Experimental study and modeling of hydraulic jump for a suddenly expanding stilling basin using different hybrid algorithms

Hydraulic jump is a highly important phenomenon for dissipation of energy. This event, which involves flow regime change, can occur in many different types of stilling basins. In this study, hydraulic jump characteristics such as relative jump length and sequent depth ratio occurring in a suddenly expanding stilling basin were estimated using hybrid extreme learning machine (ELM). To hybridize ELM, imperialist competitive algorithm (ICA), firefly algorithm (FA) and particle swarm optimization (PSO) metaheuristic algorithms were implemented. In addition, six different models were established to determine effective dimensionless (relative) input variables. A new data set was constructed by adding the data obtained from the experimental study in the present research to the data obtained from the literature. The performance of each model was evaluated using k-fold cross-validation. Results showed that ICA hybridization slightly outperformed FA and PSO methods. Considering relative input parameters, Froude number (Fr), expansion ratio (B) and relative sill height (S), effective input combinations were Fr–B–S and Fr–B for the prediction of the sequent depth ratio (Y) and relative hydraulic jump length (Lj/h1), respectively.