Support Vector Machine to predict the discharge coefficient of Sharp crested w-planform weirs

Document Type : Research Article

Authors

Water Engineering Department, Lorestan University, Khorramabad, Iran

Abstract

In this paper, the discharge coefficient (Cd) of triangular labyrinth weir was predicted
using Multilayer Perceptron Neural Network (MLPNN), Radial Basis Neural Network (RBFNN) and
support vector machine (SVM). To this end, 223 data sets related to the effective parameters on Cd were
collected. Using dimensional analysis techniques, the involved dimensionless parameters on Cd were
derived. To find out the most effective parameters on Cd, the Gamma test (GT) was analyzed. Results of
GT demonstrated that H/P, Lw/Lc, and Lw/Wm are the most effective parameters on Cd. To develop ANN
and SVM, different types of transfer and kernel functions were tested. During the testing of transfer and
kernel functions for developing the ANN and SVM models, respectively, it was found that tensing and
RBFNN have the best performance for predicting the Cd. Overall evaluation of the results of developed
models indicated that both models have a suitable accuracy in predicting the Cd; however, the SVM is a
bit more accurate. Comparing the outcomes of the applied models in terms of DDR index shows that the
data dispersivity of SVM is less than the others; therefore, this model is more reliable.

Highlights

[1] R. M. Anderson and B. P. Tullis, “Comparison of Piano Key and Rectangular Labyrinth Weir Hydraulics.” Journal of Hydraulic Engineering, 138(4) (2012) 358- 361.

[2] R. M. Anderson and B. P. Tullis, “Piano Key Weir Hydraulics and Labyrinth Weir Comparison.” Journal of Irrigation and Drainage Engineering, 139(3) (2013) 246-253.

[3] H. M. Azamathulla, A. H. Haghiabi and A. Parsaie, “Prediction of side weir discharge coefficient by support vector machine technique.” Water Science and Technology: Water Supply, 16(4) (2016) 1002-1016.

[4] S. Dehdar-behbahani and 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.

[5] M. E. Emiroglu and N. Kaya, “Discharge Coefficient for Trapezoidal Labyrinth Side Weir in Subcritical Flow.” Water Resources Management, 25(3) (2011) 1037-1058.

[6] S. Erpicum, F. Laugier, J. L. Boillat, M. Pirotton, B. Reverchon and A. Schleiss, “Labyrinth and piano key weirs—PKW 2011.” Proc., Proceedings of the International Conference on Labyrinth and Piano Key Weirs, Balkema Liege, 9-11.

[7] S. Erpicum, F. Laugier, M. Pfister, M. Pirotton, G. M. Cicero and A. J. Schleiss, . Labyrinth and Piano Key Weirs II, Taylor & Francis (2013).

[8] M. Ghodsian, “Stage–discharge relationship for a triangular labyrinth spillway.” Proceedings of the ICE-Water Management, 162(3) (2009) 173-178.

[9] A. H. Haghiabi, “Modeling River Mixing Mechanism Using Data Driven Model.” Water Resour Manage, (2016) 1-14.

[10] A. H. Haghiabi, “Prediction of longitudinal dispersion coefficient using multivariate adaptive regression splines.” Journal of Earth System Science, 125(5) (2016) 985-995.

[11] A. H. Haghiabi, H. M. Azamathulla and A. Parsaie, “Prediction of head loss on cascade weir using ANN and SVM.” ISH Journal of Hydraulic Engineering, (2016) 1-9.

[12] A. H. Haghiabi, A. Parsaie, and S. Ememgholizadeh, “Prediction of discharge coefficient of triangular labyrinth weirs using Adaptive Neuro Fuzzy Inference System.” Alexandria Engineering Journal (2017).

[13] N. Hay and G. Taylor, “Performance and design of labyrinth weirs.” Journal of the Hydraulics Division, 96(11) (1970) 2337-2357.

