A Statistical Approach to Surface Metrology for 3D-Printed Stainless Steel
A Statistical Approach to Surface Metrology for 3D-Printed Stainless Steel
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DOI：
10.1080/00401706.2021.2009034
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发表时间：
2021-11
期刊：
影响因子：
2.5
通讯作者：
Christine J. Oates;W. Kendall;L. Fleming
中科院分区：
文献类型：
--
作者：
Christine J. Oates;W. Kendall;L. Fleming
摘要 表面计量学是研究表面几何变化的工程领域。本文探讨了空间统计等现代技术作为 3D 打印不锈钢几何变化生成模型的潜力。 3D 打印组件复杂的宏观几何形状带来了传统表面计量中不存在的挑战，因为训练数据和测试数据不需要在同一流形上定义。引人注目的是，根据一个流形上的测地距离定义的协方差函数可能无法满足正定性，因此在不同流形的上下文中不能成为有效的协方差函数；这阻碍了旨在从训练数据集中学习协方差函数的标准技术的使用。另一方面，相关的协方差微分算子是局部定义的。本文建议对此类微分算子进行推理，从而促进从训练数据集的流形到测试数据集的流形的泛化。该方法在模型选择的背景下进行评估，并在 3D 打印不锈钢的有限元模型的背景下进行详细探索。
Abstract 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.