Prediction of potentially toxic elements in water resources using MLP-NN, RBF-NN, and ANFIS: a comprehensive review

Abstract

Water resources are constantly threatened by pollution of potentially toxic elements (PTEs). In efforts to monitor and mitigate PTEs pollution in water resources, machine learning (ML) algorithms have been utilized to predict them. However, review studies have not paid attention to the suitability of input variables utilized for PTE prediction. Therefore, the present review analyzed studies that employed three ML algorithms: MLP-NN (multilayer perceptron neural network), RBF-NN (radial basis function neural network), and ANFIS (adaptive neuro-fuzzy inference system) to predict PTEs in water. A total of 139 models were analyzed to ascertain the input variables utilized, the suitability of the input variables, the trends of the ML model applications, and the comparison of their performances. The present study identified seven groups of input variables commonly used to predict PTEs in water. Group 1 comprised of physical parameters (P), chemical parameters (C), and metals (M). Group 2 contains only P and C; Group 3 contains only P and M; Group 4 contains only C and M; Group 5 contains only P; Group 6 contains only C; and Group 7 contains only M. Studies that employed the three algorithms proved that Groups 1, 2, 3, 5, and 7 parameters are suitable input variables for forecasting PTEs in water. The parameters of Groups 4 and 6 also proved to be suitable for the MLP-NN algorithm. However, their suitability with respect to the RBF-NN and ANFIS algorithms could not be ascertained. The most commonly predicted PTEs using the MLP-NN algorithm were Fe, Zn, and As. For the RBF-NN algorithm, they were NO₃, Zn, and Pb, and for the ANFIS, they were NO₃, Fe, and Mn. Based on correlation and determination coefficients (R, R²), the overall order of performance of the three ML algorithms was ANFIS > RBF-NN > MLP-NN, even though MLP-NN was the most commonly used algorithm.

Keywords: Artificial neural networks; Input variable selection; Input variables; PTE prediction modeling; Soft computing models.