Profile Monitoring of Probability Density Functions via Simplicial Functional PCA with application to Image Data

09/2018

Profile Monitoring of Probability Density Functions via Simplicial Functional PCA with application to Image Data

Friday 2nd February 2018

Menafoglio, A.; Grasso, M.; Secchi, P.; Colosimo, B.M.

The advance of sensor and information technologies is leading to data-rich industrial environments, where big amounts of data are potentially available. In this scenario, image data play a relevant role, as they can easily describe many phenomena of interest. This study focuses on images where several and similar features of interest are randomly distributed and characterized by no spatially correlated structure. Examples are pores in parts obtained via casting or additive manufacturing, voids in metal foams and light-weight components, grains in metallographic analysis, etc. The proposed approach consists of summarizing the random occurrences of the observed features via its (empirical) probability density function (PDF). In particular, a novel approach for PDF monitoring is proposed. It is based on simplicial functional principal component analysis (SFPCA), which is performed by applying an isometric isomorphism between the space of density functions, i.e., the Bayes space B^2, and the space of square integrable functions L^2. A simulation study shows the enhanced monitoring performances provided by the SFPCA-based profile monitoring against other competitors proposed in the literature. Eventually, a real case study dealing with the quality control of foamed materials production is discussed, to highlight a practical use of the proposed methodology.

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A reviewed version of the manuscript has been accepted for publication in Technometrics