An evaluation of ANN methods for estimating the lengths of hydraulic jumps in U-shaped channel Larbi Houichi, Noureddine Dechemi, Salim Heddam and Bachir Achour ABSTRACT Modelling of hydraulic characteristics of jump using theoretical and empirical models has always been a difficult task. The length of jump may be defined as the distance measured from the toe of the jump to the location of the surface rise. Due to high turbulence this length cannot be determined easily by theory. However, it has been investigated experimentally so as to design the stilling basins with hydraulic jumps. In this work, the control of a hydraulic jump by broad-crested sills in a U- shaped channel is recalled theoretically and experimentally examined. The study begins with a multiple regression (MR) analysis. Then, and in order to model the relative lengths of hydraulic jumps, we have implemented and evaluated two different artificial neural networks (ANN): multilayer perceptron neural network (MLPNN) and generalized regression neural network (GRNN). The results demonstrate the predictive strength of GRNN and its potential to predict hydraulic problems with an adaptive spread value. However, the MLPNN model remains best classified by these indexes of performance. Larbi Houichi Research Laboratory in Applied Hydraulics, Department of hydraulics, University of Batna, Algeria Noureddine Dechemi Laboratory Construction and Environment, Polytechnical National School, Alger, Algeria Salim Heddam (corresponding author) Faculty of Science, Department of Agronomy, University of Skikda, Algeria E-mail: heddamsalim@yahoo.fr Bachir Achour Research Laboratory in Subterranean and Surface hydraulics, University of Biskra, Algeria Key words | artificial neural network, GRNN, lengths of hydraulic jump, MLPNN, MR, U-channel NOMENCLATURE A Cross-sectional area of flow [m 2 ] D Diameter [m] Fr Froude number [–] L j Length of jump [m] Q Discharge [m 3 /s] g Acceleration due to gravity [m/s 2 ] h Depth of flow [m] q Specific discharge [–] y Relative depth of flow [–] θ 1 Angle for semicircular cross-sectional area [rad] ABBREVIATIONS ANN Artificial neural networks GRNN Generalized regression neural network MLPNN Multilayer perceptron neural network MR Multiple regression INTRODUCTION The hydraulic jump is the discontinuous transition between supercritical and subcritical flow with varied or fixed location (Vischer & Hager ), it is characterized by a sudden increasing of the water surface with high turbulence production. This phenomenon is an example of steady non- uniform flow. Principally, the hydraulic jump is well known to hydraulic engineers as a useful means of dissipating excess energy of flowing water downstream of hydraulic structures, such as spillways, chutes and sluices (Hager ). Some of the other practical applications are: e.g. flow-metering flume, mixing of chemicals for water purifi- cation and aerating water (Chow ; Kucukali & Cokgor ). In practice, the stilling basin is seldom designed to confine the entire length of a free hydraulic jump on the paved apron, because such a basin would be too expensive. Consequently, accessories to control the jump are usually installed in the basin. The main purpose of such control is to shorten the range within which the jump will take place 147 © IWA Publishing 2013 Journal of Hydroinformatics | 15.1 | 2013 doi: 10.2166/hydro.2012.138