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


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.


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



Length of rectangular gate;


Weir sidewall length;


Width of rectangular gate;


Downstream or inlet key overhang length;


Upstream or outlet key overhang length;


Dimensionless discharge coefficient;


Gravitational acceleration;

GPK weir

Gated piano key weir;


Head over the crest;


Downstream head;


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


Upstream head;


Crest length; [L = N(Wi + Wo + 2B)].


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


Weir cycle number;


Total weir height;


Weir wall height at the center of weir;

PK weir

Piano key weir;




Inlet key slope;


Outlet key slope;


Weir wall thickness;


Total weir width or flume width;


Inlet key width;


Outlet key width;


Water dynamic viscosity;


Water density and


Water surface tension


Compliance with Ethical Standards

Conflict of Interest



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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

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