Hybrid Data-Driven Polyaxial Rock Strength Meta Model

The accurate evaluation of polyaxial rock strength is important in the mining, geomechanics, and geoengineering fields. In this research, hybrid meta models based on the boosting additive regression (AR) combined with three machine learning (ML) methods are developed for polyaxial rock strength predicting. The ML algorithms used include Gaussian process regression (GP), random tree (RT), and M5P methods. Polyaxial tests for 14 different rocks from published literature are used for assessing these data-oriented based strength criteria. The input variables are minor principal stress and intermediate principal stress data. The modeling is evaluated by coefficient of determination (R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}^{2}$$\end{document}), root mean square error (RMSE), and mean absolute error (MAE) statistical metrics. Results indicated that the hybrid AR-RT model performed superior prediction results (R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}^{2}$$\end{document} = 1, RMSE = 0 MPa, and MAE = 0 MPa) in the training phase and (R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}^{2}$$\end{document} = 0.987, RMSE = 29.771 MPa, and MAE = 22.517 MPa) in the testing phase. The findings of this study indicate that boosting-based additive regression algorithm enhanced developed hybrid models’ performances. Moreover, AR-RT and RT demonstrate promising results and are feasible for modeling polyaxial rock strength prediction. The RT and M5P models visualize variables and their thresholds in a simple and interpretable way. Also, sensitivity analysis indicates that input intermediate principal stress is the most effective parameter on the output polyaxial rock strength. Finally, successful implementation of the probabilistic and interpretable tree-based regressions can capture uncertainty of the model and be an alternative to complicated conventional strength criteria.