A Statistical Approach to Surface Metrology for 3D-Printed Stainless Steel
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Surface metrology is the area of engineering concerned with the study of geometric variation in surfaces. This paper explores the potential for modern techniques from spatial statistics to be used to characterise 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. We circumvent this by noting that, whilst covariance formulations do not generalise across manifolds, the associated covariance differential operators are locally defined. This insight enables us to formulate inference for the differential operator itself, facilitating generalisation 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.
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