An attention-based parallel model with sliding window decomposition algorithm for water quality prediction

Accurate forecasting of effluent water quality is essential for enhancing the safety and economic efficiency of wastewater treatment plants (WWTPs) due to the volatility and time-varying nature of effluent water quality. Representative neural networks, such as Long Short-Term Memory (LSTM), have been extensively employed in time-series prediction. However, as the volume of water quality data increases, these models become unstable, making accurate prediction challenging. This study proposes a hybrid prediction method, DVIBM, based on optimized decomposition for forecasting effluent water quality. DVIBM integrates the Dung Beetle Optimization (DBO) algorithm, Variational Mode Decomposition (VMD), Informer, Bidirectional Long Short-Term Memory (BiLSTM) network, and the multi-scale attention mechanism (MUSE). The DBO algorithm is employed to optimize the hyperparameters $\alpha$ and $k$ in VMD, within a sliding window framework, to determine the decomposition bandwidth and the number of modes. The original water quality time-series is decomposed into multiple sub-series, with future data excluded during the process to effectively extract features while preventing data leakage. DVIBM couples Informer and BiLSTM via the MUSE attention mechanism, adaptively fusing multi-scale long- and short-term features, thereby reducing error accumulation and propagation in cascaded or single-architecture. Across varying sliding-window parameter combinations and time steps, as well as in ablation comparisons, DVIBM achieves MAE/MSE/R² of 0.104/0.017/0.975 for effluent TN and 0.071/0.008/0.969 for TP, significantly outperforming the benchmark models. Global and local interpretability analyses of effluent TN and TP are conducted using the SHAP (Shapley Additive Explanations) algorithm, providing theoretical support for the interpretability of wastewater treatment systems.