Journal of Hydraulic Structures

Journal of Hydraulic Structures

Enhancing Clear-Water General Scour Depth Estimation at Long Channel Contractions: Integrating a Multi-Kernel Relevance Vector Machine Model with a Hybrid Optimization Approach

Articles in Press

Document Type : Research Paper

Authors
Elham Ghanbari-Adivi 1
Nariman Mehranfar 2
Mohammad khosravi-hamouleh 3
1 Department of Water Engineering, Shahrakord University, Shahrakord, Iran; Associate Professor, Water Research Center, Shahrekord University, Shahrekord, Iran.
2 Department of Civil, Mining and Geology, Faculty of Polytechnique, Montreal University, Quebec, Canada.
3 Department of Water Engineering, Shahrakord University, Shahrakord, Iran.
10.22055/jhs.2026.52378.1386
Abstract
Scour is a critical phenomenon in hydraulic engineering that can have different consequences for hydraulic structures depending on the depth. Therefore, this study focuses on the accurate estimation of general scour depth at long channel contractions under clear-water flow conditions, which is an important issue in hydraulic engineering. In the first step, a new estimation model called the multi-kernel relevance vector machine model (MKRVM) was developed. The MKRVM model combined sigmoid kernel function (SKF), polynomial kernel function (PKF), and radial basis kernel function (RKF) to improve the performance of the relevance vector machine (RVM) model in estimating scour depth. In the second step, a new optimizer called the genetic algorithm (GA)-Ali Baba forty thieves optimization (AFTOA)-sine cosine optimization (SCO) was developed to fine-tune the MKRVM parameters. Finally, a comprehensive dataset consisting of 140 experimental scour-depth records, compiled from five laboratory studies on clear-water scour at long channel contractions, was used to estimate the scour depth. The GA-AFTOA-SCO-MKRVM model was benchmarked against the GA-AFTOA- SCO-RVM-RKF, GA-AFTOA-RVM- SCO-SKF, GA-AFTOA-RVM- SCO-PKF, GA-AFTOA-SCO- multilayer perceptron (MLP), GA-AFTOA-SCO-radial basis function (RBFNN) model, and empirical models. In addition, the GA-AFTOA-SCO algorithm was compared with several established optimization algorithms. The analysis results showed that the GA-AFTOA-SCO-MKRVM model improved the testing Nash–Sutcliffe Efficiency (NSE) of the other optimized MKRVM models by 6.25-31%. Moreover, the GA-AFTOA-SCO-MKRVM model improved the testing Willmott’s index of agreement (WIA) of other estimation models by 8.6-18%.
Keywords
Scour depth
Channel contraction hydraulics
Multi kernel function
Ali Baba forty Thieves optimization
Relevance vector machine model
Subjects
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Journal of Hydraulic Structures

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Available Online from 20 October 2026