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<p>A major challenge in the geotechnical design of retaining structures is accurately predicting the depth of sheet pile embedment in heterogeneous soils. This study proposes a set of accurate and reliable predictive models by integrating random forest (RF) with four metaheuristic optimization techniques: particle swarm optimization (PSO), biogeography-based optimization (BBO), gray wolf optimization (GWO), and Harris hawks optimization (HHO). A total of 500 data points involving four variables, including the unit weight of the sand (Y<sub>1</sub>), angle of internal friction of the sand (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\phi_1\)</EquationSource> </InlineEquation>), unit weight of <b>the</b> clay (Y<sub>2</sub>), and the undrained shear strength of the clay (c<sub>2</sub>), which is often expressed as cohesion under undrained conditions are considered. The developed RF-HHO model outperforms the other models, with coefficients of determination (R<sup>2</sup>) values of 0.9968 for training, 0.9964 for validation and 0.9957 for testing datasets. Uncertainty analysis and external validation also confirmed the reliability and prediction accuracy of the RF-HHO model. The feature importance analysis reveals that ​c<sub>2</sub> is the most significant parameter, contributing 1.75 and 0.298 to the performance degradation and mean SHAP value, respectively. The developed GUI for the optimal hybrid model minimizes the reliance on iterative calculations and complex analyses, providing a practical and robust tool for geotechnical engineering.</p>

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Hybrid Random Forest Advanced Machine Learning with Nature-Inspired Optimization Approaches for Predicting the Embedment Depth of Cantilever Sheet Piles

  • 期刊论文

  • 发表日期：

    2026年2月21日

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  • Chaiyathawat Boonyong,
  • Warit Wipulanusat,
  • Suraparb Keawsawasvong

摘要

A major challenge in the geotechnical design of retaining structures is accurately predicting the depth of sheet pile embedment in heterogeneous soils. This study proposes a set of accurate and reliable predictive models by integrating random forest (RF) with four metaheuristic optimization techniques: particle swarm optimization (PSO), biogeography-based optimization (BBO), gray wolf optimization (GWO), and Harris hawks optimization (HHO). A total of 500 data points involving four variables, including the unit weight of the sand (Y1), angle of internal friction of the sand ( \(\phi_1\) ), unit weight of the clay (Y2), and the undrained shear strength of the clay (c2), which is often expressed as cohesion under undrained conditions are considered. The developed RF-HHO model outperforms the other models, with coefficients of determination (R2) values of 0.9968 for training, 0.9964 for validation and 0.9957 for testing datasets. Uncertainty analysis and external validation also confirmed the reliability and prediction accuracy of the RF-HHO model. The feature importance analysis reveals that ​c2 is the most significant parameter, contributing 1.75 and 0.298 to the performance degradation and mean SHAP value, respectively. The developed GUI for the optimal hybrid model minimizes the reliance on iterative calculations and complex analyses, providing a practical and robust tool for geotechnical engineering.