Modeling spatial point processes in video-imaging via Ripley's K-function: an application to spatter analysis in additive manufacturing

For an increasing number of applications, the quality and the stability of manufacturing processes can be determined via image and video-image data analysis and new techniques are required to extract and synthesize the relevant information content enclosed in big sensor data to draw conclusions about the process and the final part quality. This paper focuses on video image data where the phenomena under study is captured by a point process whose spatial signature is of interest. A novel approach is proposed which combines spatial data modeling via Ripley's K-function with Functional Analysis of Variance (FANOVA), i.e., Analysis of Variance on Functional data. The K-function allows to synthesize the spatial pattern information in a function while preserving the capability to capture changes in the process behavior. The method is applicable to quantities and phenomena that can be represented as clusters, or clouds, of spatial points evolving over time. In our case, the motivating case study regards the analysis of spatter ejections caused by the laser-material interaction in Additive Manufacturing via Laser Powder Bed Fusion (L-PBF). The spatial spread of spatters, captured in the form of point particles through in-situ high speed machine vision, can be used as a proxy to select the best conditions to avoid defects (pores) in the manufactured part. The proposed approach is shown to be not only an efficient way to translate the high-dimensional video image data into a lower dimensional format (the K-function curves), but also more effective than benchmark methods in detecting departures from a stable and in-control state.