Document Type : Original/Review Paper


Department of Water Engineering, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran.


Generally, length of hydraulic jump is one the most important parameters to design stilling basin. In this study, the length of hydraulic jump on sloping rough beds was predicted using Gene Expression Programming (GEP) for the first time. The Monte Carlo simulations were used to examine the ability of the GEP model. In addition, k-fold cross validation was employed in order to verify the results of the GEP model. To determine the length of hydraulic jump, five different GEP models were introduced using input parameters. Then by analyzing the GEP models results, the superior model was presented. For the superior model, correlation coefficient (R), Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) were computed 0.901, 11.517 and 1.664, respectively. According to the sensitivity analysis, the Froude number at upstream of hydraulic jump was identified as the most important parameter to model the length of hydraulic jump. Furthermore, the partial derivative sensitivity analysis (PDSA) was performed. For instance, the PDSA was calculated as positive for all input variables.


[1] Rajaratnam, N. (1968). Hydraulic jumps on rough beds. Transactions of the Engineering Institute of Canada, vol. 11, no. A-2, pp. 1-8.
[2] Hughes, W. & Flack, J. (1984). Hydraulic Jump Properties over a Rough Bed. J. Hydraul. Eng., vol. 110, no. 12, pp. 1755-1771.
[3] Mohamed Ali, H. S. (1991). Effect of roughened-bed stilling basin on length of rectangular hydraulic jump. Journal of Hydraulic Engineering, vol. 117, no. 1, pp. 83-93.
[4] Ead, S. & Rajaratnam, N. (2002). Hydraulic Jumps on Corrugated Beds. J. Hydraul. Eng., vol. 128, no. 7, pp. 656-663.
[5] Carollo, F., Ferro, V. & Pampalone, V. (2007). Hydraulic Jumps on Rough Beds. J. Hydraul. Eng., vol. 133, no. 9, pp. 989-999.
[6] Elsebaie, I. H. & Shabayek, S. (2010). Formation of hydraulic jumps on corrugated beds. International Journal of Civil & Environmental Engineering IJCEE-IJENS, vol. 10, pp. 40-50.
[7] Ahmed, H. M. A., El Gendy, M., Mirdan, A. M. H., Ali, A. A. M. & Abdel Haleem, F. S. S. (2014). Effect of corrugated beds on characteristics of submerged hydraulic jump. Ain Shams Engineering Journal. vol. 5, pp. 1033-1042.
[8] Nissi, K. & Shafaee Bajestan, M. (2008). Laboratory study of detention pond length on rough beds. Second National Conference on Irrigation and Drainage Networks Management. Shahid Chamran University of Ahvaz (In Persian).
[9] Cheng, C. T., Wu, X. Y. & Chau, K. W. (2005). Multiple criteria rainfall–runoff model calibration using a parallel genetic algorithm in a cluster of computers/Calage multi-critères en modélisation pluie–débit par un algorithme génétique parallèle mis en œuvre par une grappe d'ordinateurs. Hydrological sciences journal, vol. 50, no. 6.
[10] Fotovatikhah, F., Herrera, M., Shamshirband, S., Chau, K. W., Faizollahzadeh Ardabili, S. & Piran, M. J. (2018). Survey of computational intelligence as basis to big flood management: Challenges, research directions and future work. Engineering Applications of Computational Fluid Mechanics, vol. 12, no. 1, pp. 411-437.
[11] Taormina, R., Chau, K. W. & Sivakumar, B. (2015). Neural network river forecasting through baseflow separation and binary-coded swarm optimization. Journal of Hydrology, 529, 1788-1797.
[12] Cheng, C. T. & Chau, K. W. (2004). Flood control management system for reservoirs. Environmental Modelling & Software, vol. 19, no. 12, pp. 1141-1150.
[13] Wang, W. C., Xu, D. M., Chau, K. W. & Chen, S. (2013). Improved annual rainfall-runoff forecasting using PSO–SVM model based on EEMD. Journal of Hydroinformatics, vol. 15, no. 4, pp. 1377-1390.
[14] Wu, C. L. & Chau, K. W. (2011). Rainfall–runoff modeling using artificial neural network coupled with singular spectrum analysis. Journal of Hydrology, vol. 399, no. 3-4, pp. 394-409.
[15] Omid, M. H., Omid, M. & Esmaeeli, V. M. (2005). Modelling hydraulic jumps with artificial neural networks. Proc. Inst. Civ. Eng., Water Manage. vol. 158, no. 2, pp. 65–70.
[16] Naseri, M. & Othman, F. (2012). Determination of the length of hydraulic jumps using artificial neural networks. Advances in Engineering Software. vol. 48, pp. 27–31.
[17] Karbasi, M. & Azamathulla, H. M. (2016). GEP to predict characteristics of a hydraulic jump over a rough bed. KSCE Journal of Civil Engineering, vol. 20, no. 7, pp. 3006-3011.
[18] Ferreira, C. (2001). Gene expression programming in problem solving. 6th Online World Conference on Soft Computing in Industrial Applications (Invited Tutorial).
[19] Kumar, M. & Lodhi, A. S. (2016). Hydraulic jump over sloping rough floors. ISH Journal of Hydraulic Engineering, vol. 22, no. 2, pp. 127-134.
[20] Hager, W.H., Bremen, R. & Kawagoshi, N. (1990). Classical hydraulic jump: length of roller. Journal of Hydraulic Research, vol. 28, no. 5, pp. 591-608.
[21] Azimi, H., Bonakdari, H., Ebtehaj, I. & Michelson, D. G. (2018). Combined adaptive neuro-fuzzy inference system–firefly algorithm model for predicting the roller length of a hydraulic jump on a rough channel bed. Neural. Comput. & Applic. vol. 29, no. 6, pp. 249-258.
[22] Azimi, H., Bonakdari, H., Ebtehaj, I., Gharabaghi, B. & Khoshbin, F. (2018). Evolutionary design of generalized group method of data handling-type neural network for estimating the hydraulic jump roller length. Acta. Mechanica., vol. 229, no. 3, pp. 1197-1214.
[23] Azimi, H., Bonakdari, H. & Ebtehaj, I. (2019). Gene expression programming-based approach for predicting the roller length of a hydraulic jump on a rough bed. ISH J. Hydraul. Eng. pp. 1-11.