FiTiformer: A fluctuation–trend modulation model for multi-step forecasting of wastewater influent parameters

Abstract

Accurate multi-step forecasting of key influent parameters is of great importance for the stable operation, energy optimization and early warning of wastewater treatment plants (WWTPs). However, existing Transformer-based approaches often fail to capture the strong non-stationarity and complex local fluctuations of wastewater data. To address these challenges, we propose a novel forecasting model, termed the Fluctuation-injected Trend inverted Transformer (FiTiformer), which enhances predictions by jointly modeling trend and fluctuation components. In this model, we design a Gated Fluctuation-to-Trend Modulation (GFTM) module that adaptively injects high-frequency fluctuation signals into the trend representation, thereby enhancing robustness under non-stationary conditions. This module is complemented by an inverted Transformer network that captures inter-variable dependencies to extract informative fluctuation features, while a Patch-wise Structural Loss ensures that local patterns are preserved in predictions, rather than focusing solely on global errors. Extensive experiments on the BSM2 benchmark and a full-scale WWTP dataset validate the effectiveness of FiTiformer. On the BSM2 dataset, the model achieves an average R${}^2$ above 0.88 while reducing RMSE by more than 7.4%. On the full-scale WWTP dataset, FiTiformer attains an average R${}^2$ above 0.70 with an RMSE reduction exceeding 8.0%. These results demonstrate that FiTiformer enhances both global trend modeling and local fluctuation preservation, offering reliable and interpretable multi-step forecasting for practical WWTP operations.