Multimodal probabilistic modeling of melt pool geometry variations in additive manufacturing

Laser Powder Bed Fusion (LPBF) is commonly used to fabricate metal additive manufacturing (AM) parts. Advanced sensing empowers the collection of in-situ signals (e.g., melt pools) for real-time monitoring of AM processes. The variations of melt pool geometry are closely pertinent to mechanical and functional properties of final AM builds. Most of previous works are concerned about the extraction of melt pool features (e.g., geometric statistics, size, shape descriptors) for AM process monitoring. However, very little has been done to investigate the emission physics of photons that leads to the generation of melt pool images. To fill the gap, this work presents a novel approach to simulate the emission of photons for statistical estimation and modeling of the multimodal probability distribution function (PDF) of a melt pool. Specifically, the complex geometry of a melt pool is represented as a multimodal PDF. Photons emitted to generate melt pool images are treated as independent and identically distributed (iid) random samples drawn from the multimodal PDF. Further, we propose a new Gaussian mixture model to represent and estimate the multimodal PDF via the expectation–maximization procedures. In addition, we investigate how process conditions influence the geometric variations of melt pools. Experimental results show that the proposed methodology effectively builds the multimodal distribution model of melt pool geometric variations. Most importantly, the proposed methodology is flexible enough to take raw images as the input and shows great potentials to be generally applicable for different types of melt pool images and AM processes.