STANDARD EQUATIONS FOR PREDICTING THE DISCHARGE COEFFICIENT OF A MODIFIED HIGH-PERFORMANCE SIDE WEIR

Document Type : Article

Authors

1 Department of Civil Engineering, Razi University, Kermanshah, Iran

2 Department of Computer System, Faculty of Computer Science and Information Technology, University of Malaya, 50603 Kuala Lumpur, Malaysia

Abstract

Side weirs are hydraulic structures that are used as discharge adjustments to divert the surplus water flowing from the main channel. Predicting the discharge coefficient is one of the most important parameters in the side weir design process. In practical situations, it is preferred to predict the discharge coefficient with simple equations. The goal of this study was to develop accurate standard equations for use in predicting the discharge coefficient of a high-performance, modified triangular side weir. The Particle Swarm Optimization (PSO) algorithm was used to optimize the parameters of the equations. Four different forms of the equations and two non-dimensional input combinations were used to develop the most appropriate model. The results obtained by our simple standard equations optimized by the PSO algorithm were compared with the results of complex nonlinear regression equations, and our equations were more accurate more accurate in modeling the discharge coefficient. Our method reduced the error in the results by as much as 43% compared to the regression methods, and its simplicity makes it useful in solving practical problems.

Keywords

Main Subjects


References

1. De Marchi, G. \Lateral weirs fundamentals" [Saggio
di teoria del funzionamento degli stramazzi laterali,
L'Energia Elettrica. (In Italian), 11(11), pp. 849-860
(1934).
2. Ackers, P. \A theoretical consideration of side-weirs
as storm water over
ows", Pros. ICE, 6, pp. 250-269
(1957).
3. Yu-Tech, L. \Discussion of spatially varied
ow over
side weir", Journal of Hydrologic Engineering, 98(11),
pp. 2046-2048 (1972).
4. Singh, R., Manivannan, D., and Satyanarayana, T.
\Discharge coecient of rectangular side weirs", Journal
of Irrigation and Drainage Engineering, 120(4),
pp. 814-819 (1994).
5. Swamee, P.K., Pathak, S.K., and Ali, M.S. \Side-weir
analysis using elementary discharge coecient", Journal
of Irrigation and Drainage Engineering, 120(4),
pp. 742-755 (1994).
6. Ura, M., Kita, Y., Akiyama, J., Moriyama, H., and
Kumar, J.A. \Discharge coecient of oblique sideweirs",
Journal of Hydroscience and Hydraulic Engineering,
19(1), pp. 85-96 (2001).
7. Borghei, S.M. and Parvaneh, A. \Discharge characteristics
of a modi ed oblique side weir in subcritical

ow", Flow Measurement and Instrumentation, 22(5),
pp. 370-376 (2011).
8. Najafzadeh, M. and Barani, G.A. \Comparison of
group method of data handling based genetic programming
and back propagation systems to predict scour
depth around bridge piers", Scientia Iranica, 18(6),
pp. 1207-1213 (2011).
9. Najafzadeh, M. and Azamathulla, H.M. \Group
method of data handling to predict scour depth around
bridge piers", Neural Computing and Applications,
23(7), pp. 2107-2112 (2013).
10. Najafzadeh, M., Barani, G.-A., and Hessami Kermani,
M.R. \GMDH based back propagation algorithm to
predict abutment scour in cohesive soils", Ocean Engineering,
59, pp. 100-106 (2013).
11. Najafzadeh, M., Barani, G.-A., and Hessami-Kermani,
M.-R. \Group method of data handling to predict
scour at downstream of a ski-jump bucket spillway",
Earth Science Informatics, 7(4), pp. 231-248 (2014).
12. Najafzadeh, M. and Lim, S.Y. \Application of improved
neuro-fuzzy GMDH to predict scour depth at
sluice gates", Earth Science Informatics, 8(1), pp. 187-
196 (2015).
13. Najafzadeh, M. \Neuro-fuzzy GMDH based particle
swarm optimization for prediction of scour depth at
downstream of grade control structures", Engineering
Science and Technology, an International Journal,
18(1), pp. 42-51 (2015).
14. Grace, J.L. and Priest, M.S., Division of Flow in Open
Channel Junctions, Engineering Experiment Station,
Alabama Polytechnic Institute (1958).
15. More, J. \The Levenberg-Marquardt algorithm: Implementation
and theory", Watson, G.A. (Ed.) In
Numerical Analysis, pp. 105-116, Springer Berlin Heidelberg
(1978).
16. Chau, K., Wu, C., and Li, Y. \Comparison of several

