Registration-Free Localization of Defects in Three-Dimensional Parts from Mesh Metrology Data Using Functional Maps

Author:

Zhao Xueqi1,del Castillo Enrique1ORCID

Affiliation:

1. Engineering Statistics and Machine Learning Laboratory, Department of Industrial and Manufacturing Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802

Abstract

We consider a common problem occurring after using a statistical process control (SPC) method based on three-dimensional measurements: locate where on the surface of the part that triggered an out-of-control alarm there is a significant shape difference with respect to either an in-control part or its nominal (computer-aided design (CAD)) design. In the past, only registration-based solutions existed for this problem, which first orient and locate the part and its nominal design under the same frame of reference. Recently, spectral Laplacian methods have been proposed for the SPC of discrete parts and their measured surface meshes. These techniques provide an intrinsic solution to the SPC problem: that is, a solution exclusively based on data whose coordinates lie on the surfaces without making reference to their ambient space, thus avoiding registration. Registration-free methods avoid the computationally expensive, nonconvex registration step needed to align the parts as required by previous methods, eliminating registration errors, and they are important in industry because of the increasing use of portable noncontact scanners. In this paper, we first present a new registration-free solution to the post-SPC part defect localization problem. The approach uses a spectral decomposition of the Laplace–Beltrami operator in order to construct a functional map between the CAD and measured manifolds to locate defects on the suspected part. A computational complexity analysis demonstrates the approach scales better with the mesh size and is more stable than a registration-based approach. To reduce computational expense, a new mesh partitioning algorithm is presented to find a region of interest on the surface of the part where defects are more likely to exist. The functional map method involves a large number of point-to-point comparisons based on noisy measurements, and a new statistical thresholding method used to filter the false positives in the underlying massive multiple comparisons problem is also provided. Funding: This research was partially funded by the National Science Foundation [Grant CMMI 2121625]. Data Ethics & Reproducibility Note: There are no data ethics considerations. The code capsule is available on Code Ocean at https://codeocean.com/capsule/4615101/tree/v1 and in the e-Companion to this article (available https://doi.org/10.1287/ijds.2023.0030 ).

Publisher

Institute for Operations Research and the Management Sciences (INFORMS)

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3