Estimation of the Discharge Coefficient of a Lateral Piano Key Weir in Bends of Erodible Channels Using Artificial Intelligence and Support Vector Machine
Department of Water Engineering, Faculty of Agricultural Technology (Aburaihan), College of Agriculture and Natural Resources, University of Tehran, Tehran, Iran.
Abstract Lateral weirs are widely used in open channels to divert excess discharge and, in some cases, serve as protective hydraulic structures upstream of facilities such as inverted siphons. In recent years, Piano Key Weirs (PKWs) have attracted considerable attention from researchers due to their superior hydraulic performance. In this study, Gene Expression Programming (GEP) and Support Vector Machine (SVM) models were employed as intelligent approaches to estimate the discharge coefficient of lateral Piano Key Weirs located in bends of erodible channels. The predicted results were evaluated against experimental data. Subsequently, five different models were developed based on various combinations of the dimensionless parameters affecting the discharge coefficient. The performance of the models was assessed using the coefficient of determination (R²), root mean square error (RMSE), and mean absolute relative error (MARE). The results indicated that the SVM model incorporating all dimensionless parameters achieved the best performance, with an R² of 0.92 and an RMSE of 0.157. In contrast, the highest accuracy for the GEP model was obtained when all parameters except the ratio of sediment particle size to flow depth were considered, yielding an R² of 0.96 and an RMSE of 0.06. Overall, based on the prediction errors, the SVM model demonstrated superior performance to the GEP model in estimating the discharge coefficient of lateral Piano Key Weirs.
Mikaeeli, H., Jamshidi, M. & Soltani, J. (2026). Estimation of the Discharge Coefficient of a Lateral Piano Key Weir in Bends of Erodible Channels Using Artificial Intelligence and Support Vector Machine. International Journal of Nonlinear Analysis and Applications, (), 1–11. https://doi.org/10.22075/ijnaa.2026.42201.5763
MLA
Mikaeeli, H., Jamshidi, M., & Soltani, J. "Estimation of the Discharge Coefficient of a Lateral Piano Key Weir in Bends of Erodible Channels Using Artificial Intelligence and Support Vector Machine", International Journal of Nonlinear Analysis and Applications, , 2026, 1–11. doi: 10.22075/ijnaa.2026.42201.5763
HARVARD
Mikaeeli, H., Jamshidi, M., & Soltani, J. (2026). 'Estimation of the Discharge Coefficient of a Lateral Piano Key Weir in Bends of Erodible Channels Using Artificial Intelligence and Support Vector Machine', International Journal of Nonlinear Analysis and Applications, (), pp. 1–11. doi: 10.22075/ijnaa.2026.42201.5763
CHICAGO
Mikaeeli, H., Jamshidi, M. & Soltani, J., "Estimation of the Discharge Coefficient of a Lateral Piano Key Weir in Bends of Erodible Channels Using Artificial Intelligence and Support Vector Machine." International Journal of Nonlinear Analysis and Applications, (2026): 1–11, doi: 10.22075/ijnaa.2026.42201.5763
VANCOUVER
Mikaeeli H., Jamshidi M., Soltani J. Estimation of the Discharge Coefficient of a Lateral Piano Key Weir in Bends of Erodible Channels Using Artificial Intelligence and Support Vector Machine. IJNAA. 2026;():1–11. doi: 10.22075/ijnaa.2026.42201.5763
International Journal of Nonlinear Analysis and Applications