Deep Intrinsic Learning for On-line Process Control of Manufacturing Manifold Data

这项拨款将通过研究控制制成品质量的新方法，加强美国的工业竞争力。制造工厂的现代激光传感器可以从化工厂的离散部件或过程变量的表面收集数十万个测量值。如何最好地利用这些非常大的数据集来控制零件的质量是一个困难和开放的问题。该项目的第一部分将开发新的机器学习和数学方法，用于根据激光扫描获得的三维几何数据对制造的离散部件进行质量控制，这些数据不需要冗长的预处理。然后，该赠款将开发新方法，用于识别最能代表连续过程制造设施中较大过程变量集的变量子集，以便对较小变量集进行有效监测，从而实现对工厂的整体最佳控制，从而以更低的成本生产出更好的产品。将提供实现本研究中开发的算法的开源软件，以及在研究生和本科阶段加强代表性不足的少数民族参与的教育活动。本研究的第一部分将考虑一般自由形式的离散部分，其表面或体积扫描构成复杂几何的大型流形数据集。本研究首先利用有限元方法寻找拉普拉斯-贝尔特拉米算子的改进谱估计，特别是求解部分流形上的亥姆霍兹偏微分方程。LB算子的特征分解将被用作多变量SPC方案中监控的部分特征。一种新的基于零件及其CAD模型的LB算子的深度功能映射方法将零件表面缺陷定位，为零件定位问题提供了一种无配准的解决方案。为了发现显著的差异，需要解决大量的统计多重比较问题，这将被研究。处于控制状态的高维连续制造过程位于低维流形上，需要将地图从环境空间扩展到嵌入时间上连续收集的新观测值，这样就有可能快速确定它们是在控制流形中还是离控制流形很远。在本基金的第二部分，这个问题将用两种不同的方法来研究：a)拉普拉斯特征映射，它将通过Nystrom技术解决经典逆问题来扩展，b)深度自编码器，一种针对高维数据的神经网络。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This grant will strengthen US industrial competitiveness by studying new methods for the control of the quality of manufactured products. Modern laser sensors in manufacturing plants can collect hundreds of thousands of measurements from the surface of discrete parts or process variables in chemical plants. How to best use these very large datasets to control the quality of parts is a difficult and open problem. The first part of this project will develop new machine learning and mathematical methods for quality control of the manufactured discrete parts based on 3-dimensional geometrical data obtained from laser scans that do not require lengthy preprocessing. The grant will then develop new methods for the identification of a subset of variables that best represent the larger set of process variables in a continuous process manufacturing facility, such that effective monitoring of the smaller set of variables can lead to overall best control of the plant, resulting in better products at lower cost. Open source software that implements the algorithms developed in this research will be made available, as well as educational activities that enhance the participation of underrepresented minorities at both graduate and undergraduate level.The first part of this research will consider discrete parts of a general free-form whose surface or volumetric scans constitute large manifold datasets of complex geometry. The research first aims at finding improved spectrum estimators of the Laplace-Beltrami (LB) operator using Finite Element Methods (FEM), in particular, solving a Helmholtz partial differential equation on the part manifold. The eigendecomposition of the LB operator will be used as part features to monitor in multivariate SPC schemes. A new Deep Functional Map approach, based on the LB operators of both part and its CAD model, will localize the defect on the surface of the part, providing a registration-free solution to the part localization problem. To find significant differences requires solution of a massive statistical Multiple Comparison problem which will be investigated. High dimensional continuous manufacturing processes whose in-control state lies on a lower dimensional manifold require extending the map from ambient space to embedding for the new observations collected sequentially in time, in such a way that it is possible to determine rapidly if they are in the on-control manifold or are significantly far from it. In the second part of this grant, this problem will be studied with two alternative approaches: a) a Laplacian Eigenmap that will be extended by solving a classical inverse problem via a Nystrom technique, and b) Deep Autoencoders, a type of neural network aimed at high dimensional data.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.