Abstract
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.
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Data availability
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.
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Funding
This work was supported by the National Natural Science Foundation of China (61873096, 62073145), Guangdong Basic and Applied Basic Research Foundation (2020A1515011057), Guangdong Technology International Cooperation Project Application (2020A0505100024). Fundamental Research Funds for the central Universities, SCUT (2020ZYGXZR034), Hainan Provincial Natural Science Foundation of China (618QN254). The author thanks the anonymous referees and other people for their help to improve the article.
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Dong Li, Daoping Huang, and Yiqi Liu conceived and designed the methodologies and case study. Dong Li performed the experiments and wrote the paper. Yiqi Liu helps review and edited the manuscript. All authors read and approved the manuscript.
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Highlights
• Co-training Gaussian process regression (GPR) and least-square SVM (LS-SVM) models.
• New criteria to select unlabeled data with higher confidence for semisupervised learning.
• Two-step adaptive method to update the model from both of structures and parameters.
• Multi-output models can produce a simpler model structure and better computational efficiency.
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Li, D., Huang, D. & Liu, Y. A novel two-step adaptive multioutput semisupervised soft sensor with applications in wastewater treatment. Environ Sci Pollut Res 28, 29131–29145 (2021). https://doi.org/10.1007/s11356-021-12656-9
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DOI: https://doi.org/10.1007/s11356-021-12656-9