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September 16, 2025Open Access

Machine Learning Approaches for Simulating Temporal Changes in Bed Profiles Around Cylindrical Bridge Pier: A Comparative Analysis

AMAhad MolaviIslamic Azad University of Tabriz FKFariborz Ahmadzadeh KaleybarIslamic Azad University of Tabriz NRNamal RathnayakeJapan Agency for Marine-Earth Science and Technology

Key Points

Machine learning models effectively simulate bed profile changes around cylindrical bridge piers, demonstrating GEP's superior accuracy.
Using a dataset of 106 observations, GEP achieved high R2 values of 0.9237 during training, highlighting its robustness in flow conditions.
Models were trained on 70% of the data and tested on 30%, indicating the thorough validation of GEP's performance against other models.
Implications for bridge pier designs suggest that submerged vanes could be optimized using insights from machine learning approaches.

Abstract

Submerged vanes offer a promising solution for reducing scour depth around hydraulic structures such as bridge piers by modifying near-bed flow patterns. However, temporal changes in bed profiles around a cylindrical pier remain insufficiently quantified. This study employs three machine learning models (MLMs), gene expression programming (GEP), support vector regression (SVR), and an artificial neural network (ANN), to simulate the temporal evolution of the bed profile around a cylindrical pier under constant subcritical flow. We use a published laboratory flume dataset (106 observations) obtained for a pier of diameter D=6cm and uniform sediment with median size D50=0.43mm. Geometric/layout parameters of the submerged vanes (number n, transverse offset z, longitudinal spacing e, and distance from the pier base a) were fixed at their reported optima, and subsequent tests varied installation angles α to minimize scour. Models were trained on 70% of the data and tested on 30% using dimensionless inputs (t/te,α1,α2,α3) with t the elapsed time from the start of the run and te the equilibrium time at which scour growth becomes negligible and response s/D with s the instantaneous scour depth at time t. The GEP model with a three-gene structure achieved the best accuracy. During training and testing, GEP attained (RMSE, MAE, R2, (Ds/D)DDR(max))=(0.0864,0.0681,0.9237,4.25) and (0.0729,0.0641,0.9143,4.94), respectively, where Ds denotes scour depth at equilibrium state, D is the pier diameter, and DDR(max)≡max(Ds/D) is the maximum dimensionless depth ratio observed/predicted.

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