Multi-objective control strategy with accurate effluent concentration prediction in wastewater treatment plants

Efficient and sustainable operation of wastewater treatment plants (WWTPs) is inherently challenging due to strong nonlinear dynamics, complex multivariable interactions, and highly fluctuating influent conditions. To address these challenges, this study proposes a novel probabilistic optimization using Gaussian processes (POGP) framework that integrates uncertainty-aware modeling with intelligent real-time control for WWTP performance optimization. The framework employs Gaussian process regression (GPR) to capture complex nonlinear relationships between influent characteristics and effluent quality while explicitly quantifying predictive uncertainty to support robust decision-making. Bayesian optimization (BO) is utilized to automatically tune GPR hyperparameters, improving predictive accuracy and computational efficiency. In parallel, an NSGA-II-enhanced vector parameterization (NVP) strategy is developed to adaptively optimize PID controller parameters by balancing pollutant removal efficiency and process response time in a multi-objective setting. The proposed approach is validated on the widely used Benchmark Simulation Model No. 1 (BSM1) dataset. Experimental results demonstrate excellent predictive performance (root mean squared error [RMSE] < 0.008 and <i>R</i>² > 0.99) and significant control improvements, achieving more than 50% reduction in overshoot and settling time compared to conventional PID-based controllers. These results highlight the strong potential of the POGP framework for robust, efficient, and sustainable real-world WWTP operation.