Design of a new hybrid artificial neural network method based on decision trees for calculating the Froude number in rigid rectangular channels

Isa Ebtehaj 1 , 2 , Hossein Bonakdari 1 , 2 , Amir Hossein Zaji 1 , 2 , Charles Hin Joo Bong 3 , 4  and Aminuddin Ab Ghani 4
  • 1 Department of Civil Engineering, Razi University, 67149-67346 Baghe Abrisham, Kermanshah, Iran
  • 2 Water and Wastewater Research Center, Razi University, 67149-67346 Baghe Abrisham, Kermanshah, Iran
  • 3 Department of Civil Engineering, Faculty of Engineering, University Malaysia Sarawak, 94300 Kota Samarahan, Sarawak, Malaysia
  • 4 River Engineering and Urban Drainage Research Centre (REDAC), Universiti Sains Malaysia (USM), 14300 Nibong Tebal, Pulau Pinang, Malaysia


A vital topic regarding the optimum and economical design of rigid boundary open channels such as sewers and drainage systems is determining the movement of sediment particles. In this study, the incipient motion of sediment is estimated using three datasets from literature, including a wide range of hydraulic parameters. Because existing equations do not consider the effect of sediment bed thickness on incipient motion estimation, this parameter is applied in this study along with the multilayer perceptron (MLP), a hybrid method based on decision trees (DT) (MLP-DT), to estimate incipient motion. According to a comparison with the observed experimental outcome, the proposed method performs well (MARE = 0.048, RMSE = 0.134, SI = 0.06, BIAS = -0.036). The performance of MLP and MLP-DT is compared with that of existing regression-based equations, and significantly higher performance over existing models is observed. Finally, an explicit expression for practical engineering is also provided.

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