Identification of Latent Invariant Surface Quality Patterns via Spatial Stochastic Process Deformation

Surface quality characterization is important for ensuring product functionality and guiding production. Although a wealth of literature has been developed for mass production, unique challenges arise in additive manufacturing (AM) because of the one-off fabrication of a wide range of complex geometries. Surface quality patterns can change with built geometries and covariates such as shape size and built location. Existing statistical characterization methods are therefore not adaptive to AM due to frequent design changes and insufficient samples for each design. Since a product can be represented by a finite type of surface patches, this initial study investigates the surface quality of products with spherical patches. We propose to identify latent and invariant patterns to characterize surface quality by separating the effect of covariates. The surface quality of different domes is first described by nonstationary spatial Gaussian processes. These heterogeneous spatial stochastic processes are then mapped to one underlying base process through a spatial stochastic process deformation method. With covariate effects fully captured by the mapping function, the underlying base process characterizes the latent invariant surface quality patterns of spherical patches and the working status of the machine. Actual printed samples from an AM process are utilized for methodology demonstration. The study brings the prospect of evaluating and comparing product surface quality and process condition in one-off AM.