Machine learning-based discharge coefficient estimation in trapezoidal-arched labyrinth weirs

Weirs represent a frequently employed mechanism for regulating water surface elevations and managing flow within canals and hydraulic infrastructures. Among these, labyrinth weirs constitute a distinctive variant capable of accommodating a specific discharge while maintaining a reduced upstream water level compared to conventional linear weirs. The present investigation delved into the evaluation of the effectiveness of multilayer perceptron (MLP) networks, support vector machine (SVM), gene expression programming (GEP), and multivariate adaptive regression splines (MARS), aiming to predict the discharge coefficient (C_d) of a trapezoidal-arched labyrinth weir with an expanded central cycle. A dataset including 108 laboratory observations was utilized. The dimensionless parameters were obtained from the parameters including inside apex width of the middle cycle (w₁), inside apex width of the end cycles (w₂), weir height on the upstream side (B), unsubmerged total upstream head on the weir (H_d), and gravitational acceleration (g). The model was developed with the dimensionless parameters and C_d. Root mean square error (RMSE), determination coefficient (R²), mean absolute error (MAE), and developed discrepancy ratio (DDR) were used as performance assessment criteria. Based on these metrics, all four models exhibited the latent capacity to predict the C_d value. However, the MLP model demonstrated superior performance among the models during both training (RMSE = 0.024, MAE = 0.020, R² = 0.816, and C_d[DDRmax] = 8.07) and testing (RMSE = 0.011, MAE = 0.006, R² = 0.688, and C_d[DDRmax] = 11.32) phases. Sequentially, the subsequent standings were secured by the SVM, GEP, and MARS. MLP outperformed SVM, GEP, and MARS models in predicting C_d, achieving the highest R² and lowest RMSE/MAE values.