### 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 language | English |
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Pages (from-to) | 1956-1961 |

Number of pages | 6 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

Volume | 2 |

Publication status | Published - 1 Dec 2003 |

Externally published | Yes |

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### 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

*Proceedings of the IEEE Conference on Decision and Control*,

*2*, 1956-1961.