[14] A. Hossein Zaji, H. Bonakdari, and S. Karimi, “Radial Basis Neural Network and Particle Swarm Optimization-based equations for predicting the discharge capacity of triangular labyrinth weirs.” Flow Measurement and Instrumentation, 45 (2015) 341-347.

[15] K. Houston, “Hydraulic model study of Ute Dam labyrinth spillway.” Report GR-82-7 August 1982. 47 p, 30 Fig, 2 Tab, 4 Ref, 1 Append.

[16] A. Kabiri-Samani and A. Javaheri, “Discharge coefficients for free and submerged flow over Piano Key weirs.” Journal of Hydraulic Research, 50(1) (2012) 114-120.

[17] O. Kisi, “Pan evaporation modeling using least square support vector machine, multivariate adaptive regression splines and M5 model tree.” Journal of Hydrology, 528 (2015) 312-320.

[18] S. Kumar, Z. Ahmad and T. Mansoor, “A new approach to improve the discharging capacity of sharp-crested triangular plan form weirs.” Flow Measurement and Instrumentation, 22(3) (2011) 175-180.

[19] J. Liu, Radial Basis Function (RBF) neural network control for mechanical systems: design, analysis and Matlab simulation, Springer Science & Business Media (2013).

[20] O. Machiels, S. Erpicum, B. J. Dewals, P. Archambeau and M. Pirotton, “Experimental observation of flow characteristics over a Piano Key Weir.” Journal of Hydraulic Research, 49(3) (2011) 359-366.

[21] O. Machiels, M. Pirotton, A. Pierre, B. Dewals and S. Erpicum, “Experimental parametric study and design of Piano Key Weirs.” Journal of Hydraulic Research, 52(3) (2014) 326-335.

[22] R. Noori, A. Karbassi, A. Farokhnia, and M. Dehghani, “Predicting the Longitudinal Dispersion Coefficient Using Support Vector Machine and Adaptive Neuro- Fuzzy Inference System Techniques.” Environmental Engineering Science, 26(10) (2009) 1503-1510.

[23] R. Noori, A. R. Karbassi, A. Moghaddamnia, D. Han, M. H. Zokaei-Ashtiani, A. Farokhnia and M. G. Gousheh, “Assessment of input variables determination on the SVM model performance using PCA, Gamma test, and forward selection techniques for monthly stream flow prediction.” Journal of Hydrology, 401(3–4) (2011) 177-189.

[24] A. Parsaie, H. M. Azamathulla and A. H. Haghiabi, “Physical and numerical modeling of performance of detention dams.” Journal of Hydrology, (2017).

[25] A. Parsaie and 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, (2015) 1-13.

[26] A. Parsaie, and A. Haghiabi, “Prediction of Side Weir Discharge Coefficient by Genetic Programming Technique.” Jordan Journal of Civil Engineering, 11(1) (2017) 132-141.

[27] A. Parsaie and A. H. Haghiabi, “Predicting the longitudinal dispersion coefficient by radial basis function neural network.” Modeling Earth Systems and Environment, 1(4) (2015) 34.

[28] A. Parsaie, A. H. Haghiabi, and A. Moradinejad, “CFD modeling of flow pattern in spillway’s approach channel.” Sustainable Water Resources Management, 1(3) (2015) 245-251.

[29] A. Parsaie, A. H. Haghiabi, M. Saneie and H. Torabi, “Applications of soft computing techniques for prediction of energy dissipation on stepped spillways.” Neural Computing and Applications, (2016) 1-17.

[30] A. Parsaie, S. Najafian and Z. Shamsi, “Predictive modeling of discharge of flow in compound open channel using radial basis neural network.” Modeling Earth Systems and Environment, 2(3) (2016) 150.

[31] M. L. Ribeiro, M. Pfister, A. J. Schleiss and J.-L. Boillat, “Hydraulic design of A-type Piano Key Weirs.” Journal of Hydraulic Research, 50(4) (2012) 400-408.

