Fault detection and estimation using kernel principal component analysis
Résumé
The principal component analysis (PCA) is a linear technique widely used to retrieve a subspace that maximizes the variance of the data, making the presence of a fault easy to detect. Nevertheless, the real systems are nonlinear. To this end, we propose in this paper to use a kernel-based technique known as kernel principal component analysis (KPCA) for fault diagnosis. The main idea is to use a nonlinear transformation that projects data into a higher dimensional feature space, where conventional PCA is applied. Although detection can be defined in this space, the estimation of the fault requires the map back to the input space. In this sense, we derive an iterative pre-image technique. A study on possible initial points is done. Three initialization techniques based on different properties are presented. The relevance of the proposed technique is illustrated on simulated data.