class | Precision | Recall | F1 Score |
SABO-LSSVM(Tomek–Smote) | 0.9286 | 0.9286 | 0.9284 | 1 | 0.9333 | 1.0000 | 0.9655 |
2 | 1.0000 | 0.8571 | 0.9231 | ||||
3 | 0.8667 | 0.9286 | 0.8966 | ||||
SABO-LSSVM(Smote) | 0.8810 | 0.7857 | 0.7708 | 1 | 0.7368 | 1.0000 | 0.8485 |
2 | 0.8750 | 0.5000 | 0.6364 | ||||
3 | 0.8000 | 0.8571 | 0.8276 | ||||
SABO-LSSVM(Adasyn) | 0.9048 | 0.8095 | 0.7939 | 1 | 0.7368 | 1.0000 | 0.8485 |
2 | 1.0000 | 0.5000 | 0.6667 | ||||
3 | 0.8125 | 0.9286 | 0.8667 | ||||
SABO-LSSVM(Default) | 0.8095 | 0.8095 | 0.7939 | 1 | 0.7368 | 1.0000 | 0.8485 |
2 | 1.0000 | 0.5000 | 0.6667 | ||||
3 | 0.8125 | 0.9286 | 0.8667 | ||||
LSSVM(Tomek–Smote) | 0.7857 | 0.8095 | 0.8040 | 1 | 0.9286 | 0.9286 | 0.9286 |
2 | 0.8889 | 0.5714 | 0.6957 | ||||
3 | 0.6842 | 0.9286 | 0.7879 | ||||
SVM(Tomek–Smote) | 0.6190 | 0.6190 | 0.5583 | 1 | 1.0000 | 0.8571 | 0.9231 |
2 | 0.3333 | 0.0714 | 0.1176 | ||||
3 | 0.4815 | 0.9286 | 0.6341 |
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Xie, X.; Zhang, H. Research on Hard Rock Pillar Stability Prediction Based on SABO-LSSVM Model. Appl. Sci. 2024, 14, 7733. https://doi.org/10.3390/app14177733
Xie X, Zhang H. Research on Hard Rock Pillar Stability Prediction Based on SABO-LSSVM Model. Applied Sciences. 2024; 14(17):7733. https://doi.org/10.3390/app14177733
Chicago/Turabian StyleXie, Xuebin, and Huaxi Zhang. 2024. "Research on Hard Rock Pillar Stability Prediction Based on SABO-LSSVM Model" Applied Sciences 14, no. 17: 7733. https://doi.org/10.3390/app14177733