[32] G. K. Robertson, “Labyrinth weir hydraulics: Validation of CFD modelling.” Stellenbosch: Stellenbosch University, (2014).

[33] G. D. Singhal, N. Sharma and C. S. P. Ojha, “EXPERIMENTAL STUDY OF HYDRAULICALLY EFFICIENT PIANO KEY WEIR CONFIGURATION.” ISH Journal of Hydraulic Engineering, 17(1) (2011) 18- 33.

[34] G. Taylor, “The performance of labyrinth weirs.” Ph.D, University of Nottingham, (1968).

Keywords

References

[1] R. M. Anderson and B. P. Tullis, “Comparison of Piano Key and Rectangular Labyrinth Weir Hydraulics.” Journal of Hydraulic Engineering, 138(4) (2012) 358- 361.
[2] R. M. Anderson and B. P. Tullis, “Piano Key Weir Hydraulics and Labyrinth Weir Comparison.” Journal of Irrigation and Drainage Engineering, 139(3) (2013) 246-253.
[3] H. M. Azamathulla, A. H. Haghiabi and A. Parsaie, “Prediction of side weir discharge coefficient by support vector machine technique.” Water Science and Technology: Water Supply, 16(4) (2016) 1002-1016.
[4] S. Dehdar-behbahani and 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.
[5] M. E. Emiroglu and N. Kaya, “Discharge Coefficient for Trapezoidal Labyrinth Side Weir in Subcritical Flow.” Water Resources Management, 25(3) (2011) 1037-1058.
[6] S. Erpicum, F. Laugier, J. L. Boillat, M. Pirotton, B. Reverchon and A. Schleiss, “Labyrinth and piano key weirs—PKW 2011.” Proc., Proceedings of the International Conference on Labyrinth and Piano Key Weirs, Balkema Liege, 9-11.
[7] S. Erpicum, F. Laugier, M. Pfister, M. Pirotton, G. M. Cicero and A. J. Schleiss, . Labyrinth and Piano Key Weirs II, Taylor & Francis (2013).
[8] M. Ghodsian, “Stage–discharge relationship for a triangular labyrinth spillway.” Proceedings of the ICE-Water Management, 162(3) (2009) 173-178.
[9] A. H. Haghiabi, “Modeling River Mixing Mechanism Using Data Driven Model.” Water Resour Manage, (2016) 1-14.
[10] A. H. Haghiabi, “Prediction of longitudinal dispersion coefficient using multivariate adaptive regression splines.” Journal of Earth System Science, 125(5) (2016) 985-995.
[11] A. H. Haghiabi, H. M. Azamathulla and A. Parsaie, “Prediction of head loss on cascade weir using ANN and SVM.” ISH Journal of Hydraulic Engineering, (2016) 1-9.
[12] A. H. Haghiabi, A. Parsaie, and S. Ememgholizadeh, “Prediction of discharge coefficient of triangular labyrinth weirs using Adaptive Neuro Fuzzy Inference System.” Alexandria Engineering Journal (2017).
[13] N. Hay and G. Taylor, “Performance and design of labyrinth weirs.” Journal of the Hydraulics Division, 96(11) (1970) 2337-2357.
[14] A. Hossein Zaji, H. Bonakdari, and S. Karimi, “Radial Basis Neural Network and Particle Swarm Optimization-based equations for predicting the discharge capacity of triangular labyrinth weirs.” Flow Measurement and Instrumentation, 45 (2015) 341-347.
[15] K. Houston, “Hydraulic model study of Ute Dam labyrinth spillway.” Report GR-82-7 August 1982. 47 p, 30 Fig, 2 Tab, 4 Ref, 1 Append.
[16] A. Kabiri-Samani and A. Javaheri, “Discharge coefficients for free and submerged flow over Piano Key weirs.” Journal of Hydraulic Research, 50(1) (2012) 114-120.
[17] O. Kisi, “Pan evaporation modeling using least square support vector machine, multivariate adaptive regression splines and M5 model tree.” Journal of Hydrology, 528 (2015) 312-320.
