Advertisement

Water Resources Management

, Volume 33, Issue 11, pp 3929–3947 | Cite as

Application of Gaussian Process Regression Model to Predict Discharge Coefficient of Gated Piano Key Weir

  • Masood Akbari
  • Farzin SalmasiEmail author
  • Hadi Arvanaghi
  • Masoud Karbasi
  • Davood Farsadizadeh
Article
  • 44 Downloads

Abstract

The Piano Key (PK) weir is a new type of long crested weirs. This study was involved the addition of a gate to PK weir inlet keys. It was conducted by the Department of Water Engineering, University of Tabriz, Iran to determine if the gate increased hydraulic performance. A Gated Piano Key (GPK) weir was constructed and tested for discharge ranges of between 10 and 130 l per second. To this end, 156 experimental tests were performed and the effective parameters on the GPK weir discharge coefficient (Cd), such as gate dimensions (b and d), gate insertion depth in the inlet key (Hgate), the ratio of the inlet key width to the outlet key width (Wi/Wo) and the head over the GPK weir crest (H) were investigated. In addition, application of soft computing to estimate of Cd was carried out using MLP, GPR, SVM, GRNN, multiple linear and non-linear regressions methods using MATLAB 2018 software. This study suggests the relation for Cd with non-dimension parameters. The results of this study showed that H, Wi/Wo, Hgate and b and d, had the greatest effect on the GPK weir discharge coefficient, respectively. The GPR method was introduced as a new effective method for predicting discharge coefficient of weirs with RMSE = 0.011, R2 = 0.992 and MAPE = 1.167% and provided the best results when compared with other methods.

Keywords

Gated piano key (GPK) weir Experimental model Discharge coefficient (CdGaussian process regression (GPR) Artificial intelligence 

Abbreviations

b

Length of rectangular gate;

B

Weir sidewall length;

d

Width of rectangular gate;

Bi

Downstream or inlet key overhang length;

Bo

Upstream or outlet key overhang length;

Cd

Dimensionless discharge coefficient;

g

Gravitational acceleration;

GPK weir

Gated piano key weir;

H

Head over the crest;

Hdown

Downstream head;

Hgate

Water head from the rectangular gate center to the crest of weir;

Hup

Upstream head;

L

Crest length; [L = N(Wi + Wo + 2B)].

n

Crest length to weir width ratio; (n = L/W).

N

Weir cycle number;

P

Total weir height;

Pm

Weir wall height at the center of weir;

PK weir

Piano key weir;

Q

Discharge;

Si

Inlet key slope;

So

Outlet key slope;

Ts

Weir wall thickness;

W

Total weir width or flume width;

Wi

Inlet key width;

Wo

Outlet key width;

μ

Water dynamic viscosity;

ρ

Water density and

σ

Water surface tension

Notes

Compliance with Ethical Standards

Conflict of Interest

None.

