A novel two-step adaptive multioutput semisupervised soft sensor with applications in wastewater treatment

To make full use of unlabeled data for soft-sensor modelling and to address the coexistence of a large number of hard-to-measure variable issues, this study proposed a novel two-step adaptive heterogeneous co-training multioutput model. First, unlabeled data with the highest confidence were selected to optimize the model. Then, the proposed model co-trained Gaussian process regression (GPR) and least squares support vector machine (LSSVM) algorithms with two sets of independent labeled data. Second, at each step of the model update, the Kalman filter (KF) worked together with a moving window (MW) to strengthen the model to address process dynamics. Finally, the proposed model was demonstrated by a simulated wastewater treatment platform, BSM1, and a real sewage treatment plant. The root-mean-square error (RMSE) and root-mean sum of squares of the diagonal (RMSSD) were obviously reduced, and the correlation coefficient (R) and correlation coefficient (RR) reached 0.8 in both case studies. The results suggest that the proposed model can significantly improve prediction performance.