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

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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.