Nonlinear PCA Combining Principal Curves and RBF-Networks for Process Monitoring

Mohamed-Faouzi Harkat, Gilles Mourot, José Ragot

Research output: Contribution to journalConference article

22 Citations (Scopus)

Abstract

The use of principal component analysis (PCA) for process monitoring applications has attracted much attention recently. PCA is the optimal linear transformation with respect to minimizing the mean square prediction error but it only considers second order statistics. If the data have nonlinear dependencies, an important issue is to develop a technique which takes higher order statistics into account and which can eliminate dependencies not removed by PCA. Recognizing the shortcomings of PCA, a nonlinear extensions of PCA is developed. The purpose of this paper is to present a non linear generalization of PCA (NLPCA) by combining the principal curves and RBF-Networks. The NLPCA model consists of two RBF networks where the nonlinear transformations of the input variables (that characterize the nonlinear principal component analysis) are modelled as a linear sum of radially symmetric kernel functions by using the first network. The nonlinear principal components, which represents the desired output of the first network, are obtained by the principal curves algorithm. The second network tries to perform the inverse transformation by reproducing the original data. The proposed approach is illustrated by a simulation example.

Original languageEnglish
Pages (from-to)1956-1961
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Volume2
Publication statusPublished - 1 Dec 2003
Externally publishedYes

Fingerprint

Principal Curves
RBF Network
Radial basis function networks
Process Monitoring
Process monitoring
Nonlinear Analysis
Principal component analysis
Principal Component Analysis
Higher-order Statistics
Higher order statistics
Linear transformations
Nonlinear Transformation
Symmetric Functions
Prediction Error
Linear transformation
Principal Components
Kernel Function
Order Statistics
Mean square error
Eliminate

Keywords

  • Fault detection
  • Nonlinear PCA
  • Principal curves
  • Radial basis functions

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

Cite this

Nonlinear PCA Combining Principal Curves and RBF-Networks for Process Monitoring. / Harkat, Mohamed-Faouzi; Mourot, Gilles; Ragot, José.

In: Proceedings of the IEEE Conference on Decision and Control, Vol. 2, 01.12.2003, p. 1956-1961.

Research output: Contribution to journalConference article

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