Abstract
A side orifice is a mechanism integrated into one or both side walls of a canal to redirect or release water from the main channel, and it has numerous applications in environmental engineering and irrigation. This research paper evaluates different artificial neural network (ANN) modeling algorithms for the estimation of discharge of a circular side orifice in open channels under free flow conditions. Four training algorithm were compared, namely, Gradient Descent (ANN-GD), Levenberg–Marquardt (ANN-LM), Gradient-Descent with Momentum (GDM), and Gradient-Descent with Adaptive Learning (GDA). Among all the models developed for discharge prediction through a circular side orifice, the ANN-LM model, which employed the LM algorithm for optimization during the backpropagation process, had the best performance during both training and testing. The AARE, R, E, and RMSE values were 3.13, 0.9994, 0.9987, and 0.0005, respectively, during training and 4.43, 0.9976, 0.9952, and 0.0010, respectively, during testing. The predicted discharge from the ANN-LM model was compared to the discharge equation proposed in the literature, and the comparison revealed that the ANN-LM model reduced the error in predicted discharge by 50%.
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The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.
References
Akhbari A, Zaji AH, Azimi H, Vafaeifard M (2017) Predicting the discharge coefficient of triangular plan form weirs using radial basis function and M5’methods. Appl Res Water Wastewater 4(1):281–289
Azimi H, Bonakdari H, Ebtehaj I (2017a) A highly efficient gene expression programming model for predicting the discharge coefficient in a side weir along a trapezoidal canal. Irrig Drain 66(4):655–666
Azimi H, Shabanlou S, Ebtehaj I, Bonakdari H, Kardar S (2017b) Combination of computational fluid dynamics, adaptive neuro-fuzzy inference system, and genetic algorithm for predicting discharge coefficient of rectangular side orifices. Irrig Drain Eng 143(7):04017015
Azimi H, Bonakdari H, Ebtehaj I (2017c) Sensitivity analysis of the factors affecting the discharge capacity of side weirs in trapezoidal channels using extreme learning machines. Flow Meas Instrum 54:216–223
Azimi H, Bonakdari H, Ebtehaj I (2019) Design of radial basis function-based support vector regression in predicting the discharge coefficient of a side weir in a trapezoidal channel. App Water Sci 9(4):78
Bagherifar M, Emdadi A, Azimi H, Sanahmadi B, Shabanlou S (2020) Numerical evaluation of turbulent flow in a circular conduit along a side weir. App Water Sci 10(1):1–9
Borghei SM, Jalili MR, Ghodsian M (1999) Discharge coefficient for sharp-crested side weir in subcritical flow. J Hydraul Eng 125(10):1051–1056. https://doi.org/10.1061/(ASCE)0733-9429(1999)125:10(1051)
Ebtehaj I, Bonakdari H, Zaji AH, Azimi H, Sharifi A (2015a) Gene expression programming to predict the discharge coefficient in rectangular side weirs. Appl Soft Comput 35:618–628
Ebtehaj I, Bonakdari H, Khoshbin F, Azimi H (2015b) Pareto genetic design of group method of data handling type neural network for prediction of discharge coefficient in rectangular side orifices. Flow Meas Instrum 41:67–74
Emiroglu ME, Agaccioglu H, Kaya N (2011) Discharging capacity of rectangular side weirs in straight open channels. Flow Meas Instrum 22(4):319–330. https://doi.org/10.1016/j.flowmeasinst.2011.04.003
Gerami Moghadam R, Yaghoubi B, Rajabi A, Shabanlou S, Izadbakhsh MA (2022) Simulation of discharge coefficient of triangular lateral orifices using an evolutionary design of generalized structure group method of data handling. Iran J Sci Technol Trans Mech Eng 46(3):679–692. https://doi.org/10.1007/s40997-022-00499-9
Hagan MT, Menhaj MB (1994) Training feedforward networks with the Marquardt algorithm. IEEE Trans Neural Netw 5(6):989–993. https://doi.org/10.1109/72.329697
Hager WH (1987) Lateral outflow over side weirs. J Hydraul Eng 113(4):491–504. https://doi.org/10.1061/(ASCE)0733-9429
Hashid M, Hussain A, Ahmad Z (2015) Discharge characteristics of lateral circular intakes in open channel flow. Flow Meas Instrum 46:87–92. https://doi.org/10.1016/j.flowmeasinst.2015.10.005
Hussain A, Haroon A (2019) Numerical analysis for free flow through side rectangular orifice in an open channel. ISH J Hydraul Eng. https://doi.org/10.1080/09715010.2019.1648220
Hussain A, Ahmad Z, Asawa GL (2010) Discharge characteristics of sharp-crested circular side orifices in open channels. Flow Meas Instrum. https://doi.org/10.1016/j.flowmeasinst.2010.06.005
Hussain A, Ahmad Z, Asawa GL (2011) Flow through sharp-crested rectangular side orifices under free flow conditions in open channels. Agric Water Manag 98(10):1536–1544. https://doi.org/10.1016/j.agwat.2011.05.004
