Evolutionary design of generalized group method of data handling-type neural network for estimating the hydraulic jump roller length

Hydraulic jumps generally occur subsequent to structures such as ogee spillways, control gates, and weirs. The jump roller length is considered one of the main hydraulic jump parameters. In this study, the roller length of a hydraulic jump on a rough channel bed is predicted using a novel, evolutionary, generalized structure design of a group method of data handling (GS-GMDH)-type neural network. The topology of GMDH is designed with a genetic algorithm . Initially, the three most important non-dimensional parameters affecting hydraulic jump roller length, including the Froude number upstream of a hydraulic jump Fr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {Fr} \right) $$\end{document}, the ratio of sequent depths h2/h1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {{h_2 }/{h_1 }} \right) $$\end{document}, and the relative roughness ks/h1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {{ks}/{h_1 }} \right) $$\end{document} were used to generate four different GS-GMDH models, and the most accurate model is identified. The best new GS-GMDH model prediction statistics, including RMSE, MARE, and correlation coefficient are 1.816, 0.081, and 0.966, respectively, while the scatter index and BIAS values are 0.084 and 1.45, respectively. A partial derivative sensitivity analysis of the input parameters for the new model is also performed. The new model predictions are then compared with predictions of a number of other models. The superior performance of the new GS-GMDH over these existing models is illustrated.