References

  1. Anderson R, Tullis B (2012) Piano key weir hydraulics and labyrinth weir comparison. J Irrig Drain Eng 139:246–253.  https://doi.org/10.1061/(ASCE)IR.1943-4774.0000530 CrossRefGoogle Scholar
  2. Baum EB, Haussler D (1989) What size net gives valid generalization? In: Advances in neural information processing systems, pp 81–90Google Scholar
  3. Bilhan O, Emiroglu ME, Kisi O (2011) Use of artificial neural networks for prediction of discharge coefficient of triangular labyrinth side weir in curved channels. Adv Eng Softw 42:208–214.  https://doi.org/10.1016/j.advengsoft.2011.02.006 CrossRefGoogle Scholar
  4. Burges CJC (1998) A tutorial on support vector machines for pattern recognition. Data Min Knowl Disc 2:121–167.  https://doi.org/10.1023/a:1009715923555 CrossRefGoogle Scholar
  5. Chen S, Cowan CF, Grant PM (1991) Orthogonal least squares learning algorithm for radial basis function networks. IEEE Trans Neural Netw 2:302–309.  https://doi.org/10.1109/72.80341 CrossRefGoogle Scholar
  6. Cigizoglu HK, Alp M (2006) Generalized regression neural network in modelling river sediment yield. Adv Eng Softw 37:63–68.  https://doi.org/10.1016/j.advengsoft.2005.05.002 CrossRefGoogle Scholar
  7. Demuth HB, Beale MH, De Jess O, Hagan MT (2014) Neural network design. Martin HaganGoogle Scholar
  8. Dibike YB, Solomatine DP (2001) River flow forecasting using artificial neural networks. Physics and Chemistry of the Earth, Part B: Hydrology, Oceans and Atmosphere 26:1–7.  https://doi.org/10.1016/s1464-1909(01)85005-x CrossRefGoogle Scholar
  9. Dursun OF, Kaya N, Firat M (2012) Estimating discharge coefficient of semi-elliptical side weir using ANFIS. J Hydrol 426-427:55–62.  https://doi.org/10.1016/j.jhydrol.2012.01.010 CrossRefGoogle Scholar
  10. Ebden M (2015) Gaussian processes: A quick introduction. arXiv preprint arXiv:150502965Google Scholar
  11. Ebtehaj I, Bonakdari H, Zaji AH, Azimi H, Sharifi A (2015) Gene expression programming to predict the discharge coefficient in rectangular side weirs. Appl Soft Comput 35:618–628.  https://doi.org/10.1016/j.asoc.2015.07.003 CrossRefGoogle Scholar
  12. Emiroglu ME, Bilhan O, Kisi O (2011) Neural networks for estimation of discharge capacity of triangular labyrinth side-weir located on a straight channel. Expert Syst Appl 38:867–874.  https://doi.org/10.1016/j.eswa.2010.07.058 CrossRefGoogle Scholar
  13. Goh AT (1995) Back-propagation neural networks for modeling complex systems. Artif Intell Eng 9:143–151.  https://doi.org/10.1016/0954-1810(94)00011-s CrossRefGoogle Scholar
  14. Grbić R, Kurtagić D, Slišković D (2013) Stream water temperature prediction based on Gaussian process regression. Expert Syst Appl 40:7407–7414.  https://doi.org/10.1016/j.eswa.2013.06.077 CrossRefGoogle Scholar
  15. Haghiabi AH, Parsaie A, Ememgholizadeh S (2018) Prediction of discharge coefficient of triangular labyrinth weirs using adaptive neuro fuzzy inference system. Alexandria Engineering Journal 57:1773–1782.  https://doi.org/10.1016/j.aej.2017.05.005 CrossRefGoogle Scholar
  16. Henderson FM (1966) Open channel flowGoogle Scholar
  17. Kabiri-Samani A, Javaheri A (2012) Discharge coefficients for free and submerged flow over piano key weirs. J Hydraul Res 50:114–120.  https://doi.org/10.1080/00221686.2011.647888 CrossRefGoogle Scholar
  18. Karbasi M (2017) Forecasting of multi-step ahead reference evapotranspiration using wavelet- Gaussian process regression model. Water Resour Manag 32:1035–1052.  https://doi.org/10.1007/s11269-017-1853-9 CrossRefGoogle Scholar
  19. Laugier F (2007) Design and construction of the first piano key weir spillway at Goulours dam. International journal on hydropower and dams 14:94Google Scholar
  20. Laugier F, Lochu A, Gille C, Leite Ribeiro M, Boillat J-L (2009) Design and construction of a labyrinth PKW spillway at saint-Marc dam, France. International journal on hydropower and dams 16:100–107Google Scholar
  21. Lempérière F (2011) New labyrinth weirs triple the spillways discharge. Water and Eenrgy International 68:77–78Google Scholar
  22. Lempérière F, Ouamane A (2003) The piano keys weir: a new cost-effective solution for spillways. International Journal on Hydropower and Dams 10:144–149Google Scholar
