Document Type : Original Article

Authors

• Sasan Nejati ¹
• Mehdi Meftah halaghi ²
• Abdolreza Zahiri ³
• Younes Aminpour ⁴

¹ Ph.D Student of Water Structures,, Department of Water Engineering, Gorgan University of Agricultural Sciences and Natural Resources, Gorgan, Iran

² Water Eng. Department of water and soil Eng., Gorgan university of agricultural science and natural resources, Gorgan, Iran

³ Department of Water Engineering, Gorgan University of Agricultural Sciences and Natural Resources, Gorgan, Iran.

⁴ Department of Hydraulic Structures, Water Research Institute, Ministry of Energy, Tehran, Iran.

Abstract

Introduction
This study investigates scour downstream of triangular–triangular compound weirs, which generate unique flow patterns leading to increased turbulence and scour. Initially, laboratory experiments were conducted to identify key influencing factors, followed by dimensional analysis to determine relevant dimensionless parameters. Three artificial intelligence algorithms Artificial Neural Network (ANN), Adaptive Neuro-Fuzzy Inference System (ANFIS), and Support Vector Machine (SVM) were then used to perform sensitivity analysis and predict scour depth. The research enables a comparative evaluation of these models in predicting complex hydraulic phenomena.

Methodology
This study examines the scouring phenomenon downstream of triangular-triangular compound weirs using experimental methods and artificial intelligence models. The investigated weir was constructed by combining two triangular sections with angles of 90° and 150°, installed in a 6.7-meter long and 90-centimeter wide experimental flume at the Water Research Institute of the Ministry of Energy. Tests were conducted with four different flow rates ranging from 7.08 to 54.94 liters per second using sediments with an average diameter of 0.5 mm. The scouring profile was analyzed through digital imaging and Grapher software.
For the modeling section, four artificial intelligence methods were employed to predict scouring hole dimensions: ANN, ANFIS and SVM. These models were selected for their capability to identify nonlinear relationships and complex patterns in data, with their performance evaluated using RMSE, Nash-Sutcliffe efficiency (NS), and MARE metrics. This study provides a framework for comparing various AI methods in hydraulic problems and can contribute to improving the design of hydraulic structures.

Results and Discussion
Given the complex and uncertain nature of scour phenomena in slope control structures, as evidenced by previo research and the significant errors in conventional models, this study employed AI approaches (ANN, ANFIS and SVM) that require less understanding of underlying physical mechanisms. A Comprehensive sensitivity analysis was first conducted on dimensionless input parameters (Fr_D, t/t₀, and y_tw/y_h), with all algorithms implemented in MATLAB and Python. The models were trained on 70% of experimental data and tested on 30%, while a thorough parameter sensitivity analysis was performed across all four models to enhance prediction accuracy of scour hole dimensions.
In the ANN modeling approach, a sensitivity analysis of input parameters was conducted by varying each input by ±10% to evaluate their relative influence on scour hole dimensions. The results revealed that the particle Froude number had the greatest impact (45%) on maximum scour depth, while t/t₀ significantly affected scour hole length (32%). The SVM model's sensitivity analysis showed that the particle Froude number had the highest average influence (55%), whereas y_tw/y_h had the least (10%). Similarly, ANFIS analysis indicated the particle Froude number's dominant effect (62% average) with y_tw/y_h again showing minimal impact. Comparative evaluation of error metrics demonstrated that the SVM model outperformed the other proposed methods, exhibiting superior accuracy and performance in predicting scour characteristics.
Conclusions
This study aimed to evaluate the performance of artificial intelligence models in predicting the dimensions of the scour hole downstream of a triangular–triangular compound weir, based on laboratory data. Three AI models: Artificial Neural Network (ANN), Adaptive Neuro-Fuzzy Inference System (ANFIS), and Support Vector Machine (SVM) were assessed. The results showed that all three models were capable of estimating key scour parameters, but the SVM model outperformed the others in terms of higher accuracy, lower relative error, and better agreement with experimental data.  From a hydraulic perspective, the findings indicated that the particle Froude number was one of the most influential parameters on scour dimensions. As the Froude number increases, both the maximum scour depth and scour hole length significantly increase, highlighting the critical role of flow energy in scour development downstream of compound weirs. The results also showed that under concentrated flow conditions and with increasing relative time, the scour hole continued to expand, indicating a progressive development process. Based on these results, it is recommended that in the design of compound weirs especially triangular–triangular types the effects of the Froude number and inflow conditions should be carefully considered to prevent the formation of deep scour holes. Furthermore, the SVM model, as a precise predictive tool, can assist hydraulic structure designers in evaluating scour risk and implementing appropriate protective measures (e.g., protective aprons, stepped profiles, or more resistant materials) before construction. These findings can contribute to improving the safety of hydraulic structures, reducing scour-related damage, and optimizing future designs.

Keywords

• Sensitivity analysis
• Particle Froude number
• Experimental data
• Nash-Sutcliffe efficiency (NS)
• Neural network

Main Subjects

• Hydraulic