Modeling flow resistance and geometry of dunes bed form in alluvial channels using hybrid RANN–AHA and GEP models

Abstract

Dunes formation in sandy rivers significantly impacts flow resistance, subsequently affecting water levels, flow velocity, river navigation, and hydraulic structures performance. Accurate prediction of flow resistance and dune geometry (length and height) is essential for environmental engineering and river management. The current paper introduces two models to evaluate the flow resistance and geometry of dunes formed in sand-bed channels. The first model, RANN–AHA is a hybrid artificial intelligence model using the recurrent artificial neural network (RANN) linked with the artificial hummingbird optimization algorithm (AHA) to optimize the biases and weights of the neural network model. The second model uses gene expression programming (GEP) as a nonlinear approach based on a genetic algorithm (GA) and genetic programming (GP) to explicitly determine dune characteristics. For both models, the input parameters include flow and sediment characteristics, while Manning's roughness coefficient ( n M ), and relative dune height, h / H or h / L , were used as output parameters where h is the dune height, H is the flow depth above the dune crest, and L is the dune length. Five different published flume data sets were compiled for the analysis. Sensitivity analysis was done using different combinations of input parameters. It was found that the combination of hydraulic radius divided by median diameter ( R H / d 50 ), Reynolds number (Re), Particle densimetric Froude number ( F ∗), and grain Froude number ( F G ) yielded the best prediction accuracy for estimating Manning n M and relative height, h / H or h / L , with a root mean square error (RMSE) = 0.00027, 0.0504, and 0.0078 and a correlation coefficient ( R ) = 0.9989, 0.942, and 0.9272, respectively. Model verification proved that the RANN–AHA model outperformed the GEP model and most of the previous studies available in the literature when predicting the roughness coefficient and dune geometry in sand bed channels. • An optimized-recurrent artificial neural network (RANN–AHA) model is developed to predict the characteristics of dunes formed in sand bed channels (roughness and geometry). • Artificial hummingbird algorithm (AHA) is employed to optimize the (RANN) model biases and weights. • Gene expression programming (GEP) is utilized to deduce an explicit solutions for dunes characteristics (Manning's roughness coefficient, relative height and ratio of dune height to dune length). • Sensitivity analysis was performed to test the influence of each or possible combinations of the input parameters on the model outputs (roughness and geometry). • The performance of both models was assessed and compared to each other and to previous studies available in literature using the Taylor diagram in terms of root mean square error (RMSE), correlation coefficient (R), and standard deviation (SD) as statistical measures.