A comparison of artificial intelligence-based classification techniques in predicting flow variables in sharp curved channels

Abstract

Due to the complexity of variable distributions, it is essential to evaluate the flow patterns in sharp curved channels with different angles. It has recently become more common to use classification methods in combination with different artificial intelligence (AI) models to boost AI model performance. Gholami et al. (Appl Soft Comput 48:563–583, 2016a) obtained enhanced results by combining two common AI models with a classifier based on decision trees to estimate the flow velocity and flow depth in a 90° sharp curved channel. Their results represent the superior performance and accuracy of hybrid models over classic AI models alone. However, because the diversion angle in intake and bend channels has a considerable influence on the flow variables, the flow patterns differ in 60° and 90° bend channels. Hence, the present paper evaluates the goodness-of-fit results of the classifier multilayer perceptron (CMLP) and classifier radial basis function (CRBF) models designed based on decision trees. These models were designed to estimate the velocity and flow depth patterns in a 60° sharp curved channel based on 780 observational data for six flow rates: 5, 7.8, 13.6, 19.1, 25.3, and 30.6 l/s. According to the mean absolute relative error (MARE) and determination coefficient (R2) results of 0.0514 and 0.6 for velocity and 0.005 and 0.99 for flow depth prediction, the proposed CMLP model is more accurate than the classic MLP model. The CRBF model performed similar to CMLP, whereby CRBF predicted both velocity (MARE 0.086 and R2 = 0.9) and flow depth (MARE 0.0133 and R2 = 0.9) more accurately than the RBF model alone. Overall, the CMLP and CRBF models exhibited MARE reductions of 3% and 20% in velocity prediction and 36% and 22% in flow depth prediction compared to the individual MLP and RBF models, respectively. Moreover, CMLP and CRBF produce robust relationships based on different categories established according to various hydraulic conditions. The uncertainty analysis results show that, among the models examined, CMLP had the lowest uncertainty with the narrowest width of confidence bounds (WCB) of ± 0.1385 and ± 0.0031 in predicting velocity and flow depth, respectively. Moreover, CMLP and CRBF exhibited the greatest reliability with the lowest uncertainty indices in estimating the two flow variables in curved channels compared to the classic MLP and RBF models. Therefore, the combined AI-based classification models proposed in this study can serve as alternatives to the classic MLP and RBF models in the design and construction of curved channels with 60° and 90° bends.