Imbalanced rock burst assessment using variational autoencoder-enhanced gradient boosting algorithms and explainability

Abstract

We conducted a study to evaluate the potential and robustness of gradient boosting algorithms in rock burst assessment, established a variational autoencoder (VAE) to address the imbalance rock burst dataset, and proposed a multilevel explainable artificial intelligence (XAI) tailored for tree-based ensemble learning. We collected 537 data from real-world rock burst records and selected four critical features contributing to rock burst occurrences. Initially, we employed data visualization to gain insight into the data's structure and performed correlation analysis to explore the data distribution and feature relationships. Then, we set up a VAE model to generate samples for the minority class due to the imbalanced class distribution. In conjunction with the VAE, we compared and evaluated six state-of-the-art ensemble models, including gradient boosting algorithms and the classical logistic regression model, for rock burst prediction. The results indicated that gradient boosting algorithms outperformed the classical single models, and the VAE-classifier outperformed the original classifier, with the VAE-NGBoost model yielding the most favorable results. Compared to other resampling methods combined with NGBoost for imbalanced datasets, such as synthetic minority oversampling technique (SMOTE), SMOTE-edited nearest neighbours (SMOTE-ENN), and SMOTE-tomek links (SMOTE-Tomek), the VAE-NGBoost model yielded the best performance. Finally, we developed a multilevel XAI model using feature sensitivity analysis, Tree Shapley Additive exPlanations (Tree SHAP), and Anchor to provide an in-depth exploration of the decision-making mechanics of VAE-NGBoost, further enhancing the accountability of tree-based ensemble models in predicting rock burst occurrences.

Keywords

Gradient boosting / VAE / Ensemble learning / Explainable artificial intelligence (XAI) / Rock burst

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

CRediT authorship contribution statement

Shan Lin: Writing - review & editing, Supervision, Software, Methodology, Investigation, Funding acquisition, Conceptualization. Zenglong Liang: Writing - original draft, Visualization, Validation, Software, Resources, Methodology, Data curation, Conceptualization. Miao Dong: Writing - review & editing, Visualization, Software. Hongwei Guo: Writing - review & editing, Supervision, Software, Resources, Methodology, Investigation, Conceptualization. Hong Zheng: Supervision, Project administration, Funding acquisition.

Declaration of competing 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.

Acknowledgement

This work was supported by the National Natural Science Foundation of China (Grant Nos. 42107214 and 52130905).

References

[1] Afraei, S., Shahriar, K., & Madani, S. H. (2019). Developing intelligent classification models for rock burst prediction after recognizing significant predictor variables, Section 1: Literature review and data preprocessing procedure. Tunnelling and Underground Space Technology, 83, 324-353.

[2] Ahmad, M., Katman, H. Y., Al-Mansob, R. A., Ahmad, F., Safdar, M., & Alguno, A. C. (2022). Prediction of Rockburst Intensity Grade in Deep Underground Excavation Using Adaptive Boosting Classifier. Complexity, 2022, 615620.

[3] Bijlsma, S., Bobeldijk, L., Verheij, E. R., Ramaker, R., Kochhar, S.,Macdonald, I. A., et al. (2006). Large-scale human metabolomics studies: A strategy for data (pre-) processing and validation. Analytical Chemistry, 78(2), 567-574.

[4] Cai, M. F., Wang, J. A., & Wang, S. H. (2001). Analysis on energy distribution and prediction of rock burst during deep mining excavation in linglong gold mine. Chinese Journal of Rock Mechanics and Engineering, 20(1), 38-42 (in Chinese).

[5] Chawla, N. V., Bowyer, K. W., Hall, L. O., & Kegelmeyer, W. P. (2002). SMOTE: Synthetic minority over-sampling technique. Journal of Artificial Intelligence Research, 16, 321-357.

[6] Chen, T. Q., Guestrin, C., & Assoc Comp, M. (2016). XGBoost: A Scalable Tree Boosting System. Paper presented at the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), Aug 13- 17, San Francisco, CA.

[7] Dong, X. B., Yu, Z. W., Cao, W. M., Shi, Y. F., & Ma, Q. L. (2020). A survey on ensemble learning. Frontiers of Computer Science, 14(2), 241-258.

