1379 Prediction of pressure fluctuations on sloping stilling basins A. Güven, M. Günal, and A. Çevik Abstract: Various types of hydraulic jump occurring on horizontal and sloping channels have been analyzed experimen- tally, theoretically, and numerically and the results are available in the literature. In this study, artificial neural network models were developed to simulate the mean pressure fluctuations beneath a hydraulic jump occurring on sloping stilling basins. Multilayers feed a forward neural network with a back-propagation learning algorithm to model the pressure fluc- tuations beneath such a type of hydraulic jump (B-jump). An explicit formula that predicts the mean pressure fluctuation in terms of the characteristics that contribute most to the hydraulic jump occurring on the sloping basins is presented. The proposed neural network models are compared with linear and nonlinear regression models that were developed using considered physical parameters. The results of the neural network modelling are found to be superior to the regression models and are in good agreement with the experimental results due to relatively small values of error (mean absolute percentage error). Key words: neural networks, pressure fluctuation, hydraulic jump, sloping stilling basin, explicit NN formulation, regression analysis. Résumé : Divers types de ressauts hydrauliques se trouvant dans les canaux horizontaux et inclinés ont été analysés expérimentalement, théoriquement et numériquement et les résultats sont disponibles dans la littérature. La présente étude développe des modèles de réseaux neuronaux artificiels pour simuler les variations moyennes de pression sous les ressauts hydrauliques le long des bassins d’amortissement inclinés. Un réseau neuronal à couches non bouclé muni d’un algorithme d’apprentissage à rétropropagation est utilisé pour modéliser les variations de pression sous de tels types de ressauts hydrauliques (B-Jump). Une formule explicite qui prédit la variation moyenne de pression en termes des caractéristiques contribuant le plus au ressaut hydraulique dans les bassins d’amortissement est présentée. Les modèles de réseaux neuronaux artificiels proposés sont comparés aux modèles de régression linéaire et non linéaire développés en utilisant les paramètres physiques arrêtés. Les résultats de la modélisation des réseaux neuronaux s’avèrent supérieurs à ceux des modèles de régression et présentent une bonne corrélation avec les résultats expérimentaux en raison des valeurs relativement petites de l’erreur (pourcentage d’erreur moyenne absolue). Mots clés : réseaux neuronaux, variation de pression, ressaut hydraulique, bassin d’amortissement incliné, formulation de réseau neuronal explicite, analyse de régression. [Traduit par la Rédaction] Introduction Over the years, several aspects of hydraulic jumps forming in horizontal and sloping channels have been investigated. In an open channel, if the downstream depth is greater than the down- stream sequent depth, the jump moves upstream to submerge the incoming flow. Such a jump is called a submerged hydraulic jump. The hydraulic jump forming in the stilling basin is a free hydraulic jump if it forms at the foot of the spillway. Usually, the jump is enclosed within a stilling basin. On the other hand, if the downstream depth of the flow in the stilling basin is greater than the sequent depth, the hydraulic jump moves towards the Received 1 May 2006. Revision accepted 19 July 2006. Published on the NRC Research Press Web site at http://cjce.nrc.ca/ on 23 January 2007. A. Güven, 1 M. Günal, and A. Çevik. Department of Civil Engi- neering, Faculty of Engineering, University of Gaziantep, 27310 Gaziantep, Turkey. Written discussion of this article is welcomed and will be received by the Editor until 31 March 2007. 1 Corresponding author (e-mail: aguven@gantep.edu.tr). spillway with its toe positioned on the spillway. Such a jump is called a B-jump and a B-jump may be considered to belong to the class of submerged jumps with the entering flow at an angle to the bed of the channel (Fig. 1). Mean flow character- istics of a B-jump were investigated in detail by Hager (1989), and Ohtsu and Yasuda (1990, 1991). These studies relate to the mean velocity measurements, roller length, and length of the jump. Abdul Khader and Elongo (1974), Lopardo and Henning (1985), Toso and Bowers (1988), and Fattor et al. (2001) stud- ied statistical properties of fluctuating pressures beneath a hy- draulic jump formed downstream of the spillway. On the other hand,Vasiliev and Bukreyev (1967), Narasimhan and Bhargava (1976), Narayanan (1978), and Lopardo et al. (2004) measured the intensity of the fluctuating pressures beneath submerged and free jumps downstream of a sluice gate in the horizontal channel. Clearly, these two sets of experiments with respect to hydraulic jumps, one downstream of a spillway and the other downstream of a sluice gate, are different with respect to the up- stream conditions. It is well known that different upstream con- ditions such as the mean velocity distribution and intensity of turbulence have a strong influence on the magnitude of the pres- sure fluctuations and mean flow properties. It is worth noting Can. J. Civ. Eng. 33: 1379–1388 (2006) doi: 10.1139/L06-101 © 2006 NRC Canada