<p>This research employs conventional and optimized extreme gradient boosting (XGBoost) models to predict the end-bearing capacity (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\:{N}_{\sigma\:}\)</EquationSource> </InlineEquation>) of rock-socketed shafts. The arithmetic optimization (AOA), brainstorm optimization (BOA), and whale optimization (WOA) algorithms were used to optimize the XGBoost model. To conduct this research, a database of the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\:{N}_{\sigma\:}\)</EquationSource> </InlineEquation> of 151 rock-socketed shafts was compiled from the literature. The database (mentioned by O_Data) was preprocessed, and the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\:{N}_{\sigma\:}\)</EquationSource> </InlineEquation> of the 136 rock-socketed shafts was obtained. The Gaussian-noise technique was employed to create a synthetic database based on the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\:{N}_{\sigma\:}\)</EquationSource> </InlineEquation> of 136 rock-socketed shafts. A database of the <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\:{N}_{\sigma\:}\)</EquationSource> </InlineEquation> of 500 rock-socketed shafts was generated and preprocessed. The <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\:{N}_{\sigma\:}\)</EquationSource> </InlineEquation> of 460 rock-socketed shafts (136 original + 324 synthetic after preprocessing datasets) developed a second database (mentioned by OS_Data). The XGBoost, XGBoost_AOA, XGBoost_BOA, and XGBoost_WOA models were trained and tested using both databases. The performance analysis revealed that the XGBoost model estimated the <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\:{N}_{\sigma\:}\)</EquationSource> </InlineEquation> with a root mean square error (RMSE) of 0.9205, mean absolute error of (MAE) of 0.7024, and a performance (R) of 0.9295 using the O_Data. Later, the performance of the XGBoost_AOA model was enhanced to 0.9894 using the OS_Data. It was also observed that OS_Data improved generalizability and reduced overfitting in the XGBoost_AOA model. Moreover, the multicollinearity analysis revealed that the rock mass rating (RMR) and geological strength index (GSI) exhibit problematic multicollinearity. In addition, the sensitivity analysis demonstrated that the RMR and GSI features have contributions of 20.301% and 20.369%, respectively, in estimating <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\:{N}_{\sigma\:}\)</EquationSource> </InlineEquation>. For the first time, this research mapped a relationship between feature multicollinearity and sensitivity to analyze the overfitting of the soft computing models. Moreover, SHapley Additive exPlanations (SHAP) analysis identified compressive strength and rock mass rating as dominant predictors (0.65–1.36), while the geological strength index showed minimal influence (< 0.10). Finally, this research provides a Graphical User Interface application to help the geotechnical engineers and designers estimate the <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\:{N}_{\sigma\:}\)</EquationSource> </InlineEquation>.</p>

Improving end-bearing capacity prediction of rock-socketed shafts using Gaussian-augmented optimized extreme gradient boosting models

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2026年2月7日

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Jitendra Khatti,
Yewuhalashet Fissha,
N.Rao Cheepurupalli

摘要

This research employs conventional and optimized extreme gradient boosting (XGBoost) models to predict the end-bearing capacity ( \(\:{N}_{\sigma\:}\) ) of rock-socketed shafts. The arithmetic optimization (AOA), brainstorm optimization (BOA), and whale optimization (WOA) algorithms were used to optimize the XGBoost model. To conduct this research, a database of the \(\:{N}_{\sigma\:}\) of 151 rock-socketed shafts was compiled from the literature. The database (mentioned by O_Data) was preprocessed, and the \(\:{N}_{\sigma\:}\) of the 136 rock-socketed shafts was obtained. The Gaussian-noise technique was employed to create a synthetic database based on the \(\:{N}_{\sigma\:}\) of 136 rock-socketed shafts. A database of the \(\:{N}_{\sigma\:}\) of 500 rock-socketed shafts was generated and preprocessed. The \(\:{N}_{\sigma\:}\) of 460 rock-socketed shafts (136 original + 324 synthetic after preprocessing datasets) developed a second database (mentioned by OS_Data). The XGBoost, XGBoost_AOA, XGBoost_BOA, and XGBoost_WOA models were trained and tested using both databases. The performance analysis revealed that the XGBoost model estimated the \(\:{N}_{\sigma\:}\) with a root mean square error (RMSE) of 0.9205, mean absolute error of (MAE) of 0.7024, and a performance (R) of 0.9295 using the O_Data. Later, the performance of the XGBoost_AOA model was enhanced to 0.9894 using the OS_Data. It was also observed that OS_Data improved generalizability and reduced overfitting in the XGBoost_AOA model. Moreover, the multicollinearity analysis revealed that the rock mass rating (RMR) and geological strength index (GSI) exhibit problematic multicollinearity. In addition, the sensitivity analysis demonstrated that the RMR and GSI features have contributions of 20.301% and 20.369%, respectively, in estimating \(\:{N}_{\sigma\:}\) . For the first time, this research mapped a relationship between feature multicollinearity and sensitivity to analyze the overfitting of the soft computing models. Moreover, SHapley Additive exPlanations (SHAP) analysis identified compressive strength and rock mass rating as dominant predictors (0.65–1.36), while the geological strength index showed minimal influence (< 0.10). Finally, this research provides a Graphical User Interface application to help the geotechnical engineers and designers estimate the \(\:{N}_{\sigma\:}\) .