An earth mover's distance based multivariate generalized likelihood ratio control chart for effective monitoring of 3D point cloud surface

With the development of measurement technology, non-contact high-definition measurement (HDM) systems have allowed rapid collection of large-scale point cloud data, providing an opportunity to monitor the entire surface geometry of manufactured parts. However, traditional control charts do not apply to such large-scale point cloud data. Although some researchers have proposed the use of improved multivariate control charts for high-dimensional data, the multivariate control charts cannot be directly used for large-scale and auto-correlated point cloud data. Considering the structural characteristics and spatial properties of the point cloud, this paper proposes an earth mover's distance based multivariate generalized likelihood ratio (EMD-MGLR) control chart to effectively monitor point cloud surface by making full use of the three-dimensional (3D) information of point cloud data. The EMD method regards point cloud data as a distribution and calculates the EMD distance between the two distributions to quantify the deviation region between the point cloud surface and the nominal model. Combined with the multivariate generalized likelihood ratio control chart, the processing quality of the 3D surface can then be monitored by the statistics of EMD. The advantages of the proposed method are illustrated and verified by numerical and experimental examples. An experimental example on the 3D surfaces of combustion chambers is used to illustrate the methodology and to test its effectiveness in monitoring surface defects.