Intelligent Modeling of Discharge Coefficient of Lateral Intakes

Document Type : Research Article


1 Water Engineering Department

2 Water Engineering Department, Lorestan University, Khorramabad, Iran

3 Department of Water and Soil Conservation, Ministry of Agriculture Jihad, Kerman, Iran



Intake structures have been widely used for flow diversion in the irrigation and drainage networks. In this paper, the multivariate adaptive regression splines (MARS), artificial neural network (ANN), and support vector machine (SVM) techniques were utilized for prediction of discharge coefficient (Cd) of lateral intakes. The experimental data pertaining to dimensionless parameters on Cd were collected to develop the models. The results indicated that the best performance in modeling is related to the MARS model with R2=0.98 and RMSE=0.023 and the MARS model outperforms the ANN and SVM models. The tangent sigmoid and radial basic functions were found to be the most efficient transfer and kernel functions for ANN and SVM, respectively. Moreover, Froude number (Fr1) and the ratio of the weir height to the upstream flow depth (P/d1) were the most effective factors for predicting Cd. Evaluation of the performance of applied models in term of developed discrepancy ratio (DDR) index shows that the minimum data dispersivity is related to the MARS model.


Main Subjects

[1] H.M. Azamathulla, A.H. Haghiabi, A. Parsaie, Prediction of side weir discharge coefficient by support vector machine technique, Water Science and Technology: Water Supply, 16(4) (2016) 1002-1016.
[2] G. De Marchi, Saggio di teoria del funzionamento degli stramazzi laterali, L’Energia elettrica, 11(11) (1934) 849-860.
[3] A. Vatankhah, Water Surface Profiles along a Rectangular Side Weir in a U-Shaped Channel (Analytical Findings), Journal of Hydrologic Engineering, 18(5) (2013) 595-602.
[4] A.R. Vatankhah, Water surface profile along a side weir in a parabolic channel, Flow Measurement and Instrumentation, 32(0) (2013) 90-95.
[5] A. Vatankhah, New Solution Method for Water Surface Profile along a Side Weir in a Circular Channel, Journal of Irrigation and Drainage Engineering, 138(10) (2012) 948-954.
[6] A.H. Haghiabi, A. Parsaie, S. Ememgholizadeh, Prediction of discharge coefficient of triangular labyrinth weirs using Adaptive Neuro Fuzzy Inference System, Alexandria Engineering Journal, (2017).
[7] A. Parsaie, A.H. Haghiabi, Improving Modelling of Discharge Coefficient of Triangular Labyrinth Lateral Weirs Using SVM, GMDH and MARS Techniques, Irrigation and Drainage, 66(4) (2017) 636-654.
[8] A. Parsaie, A.H. Haghiabi, Support Vector Machine to predict the discharge coefficient of sharp crested w-planform weirs, AUT Journal of Civil Engineering, 1(2) (2017) 195-204.
[9] S. Samiee, M. Heidarpour, S. Bagheri, Flow characteristics of rectangular sharp-crested side weirs in the presence of guide vanes, ISH Journal of Hydraulic Engineering, 22(1) (2016) 109-114.
[10] A.H. Haghiabi, J. Mohammadzadeh-Habili, A. Parsaie, Development of an evaluation method for velocity distribution over cylindrical weirs using doublet concept, Flow Measurement and Instrumentation, (2018).
[11] J. Mohammadzadeh-Habili, M. Heidarpour, A. Haghiabi, Comparison the hydraulic characteristics of finite crest length weir with quarter-circular crested weir, Flow Measurement and Instrumentation, 52(Supplement C) (2016) 77-82.
[12] M. Heidarpour, J.M. Habili, A.H. Haghiabi, Application of potential flow to circular-crested weir, Journal of Hydraulic Research, 46(5) (2008) 699-702.
[13] H. Haddadi, M. Rahimpour, A discharge coefficient for a trapezoidal broad-crested side weir in subcritical flow, Flow Measurement and Instrumentation, 26(0) (2012) 63-67.
[14] S. Borghei, M. Jalili, M. Ghodsian, Discharge Coefficient for Sharp-Crested Side Weir in Subcritical Flow, Journal of Hydraulic Engineering, 125(10) (1999) 1051-1056.
[15] M. Emiroglu, N. Kaya, Discharge Coefficient for Trapezoidal Labyrinth Side Weir in Subcritical Flow, Water Resources Management, 25(3) (2011) 1037-1058.
[16] S. Bagheri, A.R. Kabiri-Samani, M. Heidarpour, Discharge coefficient of rectangular sharp-crested side weirs, Part I: Traditional weir equation, Flow Measurement and Instrumentation, 35(0) (2014) 109-115.
[17] S. Dehdar-behbahani, A. Parsaie, Numerical modeling of flow pattern in dam spillway’s guide wall. Case study: Balaroud dam, Iran, Alexandria Engineering Journal, 55(1) (2016) 467-473.