[8] Du, Z. J., Xu, M. G., Liu, Z. P., & Wu, X. (2006). Laboratory integratedevaluation method for engineering wall rock rock-burst. Gold (11), 26-30. (in Chinese).

[9] Duan, T., Avati, A., Ding, D. Y., Thai, K. K., Basu, S., Ng, A., et al. (2019). NGBoost: Natural Gradient Boosting for Probabilistic Prediction. Paper presented at the 25th Americas Conference on Information Systems of the Association-for-Information-Systems (AMCIS), Aug 15-17, Cancun, MEXICO.

[10] ElShawi, R., Sherif, Y., Al-Mallah, M., & Sakr, S. (2021). Interpretability in healthcare: A comparative study of local machine learning interpretability techniques. Computational Intelligence, 37(4), 1633-1650.

[11] Faradonbeh, R. S., Taheri, A., & Karakus, M. (2022). The propensity of the over-stressed rock masses to different failure mechanisms based on a hybrid probabilistic approach. Tunnelling and Underground Space Technology, 119, 104214.

[12] Feng, G. L., Feng, X. T., Chen, B. R., & Xiao, Y. X. (2015). Microseismic sequences associated with rockbursts in the tunnels of the Jinping II hydropower station. International Journal of Rock Mechanics and Mining Sciences, 80, 89-100.

[13] Gong, F. Q., & Li, X. B. (2007). A distance discriminant analysis method for prediction of possibility and classification of rockburst and its application. Chinese Journal of Rock Mechanics and Engineering, 26(5), 1012-1018 (in Chinese).

[14] Goodfellow, I. J., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D.,Ozair, S., et al. (2014). Generative Adversarial Networks. arXiv:1406.2661. Retrieved from https://ui.adsabs.harvard.edu/abs/2014arXiv1406.2661G. doi:10.48550/arXiv.1406.2661.

[15] Guo, J., Guo, J. W., Zhang, Q. L., & Huang, M. J. (2022). Research on Rockburst Classification Prediction Based on BP-SVM Model. Ieee Access, 10, 50427-50447.

[16] Hao, J., Shi, K. B., Wang, X. L., Bai, X. J., & Chen, G. M. (2016). Application of cloud model to rating of rockburst based on rough set of FCM algorithm. Rock and Soil Mechanics, 37(3), 859-866 (in Chinese).

[17] He, M. C., & Wang, Q. (2023). Rock dynamics in deep mining. International Journal of Mining Science and Technology, 33(9), 1065-1082.

[18] He, M. C., Xia, H. M., Jia, X. N., Gong, W. L., Zhao, F., & Liang, K. Y. (2012). Studies on classification, criteria and control of rockbursts. Journal of Rock Mechanics and Geotechnical Engineering, 4(2), 97-114.

[19] Herman, J., & Usher, W. (2017). SALib: An open-source Python library for Sensitivity Analysis. Journal of Open Source Software, 2(9), 97.

[20] Jia, Y. P. (2014). Study on prediction method and theorial model of rockburst. ( Publication No. 2 page-130) [Doctoral dissertation, Zhejiang University]. CNKI. (in Chinese).

[21] Jiang, L. F. (2008). Study on prediction and prevention of rockburst in anlu tunnel. (Publication No.12 page-88) [Master’s thesis, Southwest Jiaotong University]. (in Chinese).

[22] Ke, G. L., Meng, Q., Finley, T., Wang, T. F., Chen, W.,Ma, W. D., et al. (2017). LightGBM: A Highly Efficient Gradient Boosting Decision Tree. Paper presented at the 31st Annual Conference on Neural Information Processing Systems (NIPS), Dec 04-09, Long Beach, CA

[23] Khushi, M., Shaukat, K., Alam, T. M., Hameed, I. A., Uddin, S.,Luo, S. H., et al. (2021). A Comparative Performance Analysis of Data Resampling Methods on Imbalance Medical Data. IEEE Access, 9, 109960-109975.

[24] Kingma, D. P., & Welling, M. (2013). Auto-Encoding Variational Bayes. arXiv:1312.6114. Retrieved from https://doi.org/10.48550/arXiv.1312.6114.

[25] LeCun, Y., Bengio, Y., & Hinton, G. (2015). Deep learning. [Review]. Nature, 521(7553), 436-444.

[26] Lee, J., & Jeong, S. (2016). Experimental Study of Estimating the Subgrade Reaction Modulus on Jointed Rock Foundations. Rock Mechanics and Rock Engineering, 49(6), 2055-2064.