ood forecasting models in Yangtze River", Journal of
Hydrologic Engineering, 10(6), pp. 485-491 (2005).
17. Cheng, C., Chau, K., Sun, Y., and Lin, J. \Long-Term
Prediction of Discharges in Manwan Reservoir Using
Arti cial Neural Network Models", Wang, J., Liao, X.-
F., and Yi, Z. (Eds.), In Advances in Neural Networks -
ISNN 2005, pp. 1040-1045, Springer Berlin Heidelberg
(2005).
18. Chen, W. and Chau, K. \Intelligent manipulation and
calibration of parameters for hydrological models",
International Journal of Environment and Pollution,
28(3), pp. 432-447 (2006).
19. Firat, M. and Gungor, M. \Hydrological time-series
modelling using an adaptive neuro-fuzzy inference
system", Hydrological Processes, 22(13), pp. 2122-2132
(2008).
20. Wu, C., Chau, K., and Li, Y. \Predicting monthly
stream
ow using data-driven models coupled with
data-preprocessing techniques", Water Resources Research,
45(8), p. W08432 (2009).
21. Asadi, S., Shahrabi, J., Abbaszadeh, P., and Tabanmehr,
S. \A new hybrid arti cial neural networks
for rainfall-runo process modeling", Neurocomputing,
121, pp. 470-480 (2013).
22. Yurtseven, I. and Zengin, M. \Neural network modelling
of rainfall interception in four di erent forest
stands", Annals of Forest Research, 56(2), pp. 351-362
(2013).
23. Muttil, N. and Chau, K.-W. \Neural network and
genetic programming for modelling coastal algal
blooms", International Journal of Environment and
Pollution, 28(3), pp. 223-238 (2006).
1068 A.H. Zaji et al./Scientia Iranica, Transactions A: Civil Engineering 25 (2018) 1057{1069
24. Kisi, O. and Ozturk, O. \Adaptive neurofuzzy
computing technique for evapotranspiration estimation",
Journal of Irrigation and Drainage Engineering,
133(4), pp. 368-379 (2007).
25. Cobaner, M. \Evapotranspiration estimation by two
di erent neuro-fuzzy inference systems", Journal of
Hydrology, 398(3), pp. 292-302 (2011).
26. Hager, W.H. \Discussion of separation zone at openchannel
junctions", Journal of Hydraulic Engineering,
113(4), pp. 539-543 (1987).
27. Najafzadeh, M. and Tafarojnoruz, A. \Evaluation of
neuro-fuzzy GMDH-based particle swarm optimization
to predict longitudinal dispersion coecient in rivers",
Environmental Earth Sciences, 75(2), p. 157 (2016).
28. Maanen, B.V., Coco, G., Bryan, K.R., and Ruessink,
B. \The use of arti cial neural networks to analyze
and predict alongshore sediment transport", Nonlinear
Processes in Geophysics, 17(5), pp. 395-404 (2010).
29. Ebtehaj, I. and Bonakdari, H. \Evaluation of sediment
transport in sewer using arti cial neural network",
Engineering Applications of Computational Fluid Mechanics,
7(3), pp. 382-392 (2013).
30. Taormina, R., Chau, K.-W., and Sethi, R. \Arti cial
neural network simulation of hourly groundwater levels
in a coastal aquifer system of the Venice lagoon", Engineering
Applications of Arti cial Intelligence, 25(8),
pp. 1670-1676 (2012).
31. Pulido-Calvo, I. and Gutierrez-Estrada, J.C. \Improved
irrigation water demand forecasting using a
soft-computing hybrid model", Biosystems Engineering,
102(2), pp. 202-218 (2009).
32. Tiwari, M.K. and Adamowski, J. \Urban water demand
forecasting and uncertainty assessment using
ensemble wavelet-bootstrap-neural network models",
Water Resources Research, 49(10), pp. 6486-6507
(2013).
33. Najafzadeh, M. and Sattar, A.M.A. \Neuro-fuzzy
GMDH approach to predict longitudinal dispersion in
water networks", Water resources management, 29(7),
pp. 2205-2219 (2015).
34. Bilhan, O., Emin Emiroglu, M., and Kisi, O. \Application
of two di erent neural network techniques to
lateral out
ow over rectangular side weirs located on a
straight channel", Advances in Engineering Software,
41(6), pp. 831-837 (2010).
