Hybrid Physics-Informed Fuzzy Machine Learning for Predicting the Settling Velocity of Fractal Aggregates in Water Treatment Systems
Abstract
Accurately predicting the settling velocity of fractal aggregates is critical for optimizing sedimentation units in water treatment systems, yet remains a challenge due to the irregular, porous, and non-spherical nature of such aggregates. Traditional models often oversimplify fluid–particle interactions and fail to generalize under variable morphological conditions. In this study, we propose a hybrid modeling framework that integrates Physics-Informed Machine Learning (PIML) with fuzzy logic to enhance predictive accuracy and physical interpretability in settling velocity estimation. The approach leverages morphological descriptors extracted from image-based analysis, combined with physically consistent features such as drag force, squared radius, and Reynolds number derived from fluid mechanics theory. Two fuzzy regression models were implemented using XGBoost with early stopping: one trained on purely morphological features, and another incorporating the physics-informed variables. Both models were evaluated using cross-validation, robustness tests under Gaussian noise (1–20%), and bootstrapping to estimate predictive uncertainty. Results showed that the PIML Fuzzy Regressor outperformed the traditional model in all metrics, reducing test MAE by 43.3% and RMSE by 28.1%, while achieving a test R² of 0.938. The physics-informed model also exhibited improved robustness under noisy conditions, with slower error growth and narrower confidence intervals across all scenarios. The integration of physics-based features acted as a structural regularizer, improving model generalization and mitigating the effects of data leakage and noise. These attributes enhanced the model’s credibility and operational relevance, particularly in environments characterized by experimental variability. Overall, this study demonstrates that hybrid PIML-fuzzy models provide a reliable and interpretable tool for predicting floc settling behavior, contributing to the development of more robust, sustainable, and physically consistent sedimentation modeling frameworks in water treatment engineering.
Keywords:
Settling velocity prediction, Physics-informed learning, Fuzzy regression, Fractal aggregates, Water treatment, Sedimentation modelingReferences
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