Determination of the stress concentration factor adjacent an extracted underground coal panel using the CART and MARS algorithms

Abstract

In this study, classification and regression tree (CART) and multivariate adaptive regression spline (MARS) models are proposed to predict the stress concentration factor (SCF) around an extracted underground coal panel. Models are trained and tested using 120 collected datasets with 100 series allocated for models training and 20 datasets reserved for testing. For SCF prediction using the CART and MARS models, input parameters including overburden thickness (H), specific gravity of rock mass (γ), straight distance from the panel edge (D), and height of disturbed zone over the mined panel (H_d) are utilized, employing principal component analysis (PCA) to remove correlations. A predictive tree graph and 17 if–then rules with quantitative outputs are generated from the CART model, while a predictive equation is derived from the MARS technique for SCF prediction. The achieved values of the coefficient of determination (R²) for CART and MARS models are 0.940 and 0.957, respectively. Furthermore, obtained amounts of normalized root mean square error (NRMSE), variant account for (VAF), and performance index (PI) for CART are 0.043 92.473%, and 1.82, respectively. For the MARS model these values are 0.035, 95.419%, and 1.876,. Additionally, performance evaluations of the models using the Wilcoxon Signed Ranks and Friedman non-parametric tests, along with Taylor diagrams and error analysis demonstrate the reliability and suitability of the proposed models for SCF prediction. However, error and accuracy analyses confirm that MARS model yields more precise outputs, achieving 2.57% greater accuracy and 10.84% lower error than the CART model. Furthermore, the importance analysis demonstrated that both H and H_d have the highest importance on the SCF, while γ has the lowest, with importance values of 33.33% and 11.11%, respectively. Models verification based on the field SCF measurement confirms the models validity, as indicated by the relative errors of 6.83 for the MARS model and 7.05 for the CART model. Finally, a comparative analysis based on a case study data validates the practical application of the proposed models.