Dynamic Nonlinear Partial Least Squares Modeling Using Gaussian Process Regression

Hongbin LIU, Chong YANG, Bengt CARLSSON, S. Joe QIN*, Changkyoo YOO

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

41 Citations (Scopus)


A dynamic Gaussian process regression based partial least-squares (D-GPR-PLS) model is proposed to improve estimation ability and compared to the conventional nonlinear PLS. Considering the strong ability of GPR in nonlinear process modeling, this method is used to build a nonlinear regression between each pair of latent variables in the partial least-squares. In addition, augmented matrices are embedded into the D-GPR-PLS model to obtain better prediction accuracy in nonlinear dynamic processes. To evaluate the modeling performance of the proposed method, two simulated cases and a real industrial process based on wastewater treatment processes (WWTPs) are considered. The simulated cases use data from two high fidelity simulators: benchmark simulation model no. 1 and its long-term version. The second study uses data from a real biological wastewater treatment process. The results show the superiority of D-GPR-PLS in modeling performance for both data sets. More specifically, in terms of the prediction for effluent chemical oxygen demand of the real WWTP data, the value of the root-mean-square error is decreased by 31%, 16%, and 52%, respectively, in comparison with that for linear PLS, quadratic PLS, and least-squares support vector machine based PLS.
Original languageEnglish
Pages (from-to)16676-16686
Number of pages11
JournalIndustrial and Engineering Chemistry Research
Issue number36
Early online date7 Aug 2019
Publication statusPublished - 11 Sept 2019
Externally publishedYes

Bibliographical note

This study was supported by the Foundation of Nanjing Forestry University (No. GXL029) and the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT (No. NRF-2019H1D3A1A02071051).


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