Hybrid prediction model for multi-step wastewater influent quality using adaptive wavelet denoising and enhanced Informer

Abstract

Accurate multi-step influent quality forecasting is essential for ensuring the stable operation and regulatory compliance of wastewater treatment plants (WWTPs). However, existing models struggle with sensor noise suppression, temporal dependency modelling, and the simultaneous capture of global trends and local fluctuations, limiting their predictive accuracy and robustness. To address these challenges, we propose Dynamic Thresholding Wavelet Transform-enhanced Informer (DTWT-EInformer), a hybrid framework that integrates DTWT with an EInformer architecture. The DTWT adaptively filters non-stationary noise using level-aware thresholds while preserving key signal features. The EInformer incorporates positional and temporal encoding, ProbSparse self-attention, and Dilated Causal Convolution Distillation to jointly capture long-term dependencies and short-term fluctuations under temporal causality constraints. The model was trained and validated using influent water quality and meteorological datasets collected at 30-min resolution over a 1-year monitoring campaign from a full-scale WWTP in Yan’an, China. The target variables were chemical oxygen demand (COD) and ammonia nitrogen (NH${}_3$-N), with forecast horizons ranging from 5–45 steps ahead (2.5–22.5 h). The experimental results showed that DTWT-EInformer reduced the mean squared error (MSE) and root MSE (RMSE) by over 90% relative to baseline models, achieved $R^2$ values of 0.9976 (COD) and 0.9986 (NH${}_3$-N), and maintained symmetric mean absolute percentage error (SMAPE) below 1%. The average inference time of 291–302 ms demonstrated its suitability for real-time deployment in WWTP operations.