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Materials Science in Additive Manufacturing Interpretable GP melt track prediction

traditional manufacturing methods. However, the complex In recent years, more researchers explored combining
changes in the AM process, such as heat transfer, melting, physical models with data models to improve the
and solidification processes, are prone to cause defects, performance and generalization ability of the models by
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such as holes, cracks, and unfused parts, limiting the adding physical constraints. For example, Mahmoudi et al.
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reliability of AM technology in production applications. proposed an anomaly detection system that integrated melt
To address this issue, the introduction of remote and pool and phase field models. Utilizing high-speed thermal
in situ monitoring techniques is critical. By continuously imaging, spatial statistics, and machine learning, their
monitoring the manufacturing process, tracking key approach achieved only a 5% average error in melt track
physical phenomena during fusion, and analyzing real- width prediction. Gaikwad et al. obtained the physical
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time data from various sensors, this approach enabled the characteristics of the melt pool by utilizing different sensors,
detection of defects before they become hidden beneath such as high-speed cameras and thermocouples, and
subsequent layers. 2-5 employed neural networks to predict melt pool patterns,
At present, AM process monitoring primarily relies on process parameters, melt track width, and melt track
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analyzing in-process sensor data through data modeling, continuity. Guo et al. established a mathematical melt
using machine learning and deep learning to detect specific pool morphology model by fitting key coefficients through
defect occurrences. For example, Khanzadeh et al. extensive experiments. Their model accounts for physical
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analyzed the thermal distribution characteristics of the mechanisms, including mass conversion, heat exchange,
melt pool and successfully predicted both pore locations in and temperature fields, thereby controlling average
Ti-6Al-4V alloy parts and geometric deviations in the Fast prediction errors for melt pool dimensions (length/width/
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Fourier Transform process using self-organizing mapping depth) to 12%. Zhang et al. fused melt pool spatial-physical
(an unsupervised learning algorithm); they also investigated information through coaxial/off-axis dual detection systems.
the influence of process parameters on geometric accuracy. Using long short-term memory networks, they correlated the
Scime et al. classified the types of anomalies in the melt melt pool temperature with melt track surface morphology,
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track into six categories and proposed a monitoring achieving up to 92.87% accuracy. These researchers obtained
algorithm based on machine learning and computer vision, multimodal data through a large number of experiments
which was successfully used for post hoc quality analysis and a variety of high-precision sensors and realized the
of components. Okaro et al. applied binary labels to a identification of melt pool geometry and anomalous states
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small data subset based on defect severity and developed by combining physical processes.
a semi-supervised model using process data with singular Based on these findings, traditional physical models
value decomposition and Gaussian mixture models. This incur high experimental costs due to complex monitoring
approach achieved classification performance comparable equipment, extensive simulation data, and empirical
to fully supervised methods. Yuan et al. 10,11 proposed a two- formulas. Conversely, traditional data-driven models lack
round image processing and height map analysis algorithm physical constraints, exhibit high sensitivity to process
to predict and identify laser printing track width and parameters, and are susceptible to noise interference.
continuity in video datasets. Their approach considered To address these limitations, we propose a melt track
the characteristics of diverse data and addressed labeling morphology prediction model based on deep Gaussian
difficulties using semi-supervised learning. Mojahed processes (DGPs) with embedded physical constraints.
Yazdi et al. designed a deep neural network model that DGPs are a multilayer generalization of Gaussian
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utilizes the spatial feature image of regions of interest processes (GPs), where each layer is an independent
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(ROI) to detect and locate defects. This method achieved GP. Compared to single-layer GPs, DGPs overcome the
significantly higher defect detection rates than traditional limited expressiveness of the kernel function and also
machine learning approaches. Lopez et al. focused more maintain the flexibility, overfitting resistance, and good
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on quantifying model uncertainty. They explored melt pool prediction uncertainty of the GP model. In this study, the
width prediction by considering uncertainties arising from experimentally observed melt pool geometric feature data
thermal modeling assumptions, unknown simulation data, were used as model inputs, with physical model constraints
numerical approximations, and calibration data. While added to the data-driven DGP model to guide physical
these studies leverage the power of machine learning and information to the data model. This approach enables
deep learning to establish complex mapping relationships the prediction of geometric features of the melt track and
between monitoring data and melt track geometry, such the classification of the morphology of the melt track
prediction methods often lack physical interpretability. under different processing conditions using a softmax
In addition, they can be highly sensitive to experimental classification model. The structure of the proposed model
parameters and exhibit limited generalization ability. is displayed in Figure 1.

Volume 4 Issue 3 (2025) 2 doi: 10.36922/MSAM025200030