Evidential-bio-inspired algorithms for modeling groundwater total hardness: A pioneering implementation of evidential neural network for feature selection in water resources management

Accurate prediction of total hardness (TH) in groundwater is essential for ensuring its suitability for domestic, industrial, and agricultural use. Traditional methods often fail to capture the complex non-linear relationships that characterize water quality data, necessitating more advanced modeling techniques. In this study, three modeling schema batches were developed based on sensitivity analysis results using Evidential Neural Network (EVNN); Batch 1 (B1) include all the parameters, Batch 2 (B2) comprised of electrical conductivity (EC), residual sodium carbonate (RSC), calcium (Ca), chloride (Cl), magnesium (Mg), and nitrate (NO3), while Batch 3 (B3) composed of sulfate (SO4), sodium (Na), bicarbonate (HCO3), sodium adsorption ratio (SAR), potassium (K), groundwater level (GWL), Fluoride (F), pH, and carbonate (CO3) for modeling TH. The dataset was split into a 70:30 ratio for calibration and validation phases, respectively. The sensitivity analysis was subsequently enhanced by bio-inspired algorithms, to predict TH in groundwater, with a specific focus on optimizing feature selection. Sensitivity analysis identified key input features such as EC, RSC, Ca, and Mg as the most influential parameters. The EVNN, coupled with bio-inspired optimization algorithms, specifically the Firefly Algorithm (FA), Invasive Weed Optimization (IWO), and Anti-Bee Colony Optimization (ABC), achieved superior predictive accuracy compared to COVID optimization algorithm (COA). The EVNN-FA-ANN-B2 combination, particularly when using a refined set of features, demonstrated exceptional performance, with a coefficient of determination (R²) of 1.000 and RMSE close to zero. On the other hand, the EVNN-COA-ANN-B1 model exhibited the lowest accuracy, with an R² of 0.028 and an RMSE of 309.117. This research presents a novel, efficient, and reliable framework for predicting TH in groundwater, offering practical implications for water quality management, especially in regions where high TH levels pose significant challenges.