Comparison of Channel Geometry Effects on Discharge Coefficient of Rectangular Side Weirs in Rectangular and Trapezoidal Channels Using Optimized Machine Learning Models
Subject Areas : Application of computer in water and soil issues
Kiyoumars Roushangar
1
*
,
Aydin Panahi
2
1 - Professor, Department of Water Resources Engineering, Faculty of Civil Engineering, University of Tabriz, Tabriz, Iran.
2 - Ph.D. student, Department of Water Resources Engineering, Faculty of Civil Engineering, University of Tabriz, Tabriz, Iran.
Keywords: Discharge coefficient, Machine learning, Meta-heuristic algorithms, Sensitivity analysis, Side weir,
Abstract :
Introduction: Side weirs play a key role in flow measurement and control in hydraulic systems, especially in flood mitigation and runoff management projects. Accurate estimation of the discharge coefficient (Cd) has become a critical technical challenge due to the complex interactions between flow dynamics and channel geometry. This study introduces, for the first time, two novel hybrid models—SVM-HOA and SVM-RSA—based on SVM optimized by the Horse Optimization Algorithm and Reptile Search Algorithm, respectively. These models are applied to predict the geometry-specific discharge coefficient of sharp-crested rectangular side weirs in both rectangular and trapezoidal channel configurations.
Method: The proposed methodology involves two experimental scenarios. Scenario 1 includes 407 laboratory observations of sharp-crested rectangular side weirs located in rectangular channels, whereas Scenario 2 consists of 78 observations in trapezoidal channels. Dimensional analysis was first conducted to identify the most influential nondimensional parameters, including Fr1, P/y1, L/B, L/y1, y1/B, and m. These parameters served as inputs for training the SVM models. Each hybrid model was implemented by optimizing the SVM hyperparameters using the HOA and RSA metaheuristic algorithms, aiming to avoid local minima and enhance prediction accuracy. The dataset was split into training and testing subsets in a ratio: 80:20. To mitigate overfitting, 10-fold cross-validation was applied. Model performance was evaluated using standard statistical metrics: Root Mean Square Error (RMSE), Nash–Sutcliffe Efficiency (NSE), and correlation coefficient (R). Additionally, sensitivity analysis was conducted to assess the influence of each input variable on the final prediction.
Results: Results of the comparative evaluation showed that both SVM-HOA and SVM-RSA yielded high accuracy in predicting Cd for both channel configurations. In Scenario 1 (rectangular channel), With inputs such as the ratio of the spillway height to the initial flow depth (P/y1), the ratio of the spillway crest length to the channel bottom width (L/B), the ratio of the crest length to the flow depth (L/y1), and the upstream Froude number, the best-performing model was SVM-HOA with R = 0.953, RMSE = 0.063, and NSE = 0.904 during the testing phase. In Scenario 2 (trapezoidal channel), the optimal model also used SVM-HOA With inputs L/B, Fr1, y1/B and channel wall slope (m) and achieved R = 0.986, RMSE = 0.020, and NSE = 0.964. Taylor diagrams confirmed the robustness and higher predictive power of the SVM-HOA model compared to SVM-RSA. Sensitivity analysis revealed that in the rectangular channel setup, the P/y1 ratio was the most influential input, while in the trapezoidal channel, the upstream Froude number (Fr1) played the dominant role in determining Cd. The findings underscore the importance of accounting for geometry-specific variables and selecting appropriate optimization algorithms to fine-tune ML models for hydraulic applications.
Conclusions: This study presents a novel and geometry-aware approach to accurately predicting the discharge coefficient of sharp-crested rectangular side weirs using two advanced hybrid SVM-based models. The proposed SVM-HOA and SVM-RSA frameworks demonstrated consistently high accuracy, excellent adaptability to different channel geometries, and strong robustness against overfitting and local minima. Results indicate that SVM-HOA significantly outperforms SVM-RSA in most cases, particularly when paired with well-chosen nondimensional parameters and a properly tuned training-testing data split. The models developed in this work can effectively assist hydraulic engineers in the design, simulation, and performance analysis of side weirs under diverse flow conditions and channel types.
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