  23. Li H-Z, Guo S, Li C-J, Sun J-Q (2013) A hybrid annual power load forecasting model based on generalized regression neural network with fruit fly optimization algorithm. Knowl-Based Syst 37:378–387.  https://doi.org/10.1016/j.knosys.2012.08.015 CrossRefGoogle Scholar
  24. Lourakis M, Argyros A (2004) The design and implementation of a generic sparse bundle adjustment software package based on the levenberg-marquardt algorithm. Technical Report 340, Institute of Computer Science-FORTH, Heraklion, Crete, GreeceGoogle Scholar
  25. Machiels O, Erpicum S, Archambeau P, Dewals B, Pirotton M (2013) Parapet Wall effect on piano key weir efficiency. J Irrig Drain Eng 139:506–511.  https://doi.org/10.1061/(asce)ir.1943-4774.0000566 CrossRefGoogle Scholar
  26. Mihoub R, Chabour N, Guermoui M (2016) Modeling soil temperature based on Gaussian process regression in a semi-arid-climate, case study Ghardaia, Algeria. Geomechanics and Geophysics for Geo-Energy and Geo-Resources 2:397–403.  https://doi.org/10.1007/s40948-016-0033-3 CrossRefGoogle Scholar
  27. Neal RM (1997) Monte Carlo implementation of Gaussian process models for Bayesian regression and classification. arXiv preprint physics/9701026Google Scholar
  28. Negnevitsky M (2005) Artificial intelligence: a guide to intelligent systems. Pearson EducationGoogle Scholar
  29. Ngia LS, Sjoberg J (2000) Efficient training of neural nets for nonlinear adaptive filtering using a recursive Levenberg-Marquardt algorithm. IEEE Trans Signal Process 48:1915–1927.  https://doi.org/10.1109/78.847778 CrossRefGoogle Scholar
  30. Pal M, Deswal S (2010) Modelling pile capacity using Gaussian process regression. Comput Geotech 37:942–947.  https://doi.org/10.1016/j.compgeo.2010.07.012 CrossRefGoogle Scholar
  31. Parsaie A (2016) Predictive modeling the side weir discharge coefficient using neural network. Modeling Earth Systems and Environment 2.  https://doi.org/10.1007/s40808-016-0123-9
  32. Pasolli L, Melgani F, Blanzieri E (2010) Gaussian process regression for estimating chlorophyll concentration in subsurface waters from remote sensing data. IEEE Geosci Remote Sens Lett 7:464–468.  https://doi.org/10.1109/LGRS.2009.2039191 CrossRefGoogle Scholar
  33. Rafiq M, Bugmann G, Easterbrook D (2001) Neural network design for engineering applications. Comput Struct 79:1541–1552.  https://doi.org/10.1016/S0045-7949(01)00039-6 CrossRefGoogle Scholar
  34. Salmasi F, Yıldırım G, Masoodi A, Parsamehr P (2012) Predicting discharge coefficient of compound broad-crested weir by using genetic programming (GP) and artificial neural network (ANN) techniques. Arab J Geosci 6:2709–2717.  https://doi.org/10.1007/s12517-012-0540-7 CrossRefGoogle Scholar
  35. Shamshirband S, Bonakdari H, Zaji AH, Petkovic D, Motamedi S (2016) Improved side weir discharge coefficient modeling by adaptive neuro-fuzzy methodology. KSCE J Civ Eng 20:2999–3005.  https://doi.org/10.1007/s12205-016-1723-7 CrossRefGoogle Scholar
  36. Vapnik V (2013) The nature of statistical learning theory. Springer science & business mediaGoogle Scholar
  37. Wang Y, Chaib-draa B (2017) An online Bayesian filtering framework for Gaussian process regression: application to global surface temperature analysis. Expert Syst Appl 67:285–295.  https://doi.org/10.1016/j.eswa.2016.09.018 CrossRefGoogle Scholar
  38. Zaji AH, Bonakdari H, Shamshirband S (2016) Support vector regression for modified oblique side weirs discharge coefficient prediction. Flow Meas Instrum 51:1–7.  https://doi.org/10.1016/j.flowmeasinst.2016.08.006 CrossRefGoogle Scholar
  39. Zare M, Pourghasemi HR, Vafakhah M, Pradhan B (2012) Landslide susceptibility mapping at Vaz watershed (Iran) using an artificial neural network model: a comparison between multilayer perceptron (MLP) and radial basic function (RBF) algorithms. Arab J Geosci 6:2873–2888.  https://doi.org/10.1007/s12517-012-0610-x CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Water EngineeringUniversity of TabrizTabrizIran
  2. 2.Department of Water EngineeringUniversity of ZanjanZanjanIran

Personalised recommendations