Block adaptive kernel principal component analysis for nonlinear process monitoring

On‐line modeling of multivariate nonlinear system based on multivariate statistical methods has been studied extensively due to its industrial requirements. In order to further improve the modeling efficiency, a fast Block Adaptive Kernel Principal Component Analysis algorithm is proposed. Comparing...

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Published inAIChE journal Vol. 62; no. 12; pp. 4334 - 4345
Main Authors Xie, Lei, Li, Zhe, Zeng, Jiusun, Kruger, Uwe
Format Journal Article
LanguageEnglish
Published New York Blackwell Publishing Ltd 01.12.2016
American Institute of Chemical Engineers
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Online AccessGet full text
ISSN0001-1541
1547-5905
DOI10.1002/aic.15347

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Abstract On‐line modeling of multivariate nonlinear system based on multivariate statistical methods has been studied extensively due to its industrial requirements. In order to further improve the modeling efficiency, a fast Block Adaptive Kernel Principal Component Analysis algorithm is proposed. Comparing with the existing work, the proposed algorithm (1) does not rely on iterative computation in the calculating process, (2) combines the up‐ and downdating operations to become a single one (3) and describes the adaptation of the Gram matrix as a series of rank‐1 modification. In addition, (4) the updation of the eigenvalues and eigenvectors is of O(N) and high‐precision. The computational complexity analysis and the numerical study show that the derived strategy possesses better ability to model the time‐varying nonlinear variable interrelationships in process monitoring. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4334–4345, 2016
AbstractList On‐line modeling of multivariate nonlinear system based on multivariate statistical methods has been studied extensively due to its industrial requirements. In order to further improve the modeling efficiency, a fast Block Adaptive Kernel Principal Component Analysis algorithm is proposed. Comparing with the existing work, the proposed algorithm (1) does not rely on iterative computation in the calculating process, (2) combines the up‐ and downdating operations to become a single one (3) and describes the adaptation of the Gram matrix as a series of rank‐1 modification. In addition, (4) the updation of the eigenvalues and eigenvectors is of and high‐precision. The computational complexity analysis and the numerical study show that the derived strategy possesses better ability to model the time‐varying nonlinear variable interrelationships in process monitoring. © 2016 American Institute of Chemical Engineers AIChE J , 62: 4334–4345, 2016
On-line modeling of multivariate nonlinear system based on multivariate statistical methods has been studied extensively due to its industrial requirements. In order to further improve the modeling efficiency, a fast Block Adaptive Kernel Principal Component Analysis algorithm is proposed. Comparing with the existing work, the proposed algorithm (1) does not rely on iterative computation in the calculating process, (2) combines the up- and downdating operations to become a single one (3) and describes the adaptation of the Gram matrix as a series of rank-1 modification. In addition, (4) the updation of the eigenvalues and eigenvectors is of O (N ) and high-precision. The computational complexity analysis and the numerical study show that the derived strategy possesses better ability to model the time-varying nonlinear variable interrelationships in process monitoring. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4334-4345, 2016
On‐line modeling of multivariate nonlinear system based on multivariate statistical methods has been studied extensively due to its industrial requirements. In order to further improve the modeling efficiency, a fast Block Adaptive Kernel Principal Component Analysis algorithm is proposed. Comparing with the existing work, the proposed algorithm (1) does not rely on iterative computation in the calculating process, (2) combines the up‐ and downdating operations to become a single one (3) and describes the adaptation of the Gram matrix as a series of rank‐1 modification. In addition, (4) the updation of the eigenvalues and eigenvectors is of O(N) and high‐precision. The computational complexity analysis and the numerical study show that the derived strategy possesses better ability to model the time‐varying nonlinear variable interrelationships in process monitoring. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4334–4345, 2016
On-line modeling of multivariate nonlinear system based on multivariate statistical methods has been studied extensively due to its industrial requirements. In order to further improve the modeling efficiency, a fast Block Adaptive Kernel Principal Component Analysis algorithm is proposed. Comparing with the existing work, the proposed algorithm (1) does not rely on iterative computation in the calculating process, (2) combines the up- and downdating operations to become a single one (3) and describes the adaptation of the Gram matrix as a series of rank-1 modification. In addition, (4) the updation of the eigenvalues and eigenvectors is of [Formulaomitted] and high-precision. The computational complexity analysis and the numerical study show that the derived strategy possesses better ability to model the time-varying nonlinear variable interrelationships in process monitoring. copyright 2016 American Institute of Chemical Engineers AIChE J, 62: 4334-4345, 2016
Author Zeng, Jiusun
Xie, Lei
Li, Zhe
Kruger, Uwe
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  givenname: Zhe
  surname: Li
  fullname: Li, Zhe
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  organization: State Key Laboratory of Industrial Control Technology, Zhejiang University, 310027, Hangzhou, P.R. China
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  givenname: Uwe
  surname: Kruger
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  email: krugeu@rpi.edu, lizhe08@zju.edu.cn
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– reference: Franc V, Hlavac V. Greedy kernel principal component analysis. Lecture Notes Comput Sci. 2006;3948:87-105.
– reference: Ge ZQ, Yang CJ, Song ZH. Improved kernelpca-based monitoring approach for nonlinear processes. Chem Eng Sci. 2009;64(0):2245-2255.
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Snippet On‐line modeling of multivariate nonlinear system based on multivariate statistical methods has been studied extensively due to its industrial requirements. In...
On-line modeling of multivariate nonlinear system based on multivariate statistical methods has been studied extensively due to its industrial requirements. In...
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SubjectTerms Adaptation
Adaptive algorithms
Algorithms
block adaptive Kernel principal component analysis
Complexity
Computation
Computer applications
Computing time
Eigenvalues
Eigenvectors
Gram matrix
iterative algorithm approach
Iterative methods
Kernels
Mathematical models
Monitoring
Nonlinearity
On-line systems
online monitoring
Principal components analysis
Series (mathematics)
Statistical methods
Statistics
Title Block adaptive kernel principal component analysis for nonlinear process monitoring
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