Analyzing Nonparametric Part-to-Part Variation in Surface Point Cloud Data

Abstract

Surface point cloud data from three-dimensional optical scanners provide rich information about the surface geometry of scanned parts and potential variation in the surfaces from part-to-part. It is challenging, however, to make full use of these data for statistical process control purposes to identify sources of variation that manifest in a more complex nonparametric manner than variation in some prespecified set of geometric features of each part. We develop a framework for identifying nonparametric variation patterns that uses dissimilarity representation of the data and dissimilarity-based manifold learning, which helps discover a low-dimensional implicit manifold parameterization of the variation. Visualizing how the parts change as the manifold parameters are varied helps build an understanding of the physical characteristic of the variation. We also discuss using the nominal surface of parts when it is accessible to improve the computational expense and visualization aspects of the framework. Our approaches clearly reveal the nature of the variation patterns in a real cylindrical-part machining example and a simulated square head bolt example.

Keywords:

• Dissimilarity representation
• Manifold learning
• Phase I analysis
• Point cloud distance
• Statistical process control

Supplementary Materials

In the online supplementary materials of this article, we provide descriptions of kd-tree and its nearest neighbor search algorithm and Figures S2 and S3, mentioned in Section 5. We also illustrate the approach in Section 6 with the (revisited) cylindrical example. Additionally, files “pattern 1.gif” and “pattern 2.gif” contain the animations of the variation patterns mentioned in Section 6. Furthermore, R codes are included in the supplementary materials. The cylinder dataset of Colosimo and Pacella (2011) is available at https://figshare.com/articles/dataset/DATASET_from_Analyzing_the_effect_of_process_parameters_on_the_shape_of_3D_profiles_by_B_M_Colosimo_M_Pacella_JQT_2011/12750968.

Acknowledgments

The authors thank the editor and the anonymous associate editor and referees for helping to improve the article.