Fuzzy machine learning predictions of settling velocity based on fractal aggregate physical features in water treatment

The dynamics of gravitational sedimentation in water treatment are crucial for optimising particulate matter removal. This study addresses the effect of fractal aggregate features on settling velocity and explores fuzzy machine learning (ML) for predicting this phenomenon. Particle image velocimetry determined aggregate velocities within a sedimentation column, with features identified concurrently. Using a comprehensive methodological framework, significant predictors were selected through various statistical analyses. The fuzzy ML model, developed with the ‘FisPro’ package in R, incorporated a hierarchical partitioning scheme using Lukasiewicz and Sum operators for conjunction and disjunction processes, respectively. The Wang-Mendel method extracted fuzzy rules, with defuzzification achieved using the maximum crisp operator. Hyperparameter optimization was conducted through grid search techniques, and model performance was evaluated using 3-fold cross-validation. The findings reveal that Margination, Radius, and Clumpiness significantly impact settling velocity. The model demonstrates exceptional predictive accuracy (R2 = 0.923) across both training and validation datasets, highlighting its potential for forecasting terminal velocity in water treatment. This research suggests that precise predictions of sedimentation dynamics can improve particulate matter removal efficiency and encourages further investigations into diverse aggregate types and environmental scenarios, advocating for integrating physics-informed ML approaches to enhance the model.