The prediction of longitudinal dispersion coefficient in natural streams using LS-SVM and ANFIS optimized by Harris hawk optimization algorithm

Abstract

Accurate calculation of the longitudinal dispersion coefficient (Kx) of pollution is essential in modeling river pollution status. Various equations are presented to calculate the Kx using experimental, analytical, and mathematical methods. Although machine learning models are more reliable than experimental equations in the presence of uncertainties missing data, they have not been widely used in predicting Kx. In this study, the Kx of the river was predicted using machine learning methods, including least square-support vector machine (LS-SVM), adaptive neuro-fuzzy inference system (ANFIS), and ANFIS optimized by Harris hawk optimization (ANFIS-HHO), and the results were compared with that of the experimental methods. Several scenarios were designed by different combinations of input variables, such as the average depth of the flow (H), average flow velocity (U), and shear velocity (u⁎). The results showed that machine learning models had a more efficient performance to predict Kx than experimental equations. The ANFIS-HHO, with a scenario containing all the input variables, performed better than the other two models, with root mean square error, mean absolute percentage error, and coefficient of determination of 17.0, 0.22, and 0.97, respectively. Furthermore, the HHO algorithm slightly increased the prediction performance of the ANFIS. The discrepancy ratio (DR) evaluation criteria showed that experimental equations overestimated the values of Kx, while the machine learning models resulted in higher precision. Also, the results of Taylor's diagram showed the acceptable performance of the ANFIS-HHO model compared to other models. Given the promising results of the present study, it is expected that the proposed approach can be efficiently used for similar environmental modeling problems.