JWSS - Journal of Water and Soil Science

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Kalantar hormozi S, Zayeri M, Ghomeshi M, ِDaryaee M. Evaluation of a Hybrid Meta-Learning Model for Estimating Scour Depth Around Pile Groups. jwss 2026; 30 (2) :57-77
URL: http://jstnar.iut.ac.ir/article-1-4539-en.html

Scour is a major challenge in river engineering, as it causes bridge failures during flood events and leads to significant economic losses. This study aims to estimate the normalized scour depth (Dse/Dp) around pile groups by examining relevant hydrodynamic and geometric parameters. A dataset comprising 299 laboratory measurements collected from various sources was assembled and divided into training and testing subsets. As machine learning inputs, several models were employed, including Artificial Neural Networks (ANN), Support Vector Regression (SVR), Extreme Gradient Boosting (XGBoost), and a meta-ensemble learning model (Stacking). Hyperparameter tuning was performed using the Grid search method to achieve optimal regression performance. Model performance evaluation indicated that the ANN and SVR models achieved coefficients of determination of R² = 0.87 and R² = 0.91, respectively. The XGBoost model outperformed these approaches, yielding R² = 0.94 with an RMSE of approximately 0.28. Ultimately, the stacking ensemble model, by integrating the outputs of the base learners, demonstrated the highest predictive accuracy with R² = 0.96 and an RMSE of 0.11, representing an improvement of approximately 15% compared to ANN and 7% compared to XGBoost. Overall, the findings highlight that ensemble machine learning models—particularly the Stacking approach—provide a robust and efficient framework for predicting scour depth around pile groups and for capturing the complex flow behaviors in hydraulic systems.