Development of transparent high-frequency soft sensor of total nitrogen and total phosphorus concentrations in rivers using stacked convolutional auto-encoder and explainable AI

Abstract

Monitoring total nitrogen (TN) and total phosphorus (TP) concentrations in rivers is essential to assess the water quality and control the eutrophication risk. However, the online measurements of TN and TP are difficult due to the high costs, uncertainties, and the time lag associated with real-time monitoring. This study aims to develop a new transparent high-frequency soft sensing model for the online estimation of TN and TP concentrations, based on explainable artificial intelligence (XAI) and convolutional autoencoder (CAE) integrated with deep fully connected layers (DFC) and robust wrapper feature selection. The explainable stacked CAE-DFC-based soft sensor model can effectively capture complex nonlinear relationships among water quality parameters and provide superior prediction and interpretability using the explainable SHapley Additive exPlanations (SHAP). The explainable CAE-DFC model-based soft sensor showed a superior online prediction of TN and TP concentrations with R2 = 0.9607 and 0.9137, respectively. SHAP analysis provided a clear explanation of the proposed CAE-DFC model outcomes in the prediction of TN and TP, enhancing the reliability and transparency of the model. The developed transparent soft sensor can offer a trustworthy tool for the decision-makers to monitor TN and TP in waterbodies, avoiding the expensive acquisition cost and controlling the eutrophication risk.