Block adaptive kernel principal component analysis for nonlinear process monitoring

• Published in: AIChE journal Vol. 62; no. 12; pp. 4334 - 4345
• Main Authors: Xie, Lei, Li, Zhe, Zeng, Jiusun, Kruger, Uwe
• Format: Journal Article
• Language: English
• Published: New York Blackwell Publishing Ltd 01.12.2016; American Institute of Chemical Engineers
• Subjects: 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
• ISSN: 0001-1541; 1547-5905
• DOI: 10.1002/aic.15347

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