Determination of the surface roller length of hydraulic jumps in horizontal rectangular channels using the machine learning method

This study aims to develop and assess seven machine learning (ML) models, including an Artificial Neural Network (ANN), Gradient Boosting (GB), Extra Trees (ET), Lasso Regression (LASSO), Least Angle Regression (Lars), Random Forest (RF), and Adaptive Boosting (Adaboost), that are effective and simple in forecasting the roller length of a hydraulic jump in a rectangular horizontal canal. This study also proposes a novel approach for applying the Buckingham Pi theorem to ascertain four model inputs and one output, corresponding to five dimensionless Pi terms that have not previously been explored. The impact of channel surface roughness, fluid viscosity, channel geometry, and gravity on the hydraulic jump's roller length was considered to improve the model's performance. Furthermore, the importance of input features was determined, resulting in two model input scenarios. The scenario with four inputs containing the inflow Reynolds number Re1* surpasses the three-input scenario. Because of their high accuracy and efficiency, six ML models outperformed three empirical equations. The GB, ANN, and ET models showed the best performance in both validation and testing phases, whereas LASSO, Lars, RF, and Adaboost performed with lower precision, in descending order. Regarding the ANN model, the best has two hidden layers of sixteen neurons each. In the validation and testing phases, this model achieves the highest Nash-Sutcliffe efficiency of 0.992 and 0.933, respectively. As a result, this study recommends using the GB, ANN, and ET models to forecast the roller length of the hydraulic jump instead of empirical equations when the inflow Froude number, Fr1, varies between 2.4 and 15.9.