An efficient classified radial basis neural network for prediction of flow variables in sharp open-channel bends

Abstract

In this study, a comparative analysis is done to evaluate the ability of classified radial basis function neural network (CRBFNN) model in estimation of flow variables in sharp open-channel bends with bend angles of 60° and 90°. Accordingly, a RBFNN model is integrated with classification method to design a novel CRBFNN model to predict two velocity and flow depth parameters in a 60° sharp bend. Furthermore, Gholami et al. (Neural Comput Appl 30:1–15, 2018a) pointed out to acceptable ability and more efficiency improvement of hybrid CRBFNN model in prediction of flow variables in 90° sharp open-channel bend compared to simple RBF model. On the other hand, the flow pattern in sharp bends is more complicated than in mild open-channel bends. Moreover, the behavior of flow and its variables is varied in 60° and 90° sharp bends. Therefore, the present paper is aimed to evaluate the performance of RBF and CRBF models in two 60° and 90° (Gholami et al. 2018a) sharp open-channel bends. Available experimental data for velocity and flow depth at six different hydraulic conditions are used to train and test the CRBFNN and simple radial basis function neural network (RBFNN) networks in 60° open-channel bend. Accordingly, efficiency of both RBFNN and CRBFNN models in different bend cross sections is evaluated and compared with each other. The results show that using classified model has improved the simple RBF model performance, as in the CRBFNN model, the error root mean square error and mean absolute error value, 18% and 15.3% for the flow depth prediction and 9% and 5% for the velocity prediction compared to the simple RBFNN model is reduced, respectively. Furthermore, the comparison of model performance in 60° and 90° bends represents that both RBFNN and CRBFNN models in all discharge values in velocity prediction have more ability in 60° bend so that the mean absolute relative error (MARE) value in 60° bend is equal to 0.080 and 0.082 which are lower than MARE values in 90° bend (0.125 and 0.131 for RBFNN and CRBFNN, respectively). Furthermore, both RBFNN and CRBFNN models with lower MARE values equal to 0.015 and 0.012 in 90° bend have more accuracy than the models in 60° bend (0.017 and 0.014). Therefore, the proposed classified models can be used in design and implementation of the curved channels with various bend angles.