Point cloud data are widely used in manufacturing applications for process inspection, modeling, monitoring and optimization. The state-of-art tensor regression techniques have effectively been used for analysis of structured point cloud data, where the measurements on a uniform grid can be formed into a tensor. However, these techniques are not capable of handling unstructured point cloud data that are often in the form of manifolds. In this paper, we propose a nonlinear dimension reduction approach named Maximum Covariance Unfolding Regression that is able to learn the low-dimensional (LD) manifold of point clouds with the highest correlation with explanatory covariates. This LD manifold is then used for regression modeling and process optimization based on process variables. The performance of the proposed method is subsequently evaluated and compared with benchmark methods through simulations and a case study of steel bracket manufacturing.

翻译：点云数据广泛应用于制造过程中的检测、建模、监控与优化。现有最先进的张量回归技术可有效分析结构化点云数据（即在均匀网格上测量形成的张量），但这类方法无法处理通常以流形形式存在的非结构化点云数据。本文提出一种名为最大协方差展开回归的非线性降维方法，该方法能够学习与解释性协变量具有最高相关性的点云低维流形。随后，该低维流形被用于基于过程变量的回归建模与过程优化。通过数值仿真及钢支架制造案例研究，对所提方法的性能进行了评估，并与基准方法进行了比较。