Real-time effluent water quality prediction model based on BiLSTM and KAN for wastewater treatment plants

Abstract

Predicting effluent water quality in wastewater treatment plants (WWTPs) is essential for operation optimization, resource efficiency, and regulatory compliance. However, traditional methods struggle with complex temporal dynamics and nonlinear interactions, and current research lacks unified approaches for feature interaction, noise robustness, and multiscale modeling. In this study, we introduce a hybrid model combining bidirectional long short-term memory (BiLSTM) and Kolmogorov-Arnold networks (KAN), alongside a feature-selection mechanism that fuses Spearman, Kendall, and maximal information coefficient (MIC) metrics to identify key water-quality drivers. The feature-selection strategy integrates three methods to capture both monotonic and non-monotonic associations, reducing noise by focusing on impactful predictors. The model synergistically combines BiLSTM's bidirectional temporal feature extraction (capturing past-future context of time-series data) with KAN's strong nonlinear approximation power (modeling complex interactions via spline-based univariate function combinations, based on the Kolmogorov-Arnold theorem), optimizing spatiotemporal feature integration through a dynamic weighted gating mechanism. Experimental results show that, compared with benchmark models such as long short-term memory (LSTM), the model reduces the root mean square error (RMSE) in predicting effluent chemical oxygen demand (COD) by 7.67 % to 45.17 % and improves the coefficient of determination (R²) by 0.96 % to 14.76 %, demonstrating superior forecasting performance. Temporal differential analysis uncovers water quality fluctuations within a day, while multiscale forecasting achieves R² > 0.92, validating the model's ability to capture dynamic changes and perform nonlinear mapping. This study further applies SHapley Additive Explanation (SHAP) and Local Interpretable Model-agnostic Explanations (LIME) for interpretability: SHAP identifies key drivers while LIME clarifies how these variables influence specific predictions, aiding operational adjustments. Noise-injection tests confirm robustness, ensuring reliability under sensor drift. This framework offers a comprehensive, interpretable, and resilient solution for real-time WWTP control (e.g., dynamic carbon source dosing) and advances smart water management.