[27] Li, D. Y., Liu, Z. D., Armaghani, D. J., Xiao, P., & Zhou, J. (2022). Novel ensemble intelligence methodologies for rockburst assessment in complex and variable environments. [Article]. Scientific Reports, 12 (1), 1-23.

[28] Li, T. Z., Li, Y. X., & Yang, X. L. (2017). Rock burst prediction based on genetic algorithms and extreme learning machine. Journal of Central South University, 24(9), 2105-2113.

[29] Li, X., H., Wang, X. F., Kang, Y., & He, Z. (2005). Artificial neural network for prediction of rockburst in deep-buried long tunnel. In J. Wang, X. Liao & Z. Yi (Eds.), Advances in Neural Networks - Isnn 2005, Pt 3, Proceedings (Vol. 3498, pp. 983-986).

[30] Liang, W. Z., Sari, Y. A., Zhao, G. Y., McKinnon, S. D., & Wu, H. (2021). Probability Estimates of Short-Term Rockburst Risk with Ensemble Classifiers. Rock Mechanics and Rock Engineering, 54(4), 1799-1814.

[31] Lin, S., Liang, Z. L., Zhao, S. X., Dong, M., Guo, H. W., & Zheng, H. (2023). A comprehensive evaluation of ensemble machine learning in geotechnical stability analysis and explainability. [Article; Early Access]. International Journal of Mechanics and Materials in Design.

[32] Liu, B. K., & Lu, W. Z. (2022). Surrogate models in machine learning for computational stochastic multi-scale modelling in composite materials design. International Journal of Hydromechatronics, 5(4), 336-365.

[33] Liu, B. K., Lu, W. Z., Olofsson, T., Zhuang, X. Y., & Rabczuk, T. (2024). Stochastic interpretable machine learning based multiscale modeling in thermal conductivity of Polymeric graphene-enhanced composites. Composite Structures, 327, 117601.

[34] Liu, B. K., Penaka, S. R., Lu, W. Z., Feng, K. L., Rebbling, A., & Olofsson, T. (2023a). Data-driven quantitative analysis of an integrated open digital ecosystems platform for user-centric energy retrofits: A case study in northern Sweden. Technology in Society, 75, 102347.

[35] Liu, B. K., Vu-Bac, N., & Rabczuk, T. (2021). A stochastic multiscale method for the prediction of the thermal conductivity of Polymer nanocomposites through hybrid machine learning algorithms. Composite Structures, 273, 114269.

[36] Liu, B. K., Vu-Bac, N., Zhuang, X. Y., Fu, X. L., & Rabczuk, T. (2022a). Stochastic full-range multiscale modeling of thermal conductivity of Polymeric carbon nanotubes composites: A machine learning approach. Composite Structures, 289, 115393.

[37] Liu, B. K., Vu-Bac, N., Zhuang, X. Y., Fu, X. L., & Rabczuk, T. (2022b). Stochastic integrated machine learning based multiscale approach for the prediction of the thermal conductivity in carbon nanotube reinforced polymeric composites. Composites Science and Technology, 224, 109425.

[38] Liu, B. K., Vu-Bac, N., Zhuang, X. Y., Lu, W. Z., Fu, X. L., & Rabczuk, T. (2023b). Al-DeMat: A web-based expert system platform for computationally expensive models in materials design. Advances in Engineering Software, 176, 103398.

[39] Liu, B. K., Wang, Y. Z., Rabczuk, T., Olofsson, T., & Lu, W. Z. (2023c). Multi-scale modeling in thermal conductivity of Polyurethane incorporated with Phase Change Materials using Physics-Informed Neural Networks. arXiv:2307.16785. Retrieved from https://ui.adsabs.harvard.edu/abs/2023arXiv230716785L. https://doi.org/10.48550/arXiv.2307.16785.

[40] Liu, D. Y., & Liu, G. S. (2019). A Transformer-Based Variational Autoencoder for Sentence Generation. Paper presented at the International Joint Conference on Neural Networks (IJCNN), Jul 14- 19, Budapest, HUNGARY.

[41] Liu, B. K., Vu-Bac, N., Zhuang, X. Y., & Rabczuk, T. (2020). Stochastic multiscale modeling of heat conductivity of Polymeric clay nanocomposites. Mechanics of Materials, 142, 103280.