[18] S. Kumar, Z. Ahmad and T. Mansoor, “A new approach to improve the discharging capacity of sharp-crested triangular plan form weirs.” Flow Measurement and Instrumentation, 22(3) (2011) 175-180.
[19] J. Liu, Radial Basis Function (RBF) neural network control for mechanical systems: design, analysis and Matlab simulation, Springer Science & Business Media (2013).
[20] O. Machiels, S. Erpicum, B. J. Dewals, P. Archambeau and M. Pirotton, “Experimental observation of flow characteristics over a Piano Key Weir.” Journal of Hydraulic Research, 49(3) (2011) 359-366.
[21] O. Machiels, M. Pirotton, A. Pierre, B. Dewals and S. Erpicum, “Experimental parametric study and design of Piano Key Weirs.” Journal of Hydraulic Research, 52(3) (2014) 326-335.
[22] R. Noori, A. Karbassi, A. Farokhnia, and M. Dehghani, “Predicting the Longitudinal Dispersion Coefficient Using Support Vector Machine and Adaptive Neuro- Fuzzy Inference System Techniques.” Environmental Engineering Science, 26(10) (2009) 1503-1510.
[23] R. Noori, A. R. Karbassi, A. Moghaddamnia, D. Han, M. H. Zokaei-Ashtiani, A. Farokhnia and M. G. Gousheh, “Assessment of input variables determination on the SVM model performance using PCA, Gamma test, and forward selection techniques for monthly stream flow prediction.” Journal of Hydrology, 401(3–4) (2011) 177-189.
[24] A. Parsaie, H. M. Azamathulla and A. H. Haghiabi, “Physical and numerical modeling of performance of detention dams.” Journal of Hydrology, (2017).
[25] A. Parsaie and 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, (2015) 1-13.
[26] A. Parsaie, and A. Haghiabi, “Prediction of Side Weir Discharge Coefficient by Genetic Programming Technique.” Jordan Journal of Civil Engineering, 11(1) (2017) 132-141.
[27] A. Parsaie and A. H. Haghiabi, “Predicting the longitudinal dispersion coefficient by radial basis function neural network.” Modeling Earth Systems and Environment, 1(4) (2015) 34.
[28] A. Parsaie, A. H. Haghiabi, and A. Moradinejad, “CFD modeling of flow pattern in spillway’s approach channel.” Sustainable Water Resources Management, 1(3) (2015) 245-251.
[29] A. Parsaie, A. H. Haghiabi, M. Saneie and H. Torabi, “Applications of soft computing techniques for prediction of energy dissipation on stepped spillways.” Neural Computing and Applications, (2016) 1-17.
[30] A. Parsaie, S. Najafian and Z. Shamsi, “Predictive modeling of discharge of flow in compound open channel using radial basis neural network.” Modeling Earth Systems and Environment, 2(3) (2016) 150.
[31] M. L. Ribeiro, M. Pfister, A. J. Schleiss and J.-L. Boillat, “Hydraulic design of A-type Piano Key Weirs.” Journal of Hydraulic Research, 50(4) (2012) 400-408.
[32] G. K. Robertson, “Labyrinth weir hydraulics: Validation of CFD modelling.” Stellenbosch: Stellenbosch University, (2014).
[33] G. D. Singhal, N. Sharma and C. S. P. Ojha, “EXPERIMENTAL STUDY OF HYDRAULICALLY EFFICIENT PIANO KEY WEIR CONFIGURATION.” ISH Journal of Hydraulic Engineering, 17(1) (2011) 18- 33.
[34] G. Taylor, “The performance of labyrinth weirs.” Ph.D, University of Nottingham, (1968).
AUT Journal of Civil Engineering
Volume 1, Issue 2
December 2017
Pages 195-204

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