Application of a genetic algorithm in predicting the percentage of shear force carried by walls in smooth rectangular channels
Introduction
Numerous engineering problems such as erosion of channels, flow resistance, sediment pollutant transport and designing stable channels require knowledge of boundary shear stress distribution values. Many researchers have tried to measured shear stress distribution experimentally, as presented by Bonakdari et al. [1] in detail. Since the experimental estimation of boundary shear stress is a difficult and time consuming procedure, other researchers have attempted to calculate boundary shear stress by analytical and numerical methods [2], [3], [4], [5], [6], [7], [8], [9], [10], [11]. The use of soft computing technique in modeling complicated problems is recently expanding. Khatibi et al. [12] used the GP model to predict the outflow of a river reach from its given inflows, and by comparing the results of three methods they found the GP model made better predictions. Kisi et al. [13] estimated daily suspended sediment load using a GP model. They also compared this method with several soft computing techniques and deducted that the GP model operates better than the others. Genetic programming through bi-objective genetic algorithms was applied to model different phenomena [14], [15]. Huai et al. [16] used the ANN model to estimate the apparent shear stress acting at the vertical line between subareas of a compound channel’s cross section. The shear stress is a very important parameter in channel problems but only few studies have dealt with estimating the percentage of shear force in channels. Cobaner et al. [17] utilized an ANN model in order to estimate the shear force carried by walls in rectangular channels and ducts. Sheikh Khozani et al. [18] predicted percentage of shear force carried by walls in rectangular channels with rough boundaries by using GP and GAA methods.
In this study, two soft computing techniques, namely the GAA and GP model are extended for computing the percentage of shear force carried by walls in smooth rectangular channels. These models are explained step-by-step and the best output of models, a program and an equation for the GP and GAA respectively, are presented. The models are also compared in order to determine which has greater prediction ability. Finally, a comparison between the proposed models and the equations obtained by former researchers is carried out.
Section snippets
GAA processing
A Multi-Layer Perceptron Artificial Neural Network (MLP-ANN) consists of three types of layers: input, hidden and output layers. Each layer has some neurons that collect the weighted summation of the previous layer’s neurons and transfer the results to the next layer by a nonlinear transfer function. The number of neurons in the input layer is equal to the input variables while the number of neurons in the output layer is equal to the output variables. In this study, both the input and output
Optimum determination of the GAA and GP models
In modeling with the GAA and GP techniques, the optimum one was selected first by investigating some fitness functions. Therefore, to select the appropriate fitness functions in the GAA and GP models, the MSE and MAE functions were examined. The comparison results for the two different functions using statistical parameters are presented in Table 3. In the first step of the GAA process, the logarithmic function for input layers, purelin function for output layers and aspect ratio as input data
Conclusion
In this research, the ability of GAA and GP models to estimate the percentage of shear force carried by walls (%SFw) in smooth rectangular channels was investigated. This study demonstrated these methods step-by-step. Different fitness functions were examined in order to select the best for both models. Several transfer functions were investigated for the GAA model and finally, the best equation for the GAA model was presented by MSE fitness function and hyperbolic tangent in the hidden layer
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