Predicting Hydraulic Jump Length on Rough Beds Using Data-Driven Models

Document Type : Research Note


1 water sciences and engineering,university of kurdistan,sanandaj,iran

2 Assistant Professor at University of Kurdistan

3 water sciences and engineering department,university of kurdistan-sanandaj-iran


The hydraulic jump can be used for some purpose such as dissipating the flow energy in order to prevent bed erosion; aerating water and facilitating the mixing procedure of chemical that used for water purification. In this paper, various artificial intelligence (AI) models including gene expression programming (GEP), adaptive-neuro-fuzzy inference system with grid partition (ANFIS-GP), and neural networks (ANNs) were used to estimate developed and non-developed hydraulic jump length. Four various GEP, ANFIS-GP and ANN models including different combinations of Froude number, bed roughness height, upstream and downstream flow depth based on measured experimental data-set were developed to estimate hydraulic jump length variations. The root mean squared error (RMSE) and determination coefficient (R2) indices were applied for testing models’ accuracy. Regarding the comparison results, it was seen that the ANFIS-GP, ANN, and GEP models could be employed successfully in estimating hydraulic jump length. The comparison between three AI approaches emphasized the superiority of ANNs and ANFIS-GP over the other intelligent models for modeling developed and non-developed hydraulic jump length, respectively. For non-developed hydraulic jump, the R2 and RMSE values obtained as 0.87 and 2.84 for ANFIS-GP model. 


Main Subjects

[1] Abbaspour, A., Dalir, A.H., Farsadizadeh, D. and Sadraddini, A.A., 2009. Effect of sinusoidal corrugated bed on hydraulic jump characteristics. Journal of Hydro-environment Research, 3(2), pp.109-117.
[2] Abonyi, J., Andersen, H., Nagy, L. and Szeifert, F., 1999. Inverse fuzzy-process-model based direct adaptive control. Mathematics and Computers in Simulation, 51(1), pp.119-132.
[3] Afzal, N., Bushra, A. and Seena, A., 2011. Analysis of turbulent hydraulic jump over a transitional rough bed of a rectangular channel: universal relations. Journal of Engineering Mechanics, 137(12), pp.835-845.
[4] Ansari, M.A., 2014. Sediment removal efficiency computation in vortex settling chamber using artificial neural networks. Water and Energy International, 71(1), pp.54-67.
[5] Ansari, M.A. and Athar, M., 2013. Artificial neural networks approach for estimation of sediment removal efficiency of vortex settling basins. ISH Journal of Hydraulic Engineering, 19(1), pp.38-48.
[6] Araghinejad, S., 2013. Data-driven modeling: using MATLAB® in water resources and environmental engineering (Vol. 67). Springer Science & Business Media.
[7] Azmathullah, H.M., Deo, M.C. and Deolalikar, P.B., 2005. Neural networks for estimation of scour downstream of a ski-jump bucket. Journal of Hydraulic Engineering, 131(10), pp.898-908.
[8] Barahmand, N. and Shamsai, A., 2010. Experimental and theoretical study of density jumps on smooth and rough beds. Lakes & Reservoirs: Research & Management, 15(4), pp.285-306.
[9] Brown, M. and Harris, C.J., 1994. Neurofuzzy adaptive modelling and control. Prentice Hall.
[10] Carollo F.G., Ferro V., 2004. “Determination of Conjugated Heights Emphasis on Free Smooth Surface and Rough”, Journal of Agricultural Engineering, Vol. 4, pp. 1-12.
[11] Carollo, F.G., Ferro, V. and Pampalone, V., 2007. Hydraulic jumps on rough beds. Journal of Hydraulic Engineering, 133(9), pp.989-999.
[12] Dey, S. and Sarkar, A., 2008. Characteristics of turbulent flow in submerged jumps on rough beds. Journal of engineering mechanics, 134(1), pp.49-59.
[13] Ead, S.A. and Rajaratnam, N., 2002. Hydraulic jumps on corrugated beds. Journal of Hydraulic Engineering, 128(7), pp.656-663.
[14] Ferreira, C., 2001. Gene Expression Programming: A New Adaptive Algorithm for Solving Problems. Complex Systems 13 (2): 87-129.
[15] Ferreira, C., 2006. Gene expression programming: mathematical modeling by an artificial intelligence (Vol. 21). Springer.
[16] Gumus, V., Simsek, O., Soydan, N.G., Akoz, M.S. and Kirkgoz, M.S., 2015. Numerical modeling of submerged hydraulic jump from a sluice gate. Journal of Irrigation and Drainage Engineering, 142(1), p.04015037.
[17] Hager, W.H., 2013. Energy dissipators and hydraulic jump (Vol. 8). Springer Science & Business Media.
[18] Hager, W.H., Bremen, R. and Kawagoshi, N., 1990. Classical hydraulic jump: length of roller. Journal of Hydraulic Research, 28(5), pp.591-608.
[19] Haykin, S. (1999). Neural Networks: A Comprehensive Foundation. Printice-Hall. Inc., New Jersey.
[20] Hughes, W.C. and Flack, J.E., 1984. Hydraulic jump properties over a rough bed. Journal of Hydraulic engineering, 110(12), pp.1755-1771.
[21] Jang, J.S., 1993. ANFIS: adaptive-network-based fuzzy inference system. IEEE transactions on systems, man, and cybernetics, 23(3), pp.665-685.
[22] Jang, J. S. R., & Sun, C. T. (1997). Neuro-fuzzy and soft computing: a computational approach to learning and machine intelligence. Prentice-Hall, Upper Saddle River.
[23] Liriano, S.L. and Day, R.A., 2001. Prediction of scour depth at culvert outlets using neural networks. Journal of hydroinformatics, 3(4), pp.231-238.
[24] Mohamed Ali, H.S., 1991. Effect of roughened-bed stilling basin on length of rectangular hydraulic jump. Journal of Hydraulic Engineering, 117(1), pp.83-93.
[25] Naderpour, H., Kheyroddin A., Ghodrati Amiri, G. (2010). Prediction of FRP-confined compressive strength of concrete using artificial neural networks. Composite Structures, Vol. 92, pp. 2817–2829.
[26] Nagy, H.M., Watanabe, K.A.N.D. and Hirano, M., 2002. Prediction of sediment load concentration in rivers using artificial neural network model. Journal of Hydraulic Engineering, 128(6), pp.588-595.
[27] Naseri, M. and Othman, F., 2012. Determination of the length of hydraulic jumps using artificial neural networks. Advances in Engineering Software, 48, pp.27-31.
[28] Omid, M.H., Omid, M. and Esmaeeli Varaki, M., 2005, June. Modelling hydraulic jumps with artificial neural networks. In Proceedings of the Institution of Civil Engineers-Water Management (Vol. 158, No. 2, pp. 65-70). Thomas Telford Ltd.
[29] Pagliara, S., Lotti, I. and Palermo, M., 2008. Hydraulic jump on rough bed of stream rehabilitation structures. Journal of Hydro-Environment Research, 2(1), pp.29-38.
[30] Pagliara, S. and Palermo, M., 2015. Hydraulic jumps on rough and smooth beds: aggregate approach for horizontal and adverse-sloped beds. Journal of Hydraulic Research, 53(2), pp.243-252.
[31] Raikar, R.V., Kumar, D.N. and Dey, S., 2004. End depth computation in inverted semicircular channels using ANNs. Flow Measurement and Instrumentation, 15(5), pp.285-293.
[32] Rajaratnam, N., 1965. Submerged hydraulic jump. Journal of the Hydraulics Division, 91(4), pp.71-96.