A combined adaptive neuro-fuzzy inference system-firefly algorithm model for predicting the roller length of a hydraulic jump on a rough channel bed

Hydraulic jumps can occur downstream of hydraulic structures, such as normal weirs, gates and ogee spillways. The roller length is one of the most important parameters of hydraulic jumps in open channels. In this study, the roller length of a hydraulic jump on a rough bed is predicted using a hybrid of adaptive neuro-fuzzy inference systems and the firefly algorithm (ANFIS-FA). First, the effect of parameters including the Froude number (Fr), sequent depth (h (2)/h (1)) and relative roughness (ks/h (1)) upstream of a hydraulic jump is studied. Following the modeling result analysis, ANFIS-FA is introduced as the superior model for estimating the roller length of a hydraulic jump on a rough bed according to Fr, h (2)/h (1) and ks/h (1). The calculated MAPE, RMSE and correlation coefficient values for the superior model are 7.606, 1.771 and 0.970, respectively. ANFIS-FA predicted approximately 40 % of the results with less than 5 % error, and only 36 % of data had more than 10 % error.