期刊
CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS
卷 96, 期 2, 页码 132-143出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.chemolab.2009.01.002
关键词
Nonlinear process; Kernel PCA; Moving window; Multivariate statistical process control; Adaptive; Numerically efficient
类别
资金
- Engineering and Physical Science Research Council (EPSRC) [GR/S84354/01]
- National Natural Science Foundation of China [60721062]
- National High Technology Research and Development Program of China [2007AA04Z162]
- Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry of China
- Engineering and Physical Sciences Research Council [GR/S84354/01] Funding Source: researchfish
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(N-2), whilst batch techniques, e.g. the Lanczos method, are of O(N-3). Including the adaptation of the number of retained components and an I-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. (c) 2009 Elsevier B.V. All rights reserved.
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