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

这笔赠款将通过研究控制制成品质量的新方法来增强美国的工业竞争力。制造工厂中的现代激光传感器可以从化工厂中离散零件或工艺变量的表面收集数十万个测量值。如何更好地利用这些非常庞大的数据集来控制零件的质量是一个困难而又悬而未决的问题。该项目的第一部分将开发新的机器学习和数学方法，用于基于从激光扫描获得的不需要长时间预处理的三维几何数据，对制造的离散部件进行质量控制。然后，赠款将开发新的方法，以确定最能代表连续工艺制造设施中较大的一组过程变量的变量子集，以便对较小的变量集进行有效监控，从而实现对工厂的整体最佳控制，从而以较低的成本生产出更好的产品。这项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。研究首先利用有限元方法寻找Laplace-Beltrami(LB)算子的改进谱估计，特别是求解部分流形上的Helmholtz偏微分方程组。在多变量统计过程控制方案中，该算子的特征分解将被用来作为部分特征进行监测。一种新的深度功能图方法，基于零件及其CAD模型的LB算子，将缺陷定位到零件表面，为零件定位问题提供了一种免注册的解决方案。要找到显著的差异，需要解决大量的统计多重比较问题，这一问题将被研究。控制状态位于较低维流形上的高维连续制造过程需要将地图从周围空间扩展到嵌入时间顺序收集的新观测，这样就可以快速确定它们是在控制流形上还是在明显远离它的地方。在这笔赠款的第二部分，这个问题将用两种替代方法来研究：a)拉普拉斯特征映射，它将通过Nystrom技术解决一个经典的逆问题来扩展；b)深度自动编码器，一种针对高维数据的神经网络。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.