Hussain A, Ahmad Z, Ojha CSP (2014) Analysis of flow through lateral rectangular orifices in open channels. Flow Meas Instrum 36:32–35. https://doi.org/10.1016/j.flowmeasinst.2014.02.002
Hussain A, Ahmad Z, Ojha CSP (2016) Flow through a lateral circular orifice under free and submerged flow conditions. Flow Meas Instrum 52:57–66. https://doi.org/10.1016/j.flowmeasinst.2016.09.007
Hussain A, Shariq A, Danish M, Ansari MA (2021) Discharge coefficient estimation for rectangular side weir using GEP and GMDH methods. Adv Comput Des 2(6):135–151. https://doi.org/10.12989/acd.2021.6.2.135
Jamei M, Ahmadianfar I, Chu X, Yaseen ZM (2021) Estimation of triangular side orifice discharge coefficient under a free flow condition using data-driven models. Flow Meas Instrum 77:101878. https://doi.org/10.1016/J.FLOWMEASINST.2020.101878
Khoshbin F, Bonakdari H, Ashraf Talesh SH, Ebtehaj I, Zaji AH, Azimi H (2016) Adaptive neuro-fuzzy inference system multi-objective optimization using the genetic algorithm/singular value decomposition method for modelling the discharge coefficient in rectangular sharp-crested side weirs. Eng Optim 48(6):933–948
Mahmodian AR, Rajabi A, Izadbakhsh MA, Shabanlou S (2019) Evaluation of side orifices shape factor using the novel approach self-adaptive extreme learning machine. Model Earth Syst Environ 5(3):925–935. https://doi.org/10.1007/s40808-019-00579-x
Mahmoudian A, Yosefvand F, Shabanlou S, Izadbakhsh MA, Rajabi A (2022) Robust extreme learning machine for estimation of triangular, rectangular, and parabolic weirs. Flow Meas Instrum 88:102237. https://doi.org/10.1016/j.flowmeasinst.2022.102237
Marchi D (1934) G. Essay on the performance of lateral weirs. L Energia Electrica Milano 11(11):849–860
Marques de Sa JM, Alexandre LA et al (eds) (2007) Artificial neural networks-ICANN. In: 17th international conference Porto, Portugal, proceedings, Part I. Springer, Berlin Heidelberg, New York
Moghadam RG, Yaghoubi B, Rajabi A et al (2022) Evaluation of discharge coefficient of triangular side orifices by using regularized extreme learning machine. Appl Water Sci 12(7):145. https://doi.org/10.1007/s13201-022-01665-9
Mohammed AY, Golijanek-Jędrzejczyk A (2020) Estimating the uncertainty of the discharge coefficient predicted for oblique side weir using Monte Carlo method. Flow Meas Instrum 73:101727. https://doi.org/10.1016/j.flowmeasinst.2020.101727
Mohammed AY, Al-Talib AN, Basheer TA (2014) Simulation of flow over a side weir using simulink. Scientia Iranica 20(4):1094–1100
Ramamurthy AS, Tim US, Sarraf S (1986) Rectangular lateral orifices in open channels. J Environ Eng 112(2):292–300. https://doi.org/10.1061/(ASCE)0733-9372
Ramamurthy AS, Tim US, Rao MVJ (1987) Weir-orifice units for uniform flow distribution. J Environ Eng 113(1):155–166. https://doi.org/10.1061/(ASCE)0733-9372
Ranga Raju KG, Gupta SK, Prasad B (1979) Side weir in rectangular channel. J Hydraul Div 105(5):547–554
Schalkoff RJ (1997) Artificial neural networks. McGraw-Hill, Singapore
Shariq A, Hussain A, Ansari MA (2018) Lateral flow through the sharp crested side rectangular weirs in open channels. Flow Meas Instrum 59:8–17. https://doi.org/10.1016/j.flowmeasinst.2017.11.007
Shen G, Li S, Parsaie A, Li G, Cao D, Pandey P (2022) Prediction and parameter quantitative analysis of side orifice discharge coefficient based on machine learning. Water Supply 22(12):8880–8892. https://doi.org/10.2166/ws.2022.394
Vatankhah AR (2012) Analytical solution for water surface profile along a side weir in a triangular channel. Flow Meas Instrum 23(1):76–79. https://doi.org/10.1016/j.flowmeasinst.2011.10.001
Vatankhah AR, Mirnia SH (2018) Predicting discharge coefficient of triangular side orifice under free flow conditions. J Irrig Drain 144(10):04018030
Vatankhah AR, Rafeifar F (2020) Analytical and experimental study of flow through elliptical side orifices. Flow Meas Instrum 72:101712. https://doi.org/10.1016/j.flowmeasinst.2020.101712
Zaji AH, Bonakdari H (2014) Performance evaluation of two different neural network and particle swarm optimization methods for prediction of discharge capacity of modified triangular side weirs. Flow Meas Instrum 40:149–156. https://doi.org/10.1016/j.flowmeasinst.2014.10.002
Zurada JM (1994) Introduction to artificial neural systems. Jaico Publishing House, Mumbai
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Ayaz, M., Chourasiya, S. & Danish, M. Performance analysis of different ANN modelling techniques in discharge prediction of circular side orifice. Model. Earth Syst. Environ. 10, 273–283 (2024). https://doi.org/10.1007/s40808-023-01766-7
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DOI: https://doi.org/10.1007/s40808-023-01766-7