State Estimation for High-Dimensional Wastewater Treatment Plants Based on Dynamic Mode Decomposition

Effective state estimation is crucial for ensuring operational safety, environmental compliance, and efficient resource utilization in high-dimensional wastewater treatment plants (WWTPs). This study proposes a purely data-driven methodology based on dynamic mode decomposition (DMD) to construct a linear dynamic model capable of globally capturing the inherent nonlinearity and complexity of wastewater treatment processes. Moreover, DMD can generate system representations in both full-dimension and reduced-dimension forms and offers flexibility in modeling complex dynamics. Then, the Kalman filter and ensemble Kalman filter (EnKF) are implemented using the derived models for state estimation. A detailed analysis of estimation accuracy and computational cost is also provided. Furthermore, the performance of the proposed DMD-based method is comparatively evaluated against a traditional linearization-based approach, in which the process is linearized at a nominal operating point. Results from the high-dimensional WWTP demonstrate the effectiveness and superiority of the proposed method.