Learning a neural network-based soft sensor with double-errors parallel optimization towards effluent variable prediction in wastewater treatment plants

Abstract

With the development of machine learning and artificial intelligence (ML/AI) models, data-driven soft sensors, especially the neural network-based, have widespread utilization for the prediction of key water quality indicators in wastewater treatment plants (WWTPs). However, recent research indicates that the prediction performance and computational efficiency are greatly compromised due to the time-varying, nonlinear and high-dimensional nature of the wastewater treatment process. This paper proposes a neural network-based soft sensor with double-errors parallel optimization to achieve more accurate prediction for effluent variables timely. Firstly, relying on the Activity Based Classification (ABC) principle, an ensemble variable selection method that combines Pearson correlation coefficient (PCC) and mutual information (MI) is introduced to select the optimal process variables as auxiliary variables, thereby reducing the data dimensionality and simplifying the model complexity. Subsequently, a double-errors parallel optimization methodology with minimizing both point prediction error and distribution error simultaneously is proposed, aiming to enhancing the training efficiency and the fitting quality of neural networks. Finally, the effectiveness is quantitatively assessed in two datasets collected from the Benchmark Simulation Model no. 1 (BMS1) and an actual oxidation ditch WWTP. The experimental results illustrate that the proposed soft sensor achieves precise effluent variable prediction, with RMSE, MAE and R2 values being 0.0606, 0.0486, 0.99930, and 0.06939, 0.05381, 0.98040, respectively. Consequently, this soft sensor can expedite the convergence speed in the neural network training process and enhance the prediction performance, thereby contributing to the effective optimization management of WWTPs.