Abstract
Considering the time-varying, uncertain and non-linear properties of the wastewater treatment process (WWTPs), a novel multi-kernel relevance vector machine (MRVM) soft sensor based on time difference (TD) is proposed to predict the quality-relevant but difficult-to-measure variable. Firstly, a novel dimension reduction technique is introduced to reduce data dimension and model complexity. Secondly, the parameters of the kernel model are optimized by the intelligent optimization algorithm (PSO). Besides, the TD strategy is introduced to enhance the robustness of MRVM when exposing to dynamic environments. Finally, the proposed model was assessed through two simulation studies and a real WWTP with the results demonstrating the effectiveness of the proposed model.
Framework of Lasso-TD-MRVM soft sensor model
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Funding
This work was financially supported by the National Natural Science Foundation of China (61873096, 61673181), the Basic and Applied Basic Research Foundation of Guangdong Province (2020A1515011057), and the Science and Technology Planned Project of Guizhou Province ([2020]1Y276).
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All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Hongchao Cheng, Longhua Yuan, and Lingying Yao. The first draft of the manuscript was written by Jing Wu. The writing-review and editing were performed by Yiqi Liu. The funding was provided by Daoping Huang and Yiqi Liu. All authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Highlights
• A soft sensor is proposed to predict the quality variables in wastewater treatment.
• Multi-kernel learning is developed to enhance the relevant vector machine model.
• The Lasso is used to reduce data dimension and model complexity.
• The TD is imposed on Multi-kernel RVM to improve the dynamics of soft sensor.
• A data set with filamentous sludge bulking is used to validate the proposed framework.
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Wu, J., Cheng, H., Liu, Y. et al. Learning soft sensors using time difference–based multi-kernel relevance vector machine with applications for quality-relevant monitoring in wastewater treatment. Environ Sci Pollut Res 27, 28986–28999 (2020). https://doi.org/10.1007/s11356-020-09192-3
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DOI: https://doi.org/10.1007/s11356-020-09192-3