Nonparametric change-point detection for unstructured 3D point cloud data with an application in additive manufacturing

In contrast to key product characteristics, unstructured 3D point cloud data with coordinates at random measurement locations can be collected from 3D scanning systems to reflect product geometry entirely. However, challenges such as high dimensionality, registration complexity, and sensitivity to small process changes hinder effective modelling and monitoring of such data. Furthermore, there is very limited research on Phase I analysis of unstructured point cloud data in the literature. To this end, this paper proposes two novel nonparametric change-point detection methods for unstructured 3D point cloud data to identify the presence and location of a change point in a historical dataset. Specifically, we first introduce the Laplace-Beltrami (LB) operator spectrum as an intrinsic geometrical property of unstructured 3D point clouds by leveraging tools from differential geometry. Then, we develop two nonparametric control charts for detecting a change point among the LB spectra. Finally, we provide an effective procedure to determine critical values for the control charts. Extensive numerical simulations demonstrate the superiority of the proposed methods in detecting and estimating the change point while maintaining in-control performance. In addition, an application in additive manufacturing illustrates the implementation of the proposed methods and validates their effectiveness to pinpoint the change point.