Estimating Particle Froude Number of Sewer Pipes by Boosting Machine-Learning Models

Sediment deposition impacts the hydraulic capacity of a channel in urban drainage and sewer systems. To reduce the impact of this continuous deposition of sediment particles, sewer systems are typically designed with a self-cleansing mechanism to keep the bottom of the channel clean from sedimentation. Therefore, accurate prediction of the particle Froude number (${\text{F}}_r$) is important in designing sewer systems. This study used five data sets available in the literature, comprising wide ranges of the volumetric sediment concentration ($C_v$), dimensionless grain size of particles ($D_{gr}$), sediment median size ($d$), hydraulic radius ($R$), pipe friction factor ($\lambda$) for the condition of nondeposition with deposited bed. Five different input variable combinations were considered for the prediction of ${\text{F}}_r$. Four boosting machine-learning models, i.e., AdaboostRegressor, GradientBoostingRegressor, CatboostRegressor, and LightGBMRegressor, were developed, and the results obtained were compared with the existing empirical equations as well as state-of-the-art approaches proposed in the literature. To evaluate the proposed models, several performance metrics were used, such as index of agreement ($I_d$), mean absolute error (MAE), root-mean-square error (RMSE), $R^2$, and adjusted $R^2$. AdaboostRegressor ($I_d=0.981$, $\mathrm{MAE}=0.483$, $\mathrm{RMSE}=0.591$, $R^2=0.940$, and adjusted $R^2=0.937$) provided better results, followed by GradientBoostingRegressor, CatboostRegressor, and LightGBMRegressor. The boosting techniques used in this study performed better than multigene genetic programming, gene expression programming, multilayer perceptron (MLP), and the empirical equations proposed in the literature, indicating superior performance.