Experimental and Machine Learning Modeling of Drag Coefficients for Bridge Piers

Articles in Press

Document Type : Original Article

Authors

1 Department of Water Science Engineering, Ahv.C., Islamic Azad University, Ahvaz, Iran

2 . Department of Water Science Engineering, Ahv.C., Islamic Azad University, Ahvaz, Iran

10.22044/jhwe.2026.18291.1102

Abstract

Bridge failures during extreme floods are often associated with the combined effects of local scour and hydrodynamic loading. However, conventional design approaches commonly rely on prescribed drag and lift coefficients that may not adequately represent the complex three-dimensional interaction between flow and bridge components. This study investigates the prediction of the drag coefficient, CD, for bridge structures using laboratory experiments and machine-learning techniques. An experimental dataset was developed by measuring the hydrodynamic drag force acting on bridge piers under controlled flow conditions. Three machine learning models (MLMs)- support vector machine (SVM), gene expression programming (GEP), and multilayer perceptron artificial neural network (ANN)- were developed and evaluated using performance metrics. The optimized models showed satisfactory agreement between measured and predicted values during both the training and testing phases. Among the investigated methods, the ANN–MLP 4-8-1 architecture provided the best performance with RMSE=0.058, MAE=0.047, and R²=0.984. This represents an RMSE improvement of 52.8% and 38.9% over the SVM (RMSE=0.123) and GEP (RMSE=0.095) models, respectively. These results indicate that MLMs, particularly the optimized ANN–MLP model, can effectively estimate CD and provide a useful supplementary tool for evaluating hydrodynamic loading on bridge structures during flood conditions.

Keywords

Journal of Hydraulic and Water Engineering

Articles in Press, Accepted Manuscript
Available Online from 30 September 2026

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