[42] Liu, R., Ye, Y. C., Zhang, G. Q., Yao, N., Chen, H., & Wang, Q. H. (2019). Grading Prediction Model of Rockburst Based on Rough Set- Multidimensional Normal Cloud. Metal Mine (3), 48-55.

[43] Liu, H. X., Zhao, G. Y., Xiao, P., & Yin, Y. T. (2023). Ensemble Tree Model for Long-Term Rockburst Prediction in Incomplete Datasets. Minerals, 13(1), 103.

[44] Liu, Y. P., Jiang, H. K., Wang, Y. F., Wu, Z. H., & Liu, S. W. (2022). A conditional variational autoencoding generative adversarial networks with self-modulation for rolling bearing fault diagnosis. Measurement, 192, 110888.

[45] Micci-Barreca, D. (2001). A preprocessing scheme for high-cardinality categorical attributes in classification and prediction problems. ACM SIGKDD Explorations Newsletter, 3(1), 27-32.

[46] Mienye, I. D., & Sun, Y. X. (2023). A Deep Learning Ensemble With Data Resampling for Credit Card Fraud Detection. IEEE Access, 11, 30628-30638.

[47] Mirza, B., Haroon, D., Khan, B., Padhani, A., & Syed, T. Q. (2021). Deep Generative Models to Counter Class Imbalance: A Model-Metric Mapping With Proportion Calibration Methodology. IEEE Access, 9, 55879-55897.

[48] Pan, Y. S., & Wang, A. W. (2023). Disturbance response instability theory of rock bursts in coal mines and its application. Geohazard Mechanics, 1(1), 1-17.

[49] Prokhorenkova, L., Gusev, G., Vorobev, A., Dorogush, A. V., & Gulin, A. (2018). CatBoost: unbiased boosting with categorical features. Paper presented at the 32nd Conference on Neural Information Processing Systems (NIPS), Dec 02-08, Montreal, CANADA.

[50] Pu, Y. Y., Apel, D. B., & Xu, H. W. (2019). Rockburst prediction in kimberlite with unsupervised learning method and support vector classifier. Tunnelling and Underground Space Technology, 90, 12-18.

[51] Puh, M., & Brkic, L. (2019). Detecting Credit Card Fraud Using Selected Machine Learning Algorithms. Paper presented at the 42nd International Convention on Information and Communication Technology, Electronics and Microelectronics (MIPRO), May 20-24, Opatija, CROATIA.

[52] Ribeiro, M. T., Singh, S., Guestrin, C., & Aaai. (2018). Anchors: High- Precision Model-Agnostic Explanations. Paper presented at the 32nd AAAI Conference on Artificial Intelligence / 30th Innovative Applications of Artificial Intelligence Conference / 8th AAAI Symposium on Educational Advances in Artificial Intelligence, Feb 02-07, New Orleans, LA.

[53] Rodrigues, A. D. P., Luna, A. S., & Pinto, L. (2023). An evaluation strategy to select and discard sampling preprocessing methods for imbalanced datasets: A focus on classification models. Chemometrics and Intelligent Laboratory Systems, 240, 104933.

[54] Saltelli, Ratto, A., Andres, M., & Campol, T. (2008). Global Sensitivity Analysis. The Primer. Schmidhuber, J. (2015). Deep learning in neural networks: An overview. Neural Networks, 61, 85-117.

[55] Shi, X. Z., Zhou, J., Dong, L., Hu, H. Y., Wang, H. Y., & Chen, S. R. (2010). Application of unascertained measurement model to prediction of classification of rockburst intensity. Chinese Journal of Rock Mechanics and Engineering, 29(S1), 2720-2726 (in Chinese).

[56] Susan, S., & Kumar, A. (2020). The balancing trick: Optimized sampling of imbalanced datasets—A brief survey of the recent State of the Art. Engineering Reports, 3(4), 12298.

[57] Tao, S. T., Peng, P., Li, Y. F., Sun, H. Y., Li, Q., & Wang, H. W. (2024). Supervised contrastive representation learning with tree-structured parzen estimator Bayesian optimization for imbalanced tabular data. Expert Systems with Applications, 237, 121294.

