Document Type : Original Article
Authors
1 Masters Student in Hydroinformatics, Faculty of Water and Environmental Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
2 Assistant Professor, Department of Hydraulic Structures, Faculty of Water and Environmental Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran
3 Professor, Department of Hydraulic Structures, Faculty of Water and Environmental Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
4 Associate Professor, Department of Water Structures, Faculty of Water and Environmental Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
Abstract
Extended Abstract
Introduction
Dams, as barriers constructed across rivers, are comprised of essential components such as the body, spillway, and drainage systems. Various labyrinth spillway designs, including triangular, trapezoidal, circular, and polygonal horizontal layouts, extend the effective flow path over a fixed width compared to linear spillways. Researchers aim to identify optimal designs balancing high performance and cost-efficiency. Recent advancements highlight the integration of optimization methods and computational fluid dynamics (CFD) to improve labyrinth spillway designs. Studies have explored the hydraulic and geometric factors affecting discharge coefficients (Cd) and flow velocity. Research includes the application of artificial intelligence (AI) models such as artificial neural networks (ANNs), adaptive neuro-fuzzy inference systems (ANFIS), and regression techniques to predict Cd. Notable contributions demonstrate that AI models effectively capture complex nonlinear relationships between geometric parameters and flow rates, outperforming traditional methods. For instance, models like support vector machines (SVM) and adaptive regression spline (MARS) have demonstrated high accuracy in predicting Cd.
Despite advancements, precise predictive models for labyrinth spillways with harmonic plans remain underdeveloped. This study addresses this gap by introducing new methodologies, including SVM, random forests (RF), and MARS, to predict Cd. It also quantifies the influence of dimensionless parameters on Cd, synthesizing experimental data to enhance understanding and bridge existing research gaps.
Methodology
In this study, soft computing models were developed using experimental results from Arham Namazi and Mozaffari (2023) and Yıldız et al. (2024). To evaluate the accuracy of proposed soft computing equations in estimating the discharge coefficient (Cd) for circular labyrinth weirs arranged harmonically in open channels, the following experimental data were utilized: Yıldız et al. (2024): conducted 215 experiments for weirs with three different heights (P = 20 cm, P = 30 cm, and P = 40 cm) and three different cycle numbers (N = 2, N = 3, and N = 4). Arham Namazi and Mozaffari (2023): performed 18 experiments with a fixed weir height (P = 15 cm) configured as a single cycle (N = 1).
In total, 233 experimental results were collected for soft computing-based modeling. Among these, 175 samples (75%) were used for model training, and 58 samples (25%) were allocated for testing the developed models.
Results and Discussion
Violin plots for both measured and predicted data inferred by various machine learning models are presented. Violin plots are typically used to compare the distribution of data across different groups in terms of their shape. Additionally, a small box plot is embedded within each violin plot, where the ends of the rectangle represent the first and third quartiles, and the central point denotes the median. it can be observed that all three models—RF, SVM, and MARS—predict similar first and third quartiles and medians, compared to the measured data. In contrast, the first or third quartiles in the equations proposed by Arham Namazi and Mozaffari (2023) and Equation 18 show significant deviations from the measured values. Furthermore, from the perspective of the overall data distribution, the SVM and MARS algorithms demonstrate distributions more similar to the measured data compared to the RF algorithm. This highlights the superior predictive capability of the support vector machine (SVM) approach.
Conclusions
Labyrinth weirs are consistently proposed as an effective solution for enhancing flood discharge efficiency, particularly in cases where space for weir construction is limited. These weirs have a longer crest length compared to linear weirs, allowing floods to pass at shallower depths. Due to the complex relationship between the discharge coefficient and its associated parameters, empirical equations often fail to predict the discharge coefficient with acceptable accuracy.
In this study, three different machine learning models were developed to predict the discharge coefficient of semicircular labyrinth weirs with harmonic designs. The results confirm the advantages of the Support Vector Machine (SVM) algorithm. Key findings of the study are summarized as follows:
Parameter Sensitivity Analysis: To minimize prediction errors in the machine learning models, a sensitivity analysis was conducted to identify the relative head is importance of different input parameters. Based on this analysis, five input combinations were designed and applied to the machine learning models.
Optimal Input Combination: Statistical comparisons between predicted and experimental data revealed that the optimal input combination effectively predicted the discharge coefficient for this type of weir.
Model Performance: Using the best input combination, the results showed that the SVM and MARS algorithms outperformed tree-based models, such as Random Forest (RF), in prediction accuracy for harmonic weirs with varying cycles.
MARS Model Evaluation: Although the MARS model performed well, comparisons with other regression models from previous studies demonstrated that MARS delivered satisfactory and improved accuracy over those models.
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