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Open channel junction velocity prediction by using a hybrid self-neuron adjustable artificial neural network

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Abstract

Determining the appropriate hidden layers neuron number is one of the most important processes in modeling the Multi-Layer Perceptron Artificial Neural Network (MLP-ANN). Despite the significant effect of the MLP-ANN neurons number on predicting accuracy, there is no definite rule for its determination. In this study, a new self-neuron number adjustable, hybrid Genetic Algorithm-Artificial Neural Network (GA-ANN), is introduced and its application examined on the complex velocity field prediction of an open channel junction. The results of GA-ANN were compared with those got by the Genetic Programming (GP) method as two applications of the Genetic Algorithm (GA). The comparisons showed that the GA-ANN model can predict the open channel junction velocity with higher accuracy than the GP model, with Root Mean Squared Error (RMSE) of 0.086 and 0.156, respectively. Finally the equation, obtained by applying the GA-ANN model, predicting the velocity at the open channel junction is presented.

Introduction

Open channel junctions are widely used in hydraulic structures such as sewer networks, water transfer, and irrigation and drainage systems. Estimating the accurate velocity field in an open channel junction has a significant impact on the designing process for preventing the effects from erosion and deposition on the flow. Because of the complex 3D flow behavior in the open channel junctions, various experimental [1], [2], [3], [4] and numerical modeling [5], [6], [7], [8], [9] studies have been conducted. The MLP-ANN is used for simulating various problems as a powerful computational intelligence method. The method consists of some cells, called neurons, to establish an interconnection between the input, hidden, and output layers. MLP-ANN is widely used in problems with a complex relationship between the input and output layers. Many studies have been carried out with the goal of improving the MLP-ANN prediction performance. The studies used other artificial intelligence methods such as other neural networks and optimization algorithms for hybridization with the MLP-ANN. Choi and Park [10] focused on a hybrid ANN that could reduce the dimensions of the input variables. Sarkar and Modak [11] used the Simulated Annealing (SA) method to construct a hybrid ANN-SA method and apply it on nonlinear and time series problems. Khashei, et al. [12] used a hybrid ANN-fuzzy regression model for time series forecasting problems. Lin and Wu [13] combined the Self-Organizing Map (SOM) and the MLP-ANN to propose a hybrid model for rainfall modeling. Ghalambaz, et al. [14] used Gravitational Self Algorithm (GSA) to train the ANN and used the results for solving Wessinger's equation. Mitra, et al. [15] used the GA algorithm for optimizing the ANN weights and biases.

The aim of this study is to apply a novel code of a hybrid GA-ANN on a simulation of the complex flow velocity field of the open channel junction. Selecting the appropriate hidden layers neurons number of the MLP-ANN method has a great impact on the model performance. The proposed GA-ANN is a hybrid method that has a self-adjustability of the hidden layers neurons number. The performance of the proposed model was then compared with the GP model. To train and validate the numerical models, the experimental study of Weber, et al. [3] was employed.

Section snippets

Self- adjustable hidden layers neuron artificial neural network (GA-ANN)

A typical MLP-ANN consists of one input, one or more hidden and one output layers. The neuron number of the input layer is equal to the input variables. The output layer neurons are equal to the model outputs. Hidden layers are used to establish a nonlinear connection between the input and output layers. In this study, two hidden layers were considered. One of the most puzzling processes of MLP-ANN modeling is determination the hidden layer neuron numbers. There is not a definite rule in neuron

Results

In this section, the performance of the introduced GA-ANN method was evaluated on the complex velocity field of an open channel junction; in addition, it was compared with the GP method as two practical applications of the GA. The methods employ the non-dimensional coordinates x*, y*, and z* and the non-dimensional discharge ratio q* as the input variables besides the non-dimensional longitudinal velocity u* as the output variable. Of total dataset 70% (3826 samples) were considered as the

Conclusion

Determining the appropriate hidden neurons number is one of the puzzling phases in MLP-ANN modeling. Despite the extensive use of this method, there is not a definitive rule for neurons number determination. In this study, a modified GA was used for ANN structural optimization, and thereby a hybrid GA-ANN method comes about. The advantage of the GA-ANN is the self-adjustability of the neuron numbers. The performance of GA-ANN was investigated in modeling the open channel junction longitudinal

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