Prediction of Coefficient of Discharge for Oblique Sharp Crested Weir using ANN Model

Abstract

The application of artificial neural networks for solving complex civil engineering problems is of huge importance. This paper presents some of the positive aspects of the neural network’s model that are used for the determination of the coefficient of discharge of oblique sharp crested weir. Sharp crested weirs are used to measure flow rate and control upstream water surface in irrigation canals and laboratory flumes. The main advantages of such weirs are ease of construction and capability of measuring a wide range of flows with sufficient accuracy. ANN models have been developed to predict the discharge coefficients of oblique sharp-crested weirs for free flow cases using Borgheiet al.’s experimental data.

Introduction

I. INTRODUCTION

Especially in the field of irrigation and drainage engineering, sharp-crested weirs are widely used for measuring flow. In case of limited channel width when higher discharge is required at a relatively lower head use of an oblique weir is advantageous over the normal weir. Oblique alignment of the weir increases the effective weir length beyond the channel width which consequently increases the efficiency of the weir. A weir is basically an obstruction in an open channel flow path. When the water level downstream of the weir is above the crest level of the weir, then the weir is said to be submerged weir, the accuracy of measurement should not be expected at this point.

A range of measurement techniques was developed by Boss (1989) and USBR (1997). Thin-plate weirs are commonly used as measuring devices enabling an accurate discharge measurement with simple instruments. The commonly used cross sections of sharp-crested weirs are rectangular, trapezoidal, and triangular. Because of the large loss of accuracy, designing thin-plate weirs for submergence should be deliberately avoided. However, submergence may happen unexpectedly or may be temporarily necessary.

Rectangular sharp-crested weirs are of three types: (a) fully contracted, (b) partially contracted and (c) full width.  If the channel width is restricted, different types of weir change from type (a) to (c). With the limitation of channel width, when the amount of discharge increases, the head of water upstream of the weir increases. However, there is a disadvantage to this kind of weir, because the higher water head means higher channel walls which are more expensive.

Borghei et al. (2003) conducted an experiment in a rectangular concrete channel of length 6600mm, width 520mm, and height 800mm. The bed slope of the channel was taken as 0.005.  A standard sharp-crested weir made up of plexiglass of different heights and lengths were used. Discharge was kept between the range 0.00845m3 /s,and 0.037 m3 /s.  The experimental data set comprises a total number of 95 runs for free flow. Experiments for free flow cases were conducted on weirs of different weir lengths (520, 595, 672, 728, 801, 876, 1030,1175mm) in eight sets. Each set corresponds to a weir height (511, 505, 506, 503, 505, 460, mm) have been used to conduct experiments in seven sets.  Oblique weir is the most general case in which the weir is aligned at an angle of θ with respect to the channel axis (Fig.1).

Ayaz and Mansoor (2018) developed ANN model to predict the discharge coefficient of oblique sharp-crested rectangular weir by using Borghei et al. (2003) experimental data. In the present study, ANN models have been developed to predict the discharge coefficient of oblique sharp-crested weir for free flow.

III. ARTIFICIAL NEURAL NETWORKS (ANN) – BASIC CONCEPT

An artificial neural network (ANN) is an information-processing paradigm that is inspired by the way biological nervous systems, such as the brain, process information. It is composed of a large number of highly interconnected processing elements (neurons) working in unison to solve specific problems. Marijana Lazarevskai give detail application on ANN in civil engineering. Neurons are arranged in layers, including an input layer, hidden layers, and an output layer. There is no specific rule that dictates the number of hidden layers. The function is established largely based on the connections between the elements of the network. In the input layer, each neuron is designated for one of the input parameters. A detail description on neural computing and basic concepts of ANN is available in Zurada (1990) and Schalk off (1997).

The network learns by applying the back-propagation algorithm, which compares the neural network simulated values with the actual values and calculates the estimation errors. (Fig.2) Shows the data set in the network is divided into a learning data set, which is used to train the network, and a validation data set, which is used to test the network performance. In the present study, the neural network fitting tool of MATLAB 7.5 was used.

After training the network, verification is conducted until the success of the training can be established.

III. DEVELOPMENT OF ANN MODEL

Weir length (L), Weir height (P), and Water Head (H) are the three main factors that affect the Coefficient of Discharge (Cd) of a oblique sharp-crested weir. The primary goal of this research is to develop of ANN models using three different networks Levenberg Marquardt, Bayesian Regularization, Scaled Conjugate Gradient to predict the Coefficient of discharge (Cd) for an oblique sharp-crested weir. A detailed description about the training of neural networks using Levenberg–Marquardt algorithm is available in Hagan et al. (1996) and Hagan and Menhaj (1994).Every model consists of three layers input layer, hidden layer, and output layer. There are three neurons in the input layer and one neuron in the output layer. Fitting tool further randomly divided the experimental data as 70% for training 15% for validation and 15% for testing. Water head (H), weir height (P), and weir length (L) have been used as inputs corresponding to three neurons of input layer while the discharge coefficient (Cd) as output to the ANN models. A flow chart explaining execution of work is shown below in (Fig. 5). The performance results of all three models are shown in Table 2,3 and 4.

VII. NOTATION

Conclusion

The Levenberg Marquardt, Bayesian Regularization, Scaled Conjugate gradient algorithms are used in this study to develop the ANN models to predict the coefficient of discharge for oblique sharp crested weir\'s for free flow using experimental data of Borghei etal.(2003). The percentage error between the therotical coefficient of discharge and predicted coefficient of discharge is between±0.881%. It is concluded that the ANN model developed by Levenberg Marquardt method is accurate and recommended for prediction of coefficient of discharge as percentage error between therotical coefficient and predicted coefficient of discharge is in the range of ±0.881%. Modern multidisciplinary fields like artificial neural networks are a good illustration of how to solve a variety of engineering challenges that conventional modelling and statistical approaches were unable to address.

References

[1] Bos, M.G., (1989), Discharge Measurement Structures. International Institute for Land Reclamation and Improvement)ILRI), Publication 20, Wageningen, Netherlands. [2] Hagan, M.T., Menhaj, M., 1994. Training feed-forward networks with the Marquardt algorithm. IEEE Trans. Neural Netw. 5 (6), 989–993. [3] Schalkoff, R.J., 1997. Artificial Neural Networks. The McGraw Hill Companies, Inc., New York. [4] Hecht-Neilson, R., 1987. Komogorov’s mapping neural network existence theorem. Proceedings of the Internal Conference on Neural Networks, IEEE Press, New York 3, 11–13. [5] Borghei, S.M., Vatannia, Z., Ghodsian, M., Jalili, M.R., 2003. Oblique rectangular sharp-crested weir. Water Marit. Eng. 156 (WM2), 185–191. [6] MdAyaz ,Tailb Mansoor, Available - 19 October 2018, Discharge coefficient of Oblizue Sharp Crested Weir For Free And Submerged Flow Using Trained ANN Model , pp. 01-21. [7] Marijana Lazarevskai dr., Milos Knezevic, Meri Cvetkovska, Ana Trombeva-Gavriloska, Application of artificial neural networks in Civil Engineering ISSN 1330-3651(Print), ISSN 1848-6339 (Online).

Copyright

Copyright © 2023 Vidhi Umale . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.