Moving window kernel PCA for adaptive monitoring of nonlinear processes

Xueqin Liu, U. Kruger, Timothy Littler, L. Xie, S. Wang

Research output: Contribution to journalArticlepeer-review

172 Citations (Scopus)
13 Downloads (Pure)


This paper discusses the monitoring of complex nonlinear and time-varying processes. Kernel principal component analysis (KPCA) has gained significant attention as a monitoring tool for nonlinear systems in recent years but relies on a fixed model that cannot be employed for time-varying systems. The contribution of this article is the development of a numerically efficient and memory saving moving window KPCA (MWKPCA) monitoring approach. The proposed technique incorporates an up- and downdating procedure to adapt (i) the data mean and covariance matrix in the feature space and (ii) approximates the eigenvalues and eigenvectors of the Gram matrix. The article shows that the proposed MWKPCA algorithm has a computation complexity of O(N2), whilst batch techniques, e.g. the Lanczos method, are of O(N3). Including the adaptation of the number of retained components and an l-step ahead application of the MWKPCA monitoring model, the paper finally demonstrates the utility of the proposed technique using a simulated nonlinear time-varying system and recorded data from an industrial distillation column.
Original languageEnglish
Pages (from-to)132-143
Number of pages12
JournalChemometrics and Intelligent Laboratory Systems
Issue number2
Publication statusPublished - 15 Apr 2009

ASJC Scopus subject areas

  • Process Chemistry and Technology
  • Analytical Chemistry
  • Spectroscopy
  • Computer Science Applications
  • Software

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