Robust kernel extreme learning machines with weighted mean of vectors and variational mode decomposition for forecasting total dissolved solids

Abstract

A stable and accurate forecast of water quality parameters is crucial for planning and managing future investment programs. A well-known water quality indicator is the total dissolved solids (TDS), which measures the number of metals, minerals, and salts dissolved in a particular volume of water. This paper introduces an innovative approach, which combines the kernel extreme learning machine (KELM) with the robust weight mean of vectors (INFO) algorithm. The proposed technique stands out for its strategic integration of Boruta-XGBoost (B-XGB) as an exceptional feature selection method, along with variational mode decomposition (VMD) to decompose the input variables and enhance the accuracy of forecasting. The integrated model is termed V-KELM-INFO. INFO is an essential component that incorporates a complex exploration process. It utilizes a weighted mean of vectors, a vector combining operator to enhance population variety, and a localized search operator to expedite convergence. INFO, a potent tool, is included in the V-KELM training stage. It efficiently extracts optimum parameters and dramatically improves the accuracy of monthly TDS predictions at the Idenak station in southwest Iran. Also, the multi-criteria decision-making (MCDM) approach of weighted aggregated sum product assessment (WASPAS) is used to rank models. The V-KELM-INFO model was chosen based on the WASPAS results and statistical metrics (R = 0.962, RMSE = 57.84, WHD = 7.01, and U95 = 160.74) as the best model to forecast the TDS. In addition, the superiority of the proposed model was assessed against the metaheuristic-based V-KELM models, comprising the V-KELM grey wolf optimizer (V-KELM-GWO), V-KELM slime mold algorithm (V-KELM-SMA), and V-KELM equilibrium optimizer (V-KELM-EO). This work provided insight into improving the accuracy of modeling-based methodologies and spurred water quality modeling technology to develop sustainable and clean practices.