Elsevier

Applied Mathematics and Computation

Volume 338, 1 December 2018, Pages 400-411
Applied Mathematics and Computation

Evaluating the apparent shear stress in prismatic compound channels using the Genetic Algorithm based on Multi-Layer Perceptron: A comparative study

https://doi.org/10.1016/j.amc.2018.06.016Get rights and content

Abstract

Apparent shear stress acting on a vertical interface between the main channel and floodplain in a compound channel is used to quantify the momentum transfer between these sub-areas of a cross section. In order to simulate the apparent shear stress, two soft computing techniques, including the Genetic Algorithm-Artificial Neural Network (GA-ANN) and Genetic Programming (GP) along with Multiple Linear Regression (MLR) were used. The proposed GA-ANN is a novel self-hidden layer neuron adjustable hybrid method made by combining the Genetic Algorithm (GA) with the Multi-Layer Perceptron Artificial Neural Network (MLP-ANN) method. In order to find the optimum condition of the methods considered in modeling apparent shear stress, various input combinations, fitness functions, transfer functions (for the GAA method), and mathematical functions (for the GP method) were investigated. Finally, the results of the optimum GAA and GP methods were compared with the MLR as a basic method. The results show that the hybrid GAA method with RMSE of 0.5326 outperformed the GP method with RMSE of 0.6651. In addition, the results indicate that both GAA and GP methods performed significantly better than MLR with RMSE of 1.5409 in simulating apparent shear stress in symmetric compound channels.

Introduction

Most natural rivers are compound channels. A channel with compound sections has a deep section, namely the main channel, and some wider, shallower parts, also known as the floodplains. Because floodplains commonly have vegetated beds, they have greater roughness than the main channel. In case of flooding, the velocity tends to be greater in the main channel than the floodplains due to the cross sections’ geometry and roughness variations in compound channels. The velocity difference between the main channel and floodplains leads to lateral momentum transfer in the compound channel's cross sections. Momentum transfer increases the total flow resistance and creates an extended shear layer. Therefore, investigating compound open channel flow characteristics without considering the transverse momentum results in inaccurate models that predict greater discharge movement than in reality [1].

One of the most important parameters in modeling transverse momentum is the apparent shear stress [2]. The apparent shear force assumed at the interface plane provides insight into the magnitude of the flow interaction between the main channel and adjacent floodplains. Owing to the importance of apparent shear stress in flood characteristic simulation, various studies have been conducted with focus on calculating this parameter [3–8]. Wormleaton and Merret [9] presented empirical formulae for calculating the apparent shear stress in a straight compound channel using data from a Flood Channel Facility (FCF) on a large scale. Smart [10], Christodoulou [11] and Bousmar and Zech [12] calibrated the coefficient of apparent shear stress presented by Ervine and Baird [5]. Moreta and Martin-Vide [13] investigated the effect of a compound channel cross section's geometry and roughness on the non-dimensional friction coefficient acting on the vertical main channel-floodplain interface (Cfa). They deducted that the variation aspect ratio influences the apparent friction coefficient, but the bank side slope is not effective on Cfa. All formulae presented require awareness of the velocity gradient and the influence of roughness and channel geometry on apparent shear stress. Since determining the velocity gradient without detailed measurements is difficult and Cfa has high uncertainty with different geometry and roughness values [13], other methods of estimating apparent shear stress without a need for these parameters are required.

In the past decade, soft computing and artificial intelligence methods have been used successfully for simulating complex hydraulic engineering problems [14], [15], [16], [17], [18], [19], [20], [21], [22], [23]. On the topic of shear stress simulation, Cobaner et al. [24] used an ANN model to estimate the shear force carried by walls in smooth rectangular channels and ducts. They indicated that the ANN model is more powerful in predicting shear stress than relations obtained from experimental studies. Huai et al. [25] studied the prediction of apparent shear stress in compound channels with and without vegetation using ANN modeling. They deducted that the ANN model performs well in predicting apparent shear stress. An analysis of the literature shows that despite the superior performance of soft computing methods in modeling complex problems, few studies have been conducted on apparent shear stress prediction.

A wide range of studies have focused on improving MLP-ANN simulation performance. A common way of modifying the MLP-ANN is to link it with other artificial intelligence and evolutionary algorithm methods. Choi and Park [26] introduced a hybrid MLP-ANN method that can reduce the input variable dimensions automatically. Sarkar and Modak [27] utilized Simulated Annealing (SA) in the hybrid MLP-SA method for modeling nonlinear time series problems. Lin and Wu [28] used the hybrid Self Organizing Map (SOM) and MLP-ANN for rainfall simulation. Mitra et al. [29] introduced the auto weights adjustable hybrid GA-MLP method.

The accurate modeling of apparent shear stress is crucial in modeling the transverse momentum in compound channels. However, due to modeling complexity, there is no trustable method for practical situations. The lack of information in modeling apparent shear stress accurately is even more tangible in terms of compound channels. In the present study, the apparent shear stress acting on the main channel-floodplain interface in symmetric compound channels is modeled using the GAA method. GAA is a novel, powerful method of self-adjusting hidden nodes comprising the MLP-ANN and GA algorithms. In order to determine the performance of this method, the results of GAA are compared with GP, a well-known, powerful regression algorithm, and MLR, a basic regression method. In addition, to achieve a more universal model that can be employed in practical situations, rather than considering the training and testing datasets from only one experimental study, the datasets are obtained from four experimental studies by Knight and Hamed [6], Prinos and Townsend [7], Wormleaton and Merrett [9] and Knight and Demetriou [30]. Finally, the experimental equation derived from GAA for predicting the apparent shear stress in compound channels is presented. This equation can be compared with other methods in future studies for potential use in practical situations.

Section snippets

Materials and methods

This following section comprises three parts. The first part presents the case studies employed to develop the final dataset, which is used for modeling the apparent shear stress in compound channels. The second part describes the GAA and GP methods in detail. The last part of this section reports the statistical index formulations that are used to evaluate the accuracy of the methods considered.

Input selection

In order to find the most appropriate input variables for modeling the apparent shear stress in compound channels, various input combinations are investigated. The input combinations used were created using six different non-dimensional variables: B/b, (H–h)/h, nf/nc, h/b, H/B, H/h and BH/bh. More input variables in a numerical model lead to greater model complexity. However, in some cases, numerical models perform better with more input variables. Therefore, in this study, various input

Conclusion

The apparent shear stress at the main channel-floodplain interface is important for the momentum transfer between sub-areas in a compound channel, as it facilitates estimating the actual discharge in a compound channel cross section. Hence, owing to the importance of estimating the apparent shear stress accurately in hydraulic engineering, the main goal of the present study was to develop a reliable modeling formulation using input variables B, b, H, h, nf, and nc, which can be measured easily.

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