Adaptive self-calibrated soft sensor for reliable nutrient measurement in rivers: Two-stage stacked autoencoder with densely connected fusion network

A soft sensor effectively estimates concentrations of total nitrogen (TN) and total phosphorus (TP) in rivers by utilizing easily measurable variables. However, in practical applications, the malfunction in sensors measuring easy-to-measure variables causes a deficiency in the developed TN and TP soft sensors. This study proposes an adaptive dual-stage soft sensor model (FAE-DNet) by stacking a fusion autoencoder (FAE) with a densely connected network (DNet) to estimate TN and TP reliably. In the first stage, a dataset consisting of ten biological-chemical variables with faulty measurements was self-calibrated using the FAE model. Subsequently, the second stage utilized the self-calibrated sensor data as input to the DNet to predict the TN and TP effectively. Furthermore, an explainable artificial intelligence (XAI) analysis was employed to elucidate the performance of the developed deep AI soft sensor model. The first-stage, FAE model, effectively handled faulty measurements, with low MSE values: 0.0913 for electrical conductivity (EC) and 0.1571 for dissolved oxygen (DO). In the second stage with DNet, nutrient prediction showed a superior R 2 value of 0.9557. However, the prediction showed a very poor performance with an R 2 value of 0.0749 when faulty data were utilized as input to the DNet without calibration using the FAE, highlighting the reliability of the two-stage FAE-DNet for precise nutrient estimation. Thus, the proposed FAE-DNet model provides advanced water quality monitoring through a self-calibrated soft sensor that accurately predicts TN and TP, making it a promising tool for monitoring waterbodies. • A dual-stage DL model based soft sensor for water nutrients monitoring was newly proposed. • First-stage based on FAE outperformed in reconstructing faulty measurements (MSE = 0.0913). • Second-stage based on DNet showed explainable and superior prediction of nutrients (R2 = 0.9557). • Residual error decreases by 89.44 % and 50.68 % in calibrated case compared to faulty case. • DNet based soft sensor outperformed, DNN, RF, and XGBoost models in nutrients prediction.