[18] A. Parsaie, A. Moradinejad, A.H. Haghiabi, Numerical Modeling of Flow Pattern in Spillway Approach Channel, Jordan Journal of Civil Engineering, 12(1) (2018) 1-9.
[19] A. Parsaie, A.H. Haghiabi, Numerical routing of tracer concentrations in rivers with stagnant zones, Water Science and Technology: Water Supply, 17(3) (2017) 825-834.
[20] A. Parsaie, A. Haghiabi, The Effect of Predicting Discharge Coefficient by Neural Network on Increasing the Numerical Modeling Accuracy of Flow Over Side Weir, Water Resources Management, 29(4) (2015) 973-985.
[21] A.H. Haghiabi, H.M. Azamathulla, A. Parsaie, Prediction of head loss on cascade weir using ANN and SVM, ISH Journal of Hydraulic Engineering, (2016) 1-9.
[22] O. Bilhan, M. Emin Emiroglu, O. Kisi, Application of two different neural network techniques to lateral outflow over rectangular side weirs located on a straight channel, Advances in Engineering Software, 41(6) (2010) 831-837.
[23] O. Bilhan, M.E. Emiroglu, O. Kisi, Use of artificial neural networks for prediction of discharge coefficient of triangular labyrinth side weir in curved channels, Advances in Engineering Software, 42(4) (2011) 208-214.
[24] M. Emiroglu, O. Kisi, Prediction of Discharge Coefficient for Trapezoidal Labyrinth Side Weir Using a Neuro-Fuzzy Approach, Water Resources Management, 27(5) (2013) 1473-1488.
[25] I. Ebtehaj, H. Bonakdari, A.H. Zaji, H. Azimi, F. Khoshbin, GMDH-type neural network approach for modeling the discharge coefficient of rectangular sharp-crested side weirs, Engineering Science and Technology, an International Journal, 18(4) (2015) 746-757.
[26] M.E. Emiroglu, H. Agaccioglu, N. Kaya, Discharging capacity of rectangular side weirs in straight open channels, Flow Measurement and Instrumentation, 22(4) (2011) 319-330.
[27] M. Jalili, S. Borghei, Discussion: Discharge Coefficient of Rectangular Side Weirs, Journal of Irrigation and Drainage Engineering, 122(2) (1996) 132-132.
[28] J.H. Friedman, Multivariate adaptive regression splines, The annals of statistics, (1991) 1-67.
[29] M. Samadi, E. Jabbari, H. Azamathulla, M. Mojallal, Estimation of scour depth below free overfall spillways using multivariate adaptive regression splines and artificial neural networks, Engineering Applications of Computational Fluid Mechanics, (ahead-of-print) (2015) 1-10.
[30] V. Sharda, S. Prasher, R. Patel, P. Ojasvi, C. Prakash, Performance of Multivariate Adaptive Regression Splines (MARS) in predicting runoff in mid-Himalayan micro-watersheds with limited data/Performances de régressions par splines multiples et adaptives (MARS) pour la prévision d’écoulement au sein de micro-bassins versants Himalayens d’altitudes intermédiaires avec peu de données, Hydrological sciences journal, 53(6) (2008) 1165-1175.
[31] W. Zhang, A.T.C. Goh, Multivariate adaptive regression splines and neural network models for prediction of pile drivability, Geoscience Frontiers, (0) (2014).
[32] A.H. Haghiabi, Modeling River Mixing Mechanism Using Data Driven Model, Water Resour Manage, (2016) 1-14.
[33] A.H. Haghiabi, Prediction of River Pipeline Scour Depth Using Multivariate Adaptive Regression Splines, Journal of Pipeline Systems Engineering and Practice, (2016) 04016015.
[34] A.H. Haghiabi, Prediction of longitudinal dispersion coefficient using multivariate adaptive regression splines, Journal of Earth System Science, 125(5) (2016) 985-995.
[35] A. Parsaie, A.H. Haghiabi, Mathematical expression of discharge capacity of compound open channels using MARS technique, Journal of Earth System Science, 126(2) (2017) 20.
[36] M. Najafzadeh, A. Etemad-Shahidi, S.Y. Lim, Scour prediction in long contractions using ANFIS and SVM, Ocean Engineering, 111 (2016) 128-135.
[37] M. Najafzadeh, A. Tafarojnoruz, Evaluation of neuro-fuzzy GMDH-based particle swarm optimization to predict longitudinal dispersion coefficient in rivers, Environmental Earth Sciences, 75(2) (2016) 1-12.
[38] M. Najafzadeh, H.M. Azamathulla, Neuro-Fuzzy GMDH to Predict the Scour Pile Groups due to Waves, Journal of Computing in Civil Engineering, 29(5) (2015) 04014068.
[39] K. Roushangar, S. Akhgar, F. Salmasi, J. Shiri, Modeling energy dissipation over stepped spillways using machine learning approaches, Journal of Hydrology, 508 (2014) 254-265.
[40] K. Roushangar, S.M. Alipour, Prediction of overland flow resistance and its components based on flow characteristics using support vector machine, Water Science and Technology: Water Supply, (2017).