Time-Frequency Collaborative Representation Learning for the Prediction of Industrial Wastewater Quality under Complex Dynamic Conditions

Abstract This study proposes BiMamba-FECA, a time-frequency collaborative representation learning framework for robust prediction of industrial wastewater quality under complex dynamic conditions. The bidirectional Mamba architecture captures historical dependencies and future contextual information simultaneously, enhancing the representation of long-range temporal dynamics. Meanwhile, unlike conventional decomposition-based time-frequency forecasting methods, a frequency-enhanced channel attention mechanism operates directly on latent temporal representations learned by BiMamba and adaptively uses frequency-domain information to recalibrate informative temporal features, enabling effective identification of latent periodic variations, long-term trends, and transient disturbances. Given the complex influent conditions, variable production processes, and pronounced temporal dynamics of papermaking wastewater, we selected a papermaking wastewater treatment plant as a representative case study for long-term chemical oxygen demand (COD) prediction. Experimental results demonstrate that BiMamba-FECA consistently outperforms baseline models, particularly for long-horizon forecasting. Compared with the best-performing baseline model (graph convolutional network–convolutional neural network–gated recurrent unit–attention network (GCGA)), the proposed framework reduces mean absolute percentage error (MAPE), root-mean-square error (RMSE), and mean absolute error (MAE) by 20.93%, 25.19%, and 22.92%, respectively, demonstrating its potential for intelligent monitoring and operation optimization of industrial wastewater treatment systems.