Curvilinear component analysis in search of dimensionality and structure of some gearbox data

Our aim is to explore some gearbox vibration data characterized by 15 power spectra amplitudes. The data were gathered for two gearboxes: one being in a good state (set B) and the the other in a bad state (set A). In turn, each of the sets was gathered when the machine was operated under small/no load, and under full load. This gives 4 data sets to compare. We are concerned with two topics: 1. Is it possible to compare in a simple way the structure of the four obtained subsets? 2. Could the number of variables be reduced without losing essential information content of the data? To answer both these questions, we use a visual tool, the CCA (Curvilinear Component Analysis) method proposed by Demartines and Herault. Using this tool, we are able to answer positively the above two questions. We use the CCA algorithm in special layout, applying DxDy plots, with emphasis to estimating the overall intrinsic dimensionality of the four groups of data and capture visually the differences in their structure.