Kernel PCA in nonlinear visualization of a healthy and a faulty planetary gearbox data

Abstract

PCA (Principal Component Analysis) is a powerful method for investigating the dimensionality and extracting structure from multi-dimensional data, however it extracts only linear projections. More general projections – accounting for possible non-linearities among the observed variables – can be obtained using kPCA (Kernel PCA), that performs the same task, however working with an extended feature set. We consider planetary gearbox data given as two 15-dimensional data sets, one coming from a healthy and the other from a faulty planetary gearbox. For these data both the PCA (with 15 variables) and the kPCA (using indirectly 500 variables) is carried out. It appears that the investigated PC-s are to some extent similar; however, the first three kernel PC-s show the data structure with more details.