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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 ).
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Adaptive Exploration and Optimization of Materials Crystal Structures
A central problem of materials science is to determine whether a hypothetical material is stable without being synthesized, which is mathematically equivalent to a global optimization problem on a highly nonlinear and multimodal potential energy surface (PES). This optimization problem poses multiple outstanding challenges, including the exceedingly high dimensionality of the PES, and that PES must be constructed from a reliable, sophisticated, parameters-free, and thus very expensive computational method, for which density functional theory (DFT) is an example. DFT is a quantum mechanics-based method that can predict, among other things, the total potential energy of a given configuration of atoms. DFT, although accurate, is computationally expensive. In this work, we propose a novel expansion-exploration-exploitation framework to find the global minimum of the PES. Starting from a few atomic configurations, this “known” space is expanded to construct a big candidate set. The expansion begins in a nonadaptive manner, where new configurations are added without their potential energy being considered. A novel feature of this step is that it tends to generate a space-filling design without the knowledge of the boundaries of the domain space. If needed, the nonadaptive expansion of the space of configurations is followed by adaptive expansion, where “promising regions” of the domain space (those with low-energy configurations) are further expanded. Once a candidate set of configurations is obtained, it is simultaneously explored and exploited using Bayesian optimization to find the global minimum. The methodology is demonstrated using a problem of finding the most stable crystal structure of aluminum. History: Kwok Tsui served as the senior editor for this article. Funding: The authors acknowledge a U.S. National Science Foundation Grant DMREF-1921873 and XSEDE through Grant DMR170031. Data Ethics & Reproducibility Note: The code capsule is available on Code Ocean at https://codeocean.com/capsule/3366149/tree and in the e-Companion to this article (available at https://doi.org/10.1287/ijds.2023.0028 ).
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- Award ID(s):
- 1921873
- PAR ID:
- 10443720
- Date Published:
- Journal Name:
- INFORMS Journal on Data Science
- ISSN:
- 2694-4022
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1287/ijds.2023.0028
