Quantitative forecasting of bed sediment load in river engineering: an investigation into machine learning methodologies for complex phenomena

Abstract The intricate calculation of bed sediment load (BSL), which is influenced by hydraulic, hydrological, and sedimentary factors, is vital for informed decision-making in water resource management. Machine learning models, which are gaining popularity due to their accessibility and ability to reveal complex relationships, play a significant role in tackling these challenges. The efficacy of gene expression programming (GEP) models, support vector machines (SVMs), multi-layer perceptron (MLP), and multivariate adaptive regression splines (MARS) has been assessed through measured data of number 540 obtained from six rivers, namely Oak Creek, Nahal Yatir, Sagehen Creek, Elbow River, Jacoby River, and Goodwin Creek from 1954 to 1992. The assessment of model performance has been conducted utilizing root mean square error (RMSE), R2, Nash–Sutcliffe coefficient (NSE), and developed discrepancy ratio (DDR) as indices. Following data normalization within the range of 0–1, the data models underwent training and testing processes with a partition ratio of 80% for training and 20% for testing. Four dimensionless parameters, denoted as Fr = U/√gy, U/U*, Se, and ω = τU/γs√gyDs3, were employed as inputs in the models. The outcomes indicate that they exhibit superior performance compared to other methods, as evidenced by the following metrics in predicting BSL during the test stage: RMSE = 1.4088, NSE = 0.73054, R2 = 0.8729, and maximum QDDR(max) = 1.9564.