Hierarchical modeling of microstructural images for porosity prediction in metal additive manufacturing via two-point correlation function

Porosity is one of the most critical quality issues in Additive Manufacturing (AM). As process parameters are closely related to porosity formation, it is vitally important to study their relationship for better process optimization. In this article, motivated by the emerging application of metal AM, a three-level hierarchical mixed-effects modeling approach is proposed to characterize the relationship between microstructural images and process parameters for porosity prediction and microstructure reconstruction. Specifically, a Two-Point Correlation Function (TPCF) is used to capture the morphology of the pores quantitatively. Then, the relationship between the TPCF profile and process parameters is established. A blocked Gibbs sampling approach is developed for parameter inference. Our modeling framework can reconstruct the microstructure based on the predicted TPCF through a simulated annealing optimization algorithm. The effectiveness and advantageous features of our method are demonstrated by both the simulation study and the case study with real-world data from metal AM applications.