Accurately predicting the discharge coefficient (Cd) is fundamental to the hydraulic design and performance of side weirs. In this study, we introduced a novel artificial intelligence (AI) framework to enhance the prediction accuracy of Cd for two-cycle trapezoidal labyrinth side weirs. Using a comprehensive laboratory dataset, three distinct machine learning models (MLMs), Support Vector Machine (SVM), Artificial Neural Network (ANN), and Gene Expression Programming (GEP), were developed and rigorously compared with application of the Γ-test technique for sensitivity analysis, systematically identifying the five most influential geometric and hydraulic parameters (Fr, $ \frac{\text{L}}{\text{B}} $, $ \frac{{\text{L}}_{\text{e}}}{\text{L}} $, $ \frac{{\text{Y}}_{\text{1}}\text{-P}}{\text{P}} $, α) to serve as model inputs. The model's efficacy was evaluated across training, testing, and validation phases using multiple statistical metrics: Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Coefficient of Determination (R2), and the Maximum Developed Discrepancy Ratio (Cd(DDRmax)). The results demonstrated that the three MLMs are effective predictive tools. However, the ANN model, specifically an MLP5-7-1 architecture utilizing Atan and Identity activation functions optimized with the BFGS 385 algorithm, significantly outperformed the others. It achieved superior results (e.g., validation phase: RMSE = 0.0061, MAE = 0.0003, R2 = 0.9301, Cd(DDRmax) = 5.22), confirming its highest predictive accuracy and robustness. This research conclusively shows that MLMs, particularly ANN, offer a highly precise and efficient method for predicting Cd in complex hydraulic structures.
Citation: Mehdi Fuladipanah, Saleema Panda, Namal Rathnayake, Upaka Rathnayake, Hazi Md. Azamathulla, Yukinobu Hoshino. Artificial Intelligence for Hydraulic Engineering: Predicting discharge coefficients in trapezoidal side weirs[J]. Mathematical Biosciences and Engineering, 2025, 22(12): 3236-3261. doi: 10.3934/mbe.2025119
Accurately predicting the discharge coefficient (Cd) is fundamental to the hydraulic design and performance of side weirs. In this study, we introduced a novel artificial intelligence (AI) framework to enhance the prediction accuracy of Cd for two-cycle trapezoidal labyrinth side weirs. Using a comprehensive laboratory dataset, three distinct machine learning models (MLMs), Support Vector Machine (SVM), Artificial Neural Network (ANN), and Gene Expression Programming (GEP), were developed and rigorously compared with application of the Γ-test technique for sensitivity analysis, systematically identifying the five most influential geometric and hydraulic parameters (Fr, $ \frac{\text{L}}{\text{B}} $, $ \frac{{\text{L}}_{\text{e}}}{\text{L}} $, $ \frac{{\text{Y}}_{\text{1}}\text{-P}}{\text{P}} $, α) to serve as model inputs. The model's efficacy was evaluated across training, testing, and validation phases using multiple statistical metrics: Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Coefficient of Determination (R2), and the Maximum Developed Discrepancy Ratio (Cd(DDRmax)). The results demonstrated that the three MLMs are effective predictive tools. However, the ANN model, specifically an MLP5-7-1 architecture utilizing Atan and Identity activation functions optimized with the BFGS 385 algorithm, significantly outperformed the others. It achieved superior results (e.g., validation phase: RMSE = 0.0061, MAE = 0.0003, R2 = 0.9301, Cd(DDRmax) = 5.22), confirming its highest predictive accuracy and robustness. This research conclusively shows that MLMs, particularly ANN, offer a highly precise and efficient method for predicting Cd in complex hydraulic structures.
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Figures(6) / Tables(6)
Mehdi Fuladipanah, Saleema Panda, Namal Rathnayake, Upaka Rathnayake, Hazi Md. Azamathulla, Yukinobu Hoshino. Artificial Intelligence for Hydraulic Engineering: Predicting discharge coefficients in trapezoidal side weirs[J]. Mathematical Biosciences and Engineering, 2025, 22(12): 3236-3261. doi: 10.3934/mbe.2025119
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