A deep semi-supervised learning framework towards multi-output soft sensors development and applications in wastewater treatment processes

Soft sensors have emerged as a powerful tool for predicting quality-related but hard-to-measured variables in the wastewater treatment plants (WWTPs). However, due to high data dimensions and insufficient training data, many existing soft sensors usually suffer from low accuracy and degradation, and are unable to meet the field measurement requirements. To enhance the prediction performance and efficiency, this paper proposed a deep semi-supervised learning framework towards multi-output soft sensors in wastewater treatment processes. Firstly, a deep learning network is constructed by integrating stacked autoencoders with a multi-output neural network (SAE-MNN), which is used to eliminate redundant information from raw data and to predict multiple quality-related variables simultaneously. Secondly, the semi-supervised Co-training learning is extended to the multi-output systems and employed to address the challenge of insufficient training data. Two datasets collected from different WWTPs are provided to the effectiveness of the Co-training SAE-MNN framework, in terms of RMSSD values of 0.1073 and 0.1829, and the time consumption of 3.42 s and 12.54 s, respectively. The results demonstrate that the proposed soft sensor provides a reliable tool for multivariate prediction in WWTPs, and contributes to controlling detection costs and increasing wastewater treatment efficiency.