Droplet evolution prediction in material jetting via tensor time series analysis

Material Jetting (MJ) process is an additive manufacturing process that is able to produce structures with high resolutions. The performance and quality of the MJ printed parts extensively rely on the droplet morphology and behavior. However, obtaining consistent and stable droplet morphology and behavior is difficult because the droplets are very sensitive to different material and process parameters. Testing/studying all these parameter combinations is time-consuming due to the high-experimental and high-computational costs. We thus study the prediction of droplet behaviors under different material and process parameters. To achieve this, we propose to leverage the underlying relationships shared across droplet evolution behaviors with diverse material and process parameters (referred to as “cross-linked” relationship hereafter) as well as the spatial–temporal relationships of droplet evolution, and capture these with the Network of Tensor Time Series (N_ET³). The distinct droplet behaviors are regarded as co-evolving time series (i.e., Tensor Time Series (TTS)) since they share the same physics principles. In particular, we capture the cross-linked and spatial relationships of TTS by the Tensor Graph Convolutional Network (TGCN), and capture the temporal relationship of TTS by the Tensor Recurrent Neural Network (TRNN), respectively. The features from TGCN and TRNN are passed to Multilayer Perceptron (MLP) for predicting future droplet behaviors. The proposed methodology is demonstrated with simulated (i.e., physics-based models) and experimental (i.e., MJ printing observation with vision system) droplet evolution videos and is able to accurately and efficiently make predictions for seen (i.e., forecasting for a future time) and unseen (i.e., new droplet evolution sequence prediction) material/process parameters.