A novel approach for multivariate time series interval prediction of water quality at wastewater treatment plants

This study proposes a novel approach for predicting variations in water quality at wastewater treatment plants (WWTPs), which is crucial for optimizing process management and pollution control. The model combines convolutional bi-directional gated recursive units (CBGRUs) with adaptive bandwidth kernel function density estimation (ABKDE) to address the challenge of multivariate time series interval prediction of WWTP water quality. Initially, wavelet transform (WT) was employed to smooth the water quality data, reducing noise and fluctuations. Linear correlation coefficient (CC) and non-linear mutual information (MI) techniques were then utilized to select input variables. The CBGRU model was applied to capture temporal correlations in the time series, integrating the Multiple Heads of Attention (MHA) mechanism to enhance the model's ability to comprehend complex relationships within the data. ABKDE was employed, supplemented by bootstrap to establish upper and lower bounds of the prediction intervals. Ablation experiments and comparative analyses with benchmark models confirmed the superior performance of the model in point prediction, interval prediction, the analysis of forecast period, and fluctuation detection for water quality data. Also, this study verifies the model's broad applicability and robustness to anomalous data. This study contributes significantly to improved effluent treatment efficiency and water quality control in WWTPs.