35. Kisi, O., Emin Emiroglu, M., Bilhan, O., and Guven,
A. \Prediction of lateral out
ow over triangular
labyrinth side weirs under subcritical conditions using
soft computing approaches", Expert Systems with Applications,
39(3), pp. 3454-3460 (2012).
36. Emin Emiroglu, M., Kisi, O., and Bilhan, O. \Predicting
discharge capacity of triangular labyrinth side
weir located on a straight channel by using an adaptive
neuro-fuzzy technique", Advances in Engineering
Software, 41(2), pp. 154-160 (2010).
37. Bilhan, O., Emiroglu, M.E., and Kisi, O. \Use of
arti cial neural networks for prediction of discharge
coecient of triangular labyrinth side weir in curved
channels", Advances in Engineering Software, 42(4),
pp. 208-214 (2011).
38. Emiroglu, M.E., Bilhan, O., and Kisi, O. \Neural networks
for estimation of discharge capacity of triangular
labyrinth side-weir located on a straight channel",
Expert Systems with Applications, 38(1), pp. 867-874
(2011).
39. Neary, V. and Sotiropoulos, F. \Numerical investigation
of laminar
ows through 90-degree diversions of
rectangular cross-section", Computers & Fluids, 25(2),
pp. 95-118 (1996).
40. Khorchani, M. and Blanpain, O. \Development of a
discharge equation for side weirs using arti cial neural
networks", Journal of Hydroinformatics, 7, pp. 31-39
(2005).
41. Dursun, O.F., Kaya, N., and Firat, M. \Estimating
discharge coecient of semi-elliptical side weir using
ANFIS", Journal of Hydrology, 426, pp. 55-62 (2012).
42. Bagheri, S., Kabiri-Samani, A., and Heidarpour, M.
\Discharge coecient of rectangular sharp-crested side
weirs, Part I: Traditional weir equation", Flow Measurement
and Instrumentation, 35, pp. 109-115 (2013).
43. Kennedy, J. and Eberhart, R. \Particle swarm optimization",
Proceedings of IEEE international conference
on neural networks, Perth, Australia, pp. 1942-
1948 (1995).
44. Tripathi, P.K., Bandyopadhyay, S., and Pal, S.K.
\Multi-objective particle swarm optimization with
time variant inertia and acceleration coecients", Information
Sciences, 177(22), pp. 5033-5049 (2007).
45. Chatterjee, A. and Siarry, P. \Nonlinear inertia weight
variation for dynamic adaptation in particle swarm optimization",
Computers & Operations Research, 33(3),
pp. 859-871 (2006).
46. Helton, J., Iman, R., Johnson, J., and Leigh, C.
\Uncertainty and sensitivity analysis of a model for
multicomponent aerosol dynamics", Nuclear Technology,
73(3), pp. 320-342 (1986).
47. Iman, R.L. and Helton, J.C. \An investigation of
uncertainty and sensitivity analysis techniques for
computer models", Risk Analysis, 8(1), pp. 71-90
(1988).
48. Downing, D.J., Gardner, R., and Ho man, F. \An examination
of response-surface methodologies for uncertainty
analysis in assessment models", Technometrics,
27(2), pp. 151-163 (1985).
49. Hamby, D.M. \A review of techniques for parameter
sensitivity analysis of environmental models", Environmental
Monitoring and Assessment, 32(2), pp. 135-
154 (1994).
50. Akaike, H. \Information theory and an extension
of the maximum likelihood principle", Kotz, S. and
Johnson, N.L. (Eds.), In Breakthroughs in Statistics:
Foundations and Basic Theory, pp. 610-624, Springer
New York, New York, NY (1992).
A.H. Zaji et al./Scientia Iranica, Transactions A: Civil Engineering 25 (2018) 1057{1069 1069
51. Akaike, H. \A new look at the statistical model identi
cation", IEEE Transactions on Automatic Control,
19(6), pp. 716-723 (1974).
52. Akaike, H. \Prediction and entropy", Atkinson, A.C.
and Fienberg, S.E. (Eds.), In A Celebration of Statistics:
The ISI Centenary Volume A Volume to Celebrate
the Founding of the International Statistical
Institute in 1885, pp. 1-24, Springer New York, New
York, NY (1985).