Predicting the discharge coefficient of oblique cylindrical weir using neural network techniques

Adnan A Ismael,Nadhir Al-Ansari,Saleh J Suleiman,Raid Rafi Omar Al-Nima

doi:10.1007/s12517-021-07911-9

Abstract

Cylindrical weir shapes offer a steady-state overflow pattern, where the type of weirs can offer a simple design and provide the ease-to-pass floating debris. This study considers a coefficient of discharge (Cd) prediction for oblique cylindrical weir using three diameters, the first is of D1 = 0.11 m, the second is of D2 = 0.09 m, and the third is of D3 = 0.06.5 m, and three inclination angles with respect to channel axis, the first is of θ1 = 90 ͦ, the second is of θ2 = 45 ͦ, and the third is of θ3 = 30 ͦ. The Cd values for total of 56 experiments are estimated by using the radial basis function network (RBFN), in addition of comparing that with the back-propagation neural network (BPNN) and cascade-forward neural network (CFNN). Root mean square error (RMSE), mean square error (MSE), and correlation coefficient (CC) statics are used as metrics measurements. The RBFN attained superior performance comparing to the other neural networks of BPNN and CFNN. It is found that, for the training stage, the RBFN network benchmarked very small RMSE and MSE values of 1.35E-12 and 1.83E-24, respectively and for the testing stage, it also could benchmark very small RMSE and MSE values of 0.0082 and 6.80E-05, respectively.

Highlights

In hydro system projects, the discharge coefficient (Cd) of measuring the flow on weirs can be counted as one of the highest considerations for water controls
The results showed that the adaptive neuro-fuzzy inference system (ANFIS) technique modeled the discharge coefficient better than the multi-layer perceptron (MLP)
Where: coefficient of discharge (Cd) is the discharge coefficient, q is the discharge over the weir per unit width (m3/s/m), Hw is the energy head over the weir crest (m), R is the radius of the weir crest (m), D is weir diameter (m), L is the length of weir crest (m), H total head (m), d is the water upstream depth, the circular weir under investigation (m) g is the acceleration due to gravity (m/s2), Fig. 3 The channel setup

Summary

Introduction

The discharge coefficient (Cd) of measuring the flow on weirs can be counted as one of the highest considerations for water controls. Many efforts have been made as a result of costly experiments to apply mathematical models for classifying the hydraulic specifications of oblique weirs. Engineering., Lulea University of Technology, Lulea 971 87, Lulea, Sweden the case of mathematical modelling, the soft computing methods are stated and computational fluid dynamics (CFD) techniques are used. Exploiting the CFD for modelling the movement of an oblique cylindrical weir was reported by Yuce et al (2015). It is notable that Yuce et al (2015) have investigated the hydraulic characteristics of the weir of oblique cylindrical. It has been reported that utilizing the soft computing methods with the CFD modelling for expecting the discharge coefficient of oblique weirs.

Methods

Findings

Discussion

Conclusion