Modeling in-process machining data using spatial point cloud vs. time series data structures

Abstract

In-process machining data (e.g., cutting forces and vibrations) have been typically collected and structured as time-referenced measurements (i.e., time-series data) and utilized in this structure to develop statistical data models used in process monitoring and control methods. This paper argues that a time-only-referenced representation overlooks the 3D nature of the physical process generating the data, and that machining data can be represented alternatively as functions of the tool-workpiece relative position resulting in a spatial point cloud data structure. High-density measurements of such spatially refenced data could be highly correlated to surrounding measurements, resulting in spatial correlation structures that could be of physical meaning and value to preserve and leverage. Using a simulated data study, this paper shows that preserving the spatial correlation structure of the data clearly improves the relative modeling performance when utilizing machining data point clouds versus the traditional time-referenced data structure. Specifically, this simulation study investigated the hypothesis that “considering the Gaussian process model class, the best model among all possible models developed using the spatial point cloud data structure has smaller/equal modeling and prediction errors compared to the best model among all possible models developed using the time-referenced data structure.” While this investigation was limited to considering the case of stationary isotropic processes, it demonstrated that the performance gap was relatively large. This encourages further investigations using real-world data to better understand the types of spatial correlations that exist in machining data and the specific machining regimes and process variables that would benefit the most from the spatial point cloud representation of the data.