Document Type : Research Paper

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Introduction

Semi-circular side weirs are crucial hydraulic structures designed for diverting and regulating flow in open channel systems. These structures are widely applied in irrigation networks, stormwater drainage, and treatment facilities. One of the key parameters for evaluating the hydraulic performance of side weirs is the discharge coefficient (C_d), which plays a vital role in estimating flow profiles and managing water resources effectively. Although several empirical and theoretical models have been proposed for estimating C_d, their performance is often limited by specific experimental conditions and a lack of generalizability.

Recent advancements in soft computing and machine learning have provided powerful tools for capturing complex, nonlinear relationships in hydraulic phenomena. In this context, this study introduces and evaluates two novel hybrid models that combine Support Vector Machine (SVM) regression with Horse Optimization Algorithm (HOA) and Reptile Search Algorithm (RSA) to enhance the prediction accuracy of C_d in sharp-crested semi-circular side weirs.

Method

A total of 212 experimental data points were compiled from two previous studies under subcritical flow regimes. The predictive models were developed using key dimensionless input variables derived through Buckingham Pi theorem, including ratios such as h₁/D, P/B, and Fr₁. The data were randomly split into training (80 percent) and testing (20 percent) sets, and a 10-fold cross-validation approach was applied to minimize overfitting. SVM models were optimized using HOA and RSA algorithms, which aimed to find the best hyperparameters for the regression process by minimizing RMSE.

The HOA algorithm mimics the social behavior of horse herds in search and exploration, while RSA draws inspiration from crocodile hunting behavior. Each optimization algorithm was applied independently to train the SVM model, and their performance was compared based on three key statistical indices: R², RMSE, and NSE.

Results

The results show that the SVM-HOA model consistently outperformed SVM-RSA in most scenarios. The best performance was observed in scenario SC5, where SVM-HOA achieved NSE = 0.887, RMSE = 0.025, and R² = 0.899, indicating a high level of prediction accuracy. Sensitivity analysis revealed that the ratio of upstream flow depth over the weir crest to the weir diameter (h₁/D) and the ratio of weir crest height to channel width (P/B) were the most influential parameters for accurate prediction. The Taylor diagram and comparative scatter plots further confirmed the superiority of SVM-HOA in both training and testing phases.

Conclusions

This study demonstrates that hybrid SVM models enhanced with HOA and RSA significantly improve the prediction of discharge coefficients in semi-circular side weirs. The SVM-HOA model, in particular, outperformed its counterpart across all evaluation metrics, showcasing better generalization and resistance to overfitting. Given the complexity and nonlinearity of hydraulic flow behavior, such intelligent models can serve as reliable tools in practical hydraulic engineering. Future work should explore the applicability of these models under submerged and supercritical flow conditions and investigate other advanced AI algorithms for further refinement.

Author Contributions

Kiomars Roshangar: Project management, study design, and result interpretation. Aydin Panahi: Methodology development, data analysis, and manuscript drafting. Arman Alizadeh Sadeghiani: Data collection and manuscript review. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Data used in this study are available from the corresponding author upon request.

Ethical considerations

The authors avoided data fabrication, falsification, plagiarism, and misconduct

Conflict of Interest

The authors declare no conflicts of interest related to this work.