Modelling hydraulic jumps with artificial neural networks

Abstract

An artificial neural network (ANN) approach was adapted to model sequent depth and jump length, both important parameters in the design of stilling basins with hydraulic jumps. A total of 611 experimental data on sequent depth and jump length with gradually expanding jumps having rectangular and trapezoidal sections and for a wide range of divergent angles and side wall slopes were collected. In developing the ANN models, 16 configurations, each with different numbers of hidden layers and/or neurons, were evaluated. The optimal models were capable of predicting sequent depth and jump length for a wide range of conditions with a mean square error (MSE) of 10%. In each case, the configuration resulting in the highest coefficient of determination, R2, value was selected as the optimal model. For the rectangular section, the simplest ANN model, which had two hidden layers and four neurons, i.e. 4–4–4–1 configuration, predicted jump length and sequent depth values with R2 = 0·94, MSE = 0·048 and R2 = 0·92, MSE = 0·0192, respectively. In the case of a trapezoidal section, the simplest ANN model for jump length had a 5–13–1 configuration with 13 neurons in the hidden layer (R2 = 0·94, MSE = 0·0213); for sequent depth the model had a 5–8–8–1 configuration with eight neurons in each of the two hidden layers (R2 = 0·80, MSE = 0·005).