Enhanced TDS Modeling Using an AI Framework Integrating Grey Wolf Optimization with Kernel Extreme Learning Machine

Abstract

Predictions of total dissolved solids (TDS) in water bodies including rivers and lakes are challenging but essential for the effective management of water resources in agricultural and drinking water sectors. This study developed a hybrid model combining Grey Wolf Optimization (GWO) and Kernel Extreme Learning Machine (KELM) called GWO-KELM to model TDS in water bodies. Time series data for TDS and its driving factors, such as chloride, temperature, and total hardness, were collected from 1975 to 2016 to train and test machine learning models. The study aimed to assess the performance of the GWO-KELM model in comparison to other state-of-the-art machine learning algorithms. Results showed that the GWO-KELM model outperformed all other models (such as Artificial Neural Network, Gaussian Process Regression, Support Vector Machine, Linear Regression, Classification and Regression Tree, and Boosted Regression Trees), achieving the highest coefficient of determination (R²) value of 0.974, indicating excellent predictive accuracy. It also recorded the lowest root mean square error (RMSE) of 55.75 and the lowest mean absolute error (MAE) of 34.40, reflecting the smallest differences between predicted and actual values. The values of R², RMSE, and MAE for other machine learning models were in the ranges of 0.969–0.895, 60.13–108.939, and 38.25–53.828, respectively. Thus, it can be concluded that the modeling approaches in this study were in close competition with each other and, finally, the GWO-KELM model had the best performance.