Developing risk-decision rules for aeration in wastewater treatment plants using copula-enhanced machine learning with feature smoothing.

Operational instability in biological wastewater treatment systems can lead to inefficient aeration and elevated energy consumption. Accurate prediction of key process variables, including ammonia nitrogen, dissolved oxygen (DO), and mixed liquor suspended solids (MLSS), is essential for maintaining stable nitrification and energy-efficient aeration control. However, imbalanced data distributions and rare abnormal events often reduce model robustness. To address this challenge, this study develops an integrated predictive and risk assessment framework that incorporates feature distribution smoothing (FDS) into several machine learning models, including long short-term memory (LSTM), extreme gradient boosting (XGBoost), temporal convolutional networks (TCN), and support vector machines (SVM). Two input schemes are evaluated, namely direct historical time series and combined with the FDS method. Results show that the FDS-enhanced scheme significantly improves predictive stability across all variables, with the TCN model achieving the most consistent performance. Furthermore, copula-based joint probability analysis was applied to characterize compound abnormal states involving simultaneous fluctuations in ammonia nitrogen, DO, and MLSS. The resulting probabilistic relationships enable risk-informed aeration management and early warning of potential process instability, providing a practical tool for improving the stability and energy efficiency of biological wastewater treatment systems.