Page 79 - AJWEP-22-6

Asian Journal of Water, Environment and Pollution. Vol. 22, No. 6 (2025), pp. 73-88.
doi: 10.36922/AJWEP025120081

ORIGINAL RESEARCH ARTICLE

Machine learning-based discharge coefficient estimation
in trapezoidal-arched labyrinth weirs

Mohammad Heidarnejad * , Jamal Feili , Mehdi Fuladipanah ,
2
1
3
and Upaka Rathnayake *
4
1 Department of Water Science Engineering, Ahv. C., Islamic Azad University, Ahvaz, Iran
2 Khuzestan Water and Power Organization, Ahvaz, Khuzestan, Iran
3 Department of Civil Engineering, Ramh. C., Islamic Azad University, Ramhormoz, Iran
4 Department of Civil Engineering and Construction, Faculty of Engineering and Design,
Atlantic Technological University, Sligo, Connacht, Ireland
*Corresponding authors: Mohammad Heidarnejad (mo.heidar@iau.ac.ir); Upaka Rathnayake (upaka.rathnayake@atu.ie)

Received: March 17, 2025; 1st revised: June 17, 2025; 2nd revised: July 8, 2025;
Accepted: July 9, 2025; Published online: August 13, 2025

Abstract: Weirs represent a frequently employed mechanism for regulating water surface elevations and managing
flow within canals and hydraulic infrastructures. Among these, labyrinth weirs constitute a distinctive variant
capable of accommodating a specific discharge while maintaining a reduced upstream water level compared to
conventional linear weirs. The present investigation delved into the evaluation of the effectiveness of multilayer
perceptron (MLP) networks, support vector machine (SVM), gene expression programming (GEP), and multivariate
adaptive regression splines (MARS), aiming to predict the discharge coefficient (C ) of a trapezoidal-arched
d
labyrinth weir with an expanded central cycle. A dataset including 108 laboratory observations was utilized. The
dimensionless parameters were obtained from the parameters including inside apex width of the middle cycle (w ),
1
inside apex width of the end cycles (w ), weir height on the upstream side (B), unsubmerged total upstream head on
2
the weir (H ), and gravitational acceleration (g). The model was developed with the dimensionless parameters and
d
C . Root mean square error (RMSE), determination coefficient (R ), mean absolute error (MAE), and developed
2
d
discrepancy ratio (DDR) were used as performance assessment criteria. Based on these metrics, all four models
exhibited the latent capacity to predict the C value. However, the MLP model demonstrated superior performance
d
among the models during both training (RMSE = 0.024, MAE = 0.020, R = 0.816, and C d[DDRmax] = 8.07) and testing
2
(RMSE = 0.011, MAE = 0.006, R = 0.688, and C d[DDRmax] = 11.32) phases. Sequentially, the subsequent standings
2
were secured by the SVM, GEP, and MARS. MLP outperformed SVM, GEP, and MARS models in predicting
C , achieving the highest R² and lowest RMSE/MAE values.
d
Keywords: Discharge coefficient; Laboratory observations; Machine learning models; Prediction; Trapezoidal-
arched labyrinth weir

1. Introduction of excess flow and the precise management of water
levels. These structures form an integral component
Weirs, both linear and non-linear in configuration, are of hydraulic systems, serving a pivotal role in flow
critical hydraulic structures designed for the regulation regulation. Engineering applications incorporate
1

Volume 22 Issue 6 (2025) 73 doi: 10.36922/AJWEP025120081