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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 761280, 9 pages
Research Article

Recursive Gaussian Process Regression Model for Adaptive Quality Monitoring in Batch Processes

1State Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou, Zhejiang 310027, China
2Department of Chemical Engineering, Chung-Yuan Christian University, Chung-Li 320, Taiwan

Received 5 November 2014; Revised 23 December 2014; Accepted 23 December 2014

Academic Editor: Gang Li

Copyright © 2015 Le Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In chemical batch processes with slow responses and a long duration, it is time-consuming and expensive to obtain sufficient normal data for statistical analysis. With the persistent accumulation of the newly evolving data, the modelling becomes adequate gradually and the subsequent batches will change slightly owing to the slow time-varying behavior. To efficiently make use of the small amount of initial data and the newly evolving data sets, an adaptive monitoring scheme based on the recursive Gaussian process (RGP) model is designed in this paper. Based on the initial data, a Gaussian process model and the corresponding SPE statistic are constructed at first. When the new batches of data are included, a strategy based on the RGP model is used to choose the proper data for model updating. The performance of the proposed method is finally demonstrated by a penicillin fermentation batch process and the result indicates that the proposed monitoring scheme is effective for adaptive modelling and online monitoring.