Multilinear principal component analysis for statistical modeling of cylindrical surfaces: a case study

This paper focuses the problem of modeling manufactured surfaces for statistical process control. The application of Multilinear principal component analysis (MPCA) is introduced. MPCA is the generalization of the regular principal component analysis where the input can be not only vectors, but also tensors. The objective of this work is basically to explore the MPCA, as well as some basic concepts of multilinear algebra, for modeling manufactured surfaces. A real case study concerning cylindrical surfaces obtained by a lathe-turning process is taken as reference. The measurements related to a specific surface are stored in a matrix addressed by 2 index variables, while the observed data set related to several surfaces is stored in a 3rd-order tensor addressed by 3 indexes. Since the targeted application involves only the use of 3rd-order tensors of real entries, in this study the implementation of MPCA is limited to this specific case. Although a specific geometry is used herein as reference case study, any 2.5-dimensional surface (i.e. where scalar measurements are sampled for each item by using a fixed grid of two spatial index variables) can be modeled with the proposed MPCA-based approach.