Practical implementation of an End-to-end methodology for SPC of 3-D part geometry: A case study

Del Castillo and Zhao have recently proposed a new methodology for the Statistical Process Control (SPC) of discrete parts whose 3-dimensional (3D) geometrical data are acquired with non-contact sensors. The approach is based on monitoring the spectrum of the Laplace–Beltrami (LB) operator of each scanned part estimated using finite element methods (FEM). The spectrum of the LB operator is an intrinsic summary of the geometry of a part, independent of the ambient space. Hence, registration of scanned parts is unnecessary when comparing them. The primary goal of this case study paper is to demonstrate the practical implementation of the spectral SPC methodology through multiple examples using real scanned parts acquired with an industrial-grade laser scanner, including 3D-printed parts and commercial parts. We discuss the scanned mesh preprocessing needed in practice, including the type of remeshing found to be most beneficial for the FEM computations. For each part type, both the “phase I” and “phase II” stages of the spectral SPC methodology are showcased. In addition, we provide a new principled method to determine the number of eigenvalues of the LB operator to consider for efficient SPC of a given part geometry, and present an improved algorithm to automatically define a region of interest, particularly useful for large meshes. Computer codes that implement every method discussed in this paper, as well as all scanned part datasets used in the case studies, are made available and explained in the supplementary materials.

Del Castillo与Zhao近期提出了一种面向离散零件统计过程控制（Statistical Process Control, SPC）的全新方法论，该方法依托非接触式传感器采集离散零件的三维（3D）几何数据。该方法的核心是对每个扫描零件的拉普拉斯-贝尔特拉米（Laplace–Beltrami, LB）算子谱进行监测，其谱估计通过有限元法（Finite Element Method, FEM）完成。拉普拉斯-贝尔特拉米算子的谱是零件几何的内在表征，与所处环境空间无关，因此在对比扫描零件时无需进行配准操作。本案例研究论文的核心目标是，通过使用工业级激光扫描仪采集的真实扫描零件（包括3D打印零件与商用零件）的多个实例，展示该谱统计过程控制方法的实际落地实现。我们将讨论实际应用中所需的扫描网格预处理流程，包括经验证对有限元计算最为有益的重新网格化方案。针对每种零件类型，本文均展示了谱统计过程控制方法的“第一阶段”与“第二阶段”实施流程。此外，我们提出了一种全新的规范化方法，用于确定针对给定零件几何开展高效统计过程控制所需考虑的拉普拉斯-贝尔特拉米算子特征值数量，并提出了一种改进算法以自动定义感兴趣区域，该算法对大型网格尤为实用。本文所讨论的所有方法的实现代码，以及本案例研究中使用的全部扫描零件数据集，均已在补充材料中公开并予以详细说明。