On the use of principal component analysis to identify systematic patterns in roundness profiles

In many industrial applications, quality of products or processes is related to profiles. With reference to mechanical components, profiles and surfaces play a relevant role, as shown by the high number of geometric specifications characterizing most of the technical drawings. In this framework, an important step consists in identifying the systematic pattern which characterizes all the profiles machined while the process is in its standard or nominal state. With reference to this aim, this paper focuses on the use of principal component analysis (PCA) for profile data (Functional PCA). Since a usual objection to PCA is that principal components (PCs) are often difficult or impossible to interpret, this paper explores what types of profile features allow one to obtain interpretable PCs. Within the paper, a real case study related to roundness profiles of mechanical components is used as reference. In particular, functional PCA is applied to the set of real profile data to derive the significant PCs and the corresponding eigenfunctions. In order to gain insight into the information behind the retained PCs, both simulations and analytical results are used. In particular, the analytical results, outlined in the literature on functional data analysis, allow one to link the eigenfunctions to specific profile features, given that profile data admit an orthogonal basis series expansion.