[58] Tasci, E., Zhuge, Y., Camphausen, K., & Krauze, A. V. (2022). Bias and class imbalance in oncologic data-towards inclusive and transferrable ai in large scale oncology data sets. Cancers, 14(12), 2897.

[59] Tholke, P., Mantilla-Ramos, Y. J., Abdelhedi, H., Maschke, C., Dehgan, A.,Harel, Y., et al. (2023). Class imbalance should not throw you off balance: Choosing the right classifiers and performance metrics for brain decoding with imbalanced data. Neuroimage, 277, 120253.

[60] Tian, R. (2021). Research and Application of Rockburst Intensity Classification Prediction Model Based on Machine Learning Algorithm. (Publication No.5 page-143) [Doctoral dissertation, Inner Mongolia University Of Science & Technology]. (in Chinese).

[61] Topuz, B., & Alp, N. C. (2023). Machine learning in architecture. Automation in Construction, 154, 105012.

[62] Wagner, H. (2019). Deep mining: A rock engineering challenge. Rock Mechanics and Rock Engineering, 52(5), 1417-1446.

[63] Wang, C. L., Chen, Z., Liao, Z. F., Hou, X. L., Li, H. T.,Wang, A. W., et al. (2020). Experimental investigation on predicting precursory changes in entropy for dominant frequency of rockburst. Journal of Central South University, 27(10), 2834-2848.

[64] Wang, J., Liu, P., Ma, L., & He, M. C. (2022). A rockburst proneness evaluation method based on ultidimensional cloud model improved by control variable method and rockburst database. Lithosphere, 2021.

[65] Wang, J. C., Ma, H. J., & Yan, X. H. (2023a). rockburst intensity classification prediction based on multi-model ensemble learning algorithms. Mathematics, 11(4), 838.

[66] Wang, Y. T., Wei, Y. X., & Wang, H. (2023b). A class imbalanced wafer defect classification framework based on variational autoencoder generative adversarial network. Measurement Science and Technology, 34(2), 024008.

[67] Waqar, M. F., Guo, S. F., & Qi, S. W. (2023). A comprehensive review of mechanisms, predictive techniques, and control strategies of rockburst. Applied Sciences-Basel, 13(6), 3950.

[68] Xia, B. W. (2007). Study on prediction and forecast of geologic disaster in highway tunned construction. (Publication No.1 page-94) [Master’s thesis, Chongqing University]. (in Chinese).

[69] Xia, Y. Y., Zhang, C., Wang, C. X., Liu, H. J., Sang, X. X., Liu, R., et al. (2023). Prediction of bending strength of glass fiber reinforced methacrylate-based pipeline UV-CIPP rehabilitation materials based on machine learning. Tunnelling and Underground Space Technology, 140, 105319.

[70] Xing, Y., Kulatilake, P., & Sandbak, L. A. (2018). Effect of rock mass and discontinuity mechanical properties and delayed rock supporting on tunnel stability in an underground mine. Engineering Geology, 238, 62-75.

[71] Xu, L. M., Lu, K. X., Pan, Y. S., & Qin, Z. J. (2022). Study on rock burst characteristics of coal mine roadway in China. Energy Sources Part a- Recovery Utilization and Environmental Effects, 44(2), 3016-3035.

[72] Xu, M. G., Du, Z. J., Yao, G. H., & Liu, Z. P. (2008). Rockburst prediction of chengchao iron mine during deep mining. Chinese Journal of Rock Mechanics and Engineering, S1, 2921-2928.

[73] Xue, Y. G., Bai, C. H., Kong, F. M., Qiu, D. H., Li, L. P.,Su, M. X., et al. (2020a). A two-step comprehensive evaluation model for rockburst prediction based on multiple empirical criteria. Engineering Geology, 268, 105515.

[74] Xue, Y. G., Bai, C. H., Qiu, D. H., Kong, F. M., & Li, Z. Q. (2020b). Predicting rockburst with database using particle swarm optimization and extreme learning machine. Tunnelling and Underground Space Technology, 98, 103287.

[75] Xue, Y. G., Li, Z. Q., Li, S. C., Qiu, D. H., Tao, Y. F.,Wang, L., et al. (2019). Prediction of rock burst in underground caverns based on rough set and extensible comprehensive evaluation. Bulletin of Engineering Geology and the Environment, 78(1), 417-429.

