A Statistical Approach to Surface Metrology for 3D-Printed Stainless Steel

Surface metrology is the area of engineering concerned with the study of\ngeometric variation in surfaces. This paper explores the potential for modern\ntechniques from spatial statistics to act as generative models for geometric\nvariation in 3D-printed stainless steel. The complex macro-scale geometries of\n3D-printed components pose a challenge that is not present in traditional\nsurface metrology, as the training data and test data need not be defined on\nthe same manifold. Strikingly, a covariance function defined in terms of\ngeodesic distance on one manifold can fail to satisfy positive-definiteness and\nthus fail to be a valid covariance function in the context of a different\nmanifold; this hinders the use of standard techniques that aim to learn a\ncovariance function from a training dataset. On the other hand, the associated\ncovariance differential operators are locally defined. This paper proposes to\nperform inference for such differential operators, facilitating generalisation\nfrom the manifold of a training dataset to the manifold of a test dataset. The\napproach is assessed in the context of model selection and explored in detail\nin the context of a finite element model for 3D-printed stainless steel.\n