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

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