[76] Yao, J. M., & He, F. L. (2008). Countermeasure research on preventing rock burst with hard roof by energy mechanism. Paper presented at the International Young Scholars Symposium on Rock Mechanics, Apr 28-May 02, Beijing, Peoples R China.

[77] Yong, T., Reed, P. M., Wagener, T., & Werkhoven, K. V. (2008). Comparison of parameter sensitivity analysis methods for lumped watershed model. Paper presented at the World Environmental & Water Resources Congress.

[78] Zhang, K., Schölkopf, B., Muandet, K., & Wang, Z. (2013). Domain adaptation under target and conditional shift. Paper presented at the Proceedings of the 30th International Conference on International Conference on Machine Learning - Volume 28.

[79] Zhang, L. W., Zhang, D. Y., & Qiu, D. H. (2010). Application of extension evaluation method in rockburst prediction based on rough set theory. Journal of China Coal Society, 35(9), 1461-1465 (in Chinese).

[80] Zhang, L. W., Zhang, X. Y., Wu, J., Zhao, D. K., & Fu, H. (2020). Rockburst prediction model based on comprehensive weight and extension methods and its engineering application. Bulletin of Engineering Geology and the Environment, 79(9), 4891-4903.

[81] Zhang, Y., & Liu, Q. (2022). On IoT intrusion detection based on data augmentation for enhancing learning on unbalanced samples. Future Generation Computer Systems-the International Journal of Escience, 133, 213-227.

[82] Zhang, Y., Su, G. S., & Yan, L. B. (2011). Method of identifying rockburst grades based on gaussian process machine learning. Chinese Journal of Underground Space and Engineering, 7(02), 392-397 (in Chinese).

[83] Zhao, H. B. (2005a). Classification of rockburst using support vector machine. Rock and Soil Mechanics(04), 642-644. (in Chinese).

[84] Zhao, H. B. (2005b). Rockburst prediction using evolutionary support vector machine. Paper presented at the Asia Pacific Symposium on Safety 2005, Nov 02-04, Shaoxing, Peoples R China.

[85] Zhao, H. B., & Chen, B. R. (2020). Data-Driven Model for Rockburst Prediction. Mathematical Problems in Engineering, 2020, 5735496.

[86] Zhao, J., Song, Y., Wang, L., Guo, H., Marigentti, F., & Liu, X. (2023). Forecasting the eddy current loss of a large turbo generator using hybrid ensemble Gaussian process regression. Engineering Applications of Artificial Intelligence, 121, 106022.

[87] Zhao, Y., Nasrullah, Z., & Li, Z. (2019). PyOD: A Python Toolbox for Scalable Outlier Detection. Journal ofMachineLearningResearch,20,96.

[88] Zhou, H., Chen, S. K., Li, H. R., Liu, T., & Wang, H. L. (2021). Rockburst prediction for hard rock and deep-lying long tunnels based on the entropy weight ideal point method and geostress field inversion: A case study of the Sangzhuling Tunnel. Bulletin of Engineering Geology and the Environment, 80(5), 3885-3902.

[89] Zhou, H., Chen, S. K., Zhang, G. Z., Wang, H. L., He, H. D., & Feng, J. (2020a). Efficiency coefficient method and ground stress field inversion for rockburst prediction in deep and long tunnel. Journal of Engineering Geology, 28(06), 1386-1396 (in Chinese).

[90] Zhou, J., Li, X. B., & Mitri, H. S. (2016). Classification of Rockburst in Underground Projects: Comparison of Ten Supervised Learning Methods. Journal of Computing in Civil Engineering, 30(5), 4016003.

[91] Zhou, S., Jia, Y., & Wang, C. (2020b). Global Sensitivity Analysis for the Polymeric Microcapsules in Self-Healing Cementitious Composites. Polymers, 12(12), 2990.

[92] Zhu, H. L., Wu, X., Luo, Y. L., Jia, Y., Wang, C.,Fang, Z., et al. (2023). Prediction of Early Compressive Strength of Ultrahigh-Performance Concrete Using Machine Learning Methods. International Journal of Computational Methods, 20(8), 2141023.

[93] Zhuang, X. Y., & Zhou, S. (2019). The Prediction of Self-Healing Capacity of Bacteria-Based Concrete Using Machine Learning Approaches. Cmc-Computers Materials & Continua, 59(1), 57-77.