#  ThermoPore: Predicting Part Porosity Based on Thermal Images Using Deep
Learning

Peter Myung-Won Pak<EMAIL_ADDRESS>Department of Mechanical Engineering,
Carnegie Mellon University, Pittsburgh, PA, USA  Francis Ogoke
<EMAIL_ADDRESS>Department of Mechanical Engineering, Carnegie Mellon
University, Pittsburgh, PA, USA  Andrew Polonsky<EMAIL_ADDRESS>Sandia
National Laboratories  Anthony Garland<EMAIL_ADDRESS>Sandia National
Laboratories  Dan S. Bolintineanu<EMAIL_ADDRESS>Sandia National
Laboratories  Dan R. Moser<EMAIL_ADDRESS>Sandia National Laboratories
Michael J. Heiden<EMAIL_ADDRESS>Sandia National Laboratories  Amir
Barati Farimani<EMAIL_ADDRESS>Department of Mechanical Engineering, Carnegie
Mellon University, Pittsburgh, PA, USA

###### Abstract

We present a deep learning approach for quantifying and localizing ex-situ
porosity within Laser Powder Bed Fusion fabricated samples utilizing in-situ
thermal image monitoring data. Our goal is to build the real time porosity map
of parts based on thermal images acquired during the build. The quantification
task builds upon the established Convolutional Neural Network model
architecture to predict pore count and the localization task leverages the
spatial and temporal attention mechanisms of the novel Video Vision
Transformer model to indicate areas of expected porosity. Our model for
porosity quantification achieved a $\text{R}^{2}$ score of 0.57 and our model
for porosity localization produced an average IoU score of 0.32 and a maximum
of 1.0. This work is setting the foundations of part porosity ”Digital Twins”
based on additive manufacturing monitoring data and can be applied downstream
to reduce time-intensive post-inspection and testing activities during part
qualification and certification. In addition, we seek to accelerate the
acquisition of crucial insights normally only available through ex-situ part
evaluation by means of machine learning analysis of in-situ process monitoring
data.

###### keywords:

American Chemical Society, LaTeX

Machine Learning Department, Carnegie Mellon University, Pittsburgh, PA, USA
IR,NMR,UV

##  1 Introduction

Additive manufacturing (AM) presents a competitive alternative to the
conventional approaches in manufacturing with the advantages of efficient
material utilization, design consolidation, and fast iteration1, 2, 3, 4.
However, a significant area of improvement lies within defect prevention as
printed parts present their own set of challenges in porosity, distortion, and
cracking1. These issues are often uncovered through ex-situ non-destructive
testing methods and can sometimes be addressed through lengthy post-processing
means such as hot isostatic pressing (HIPing) before they are certified 5, 6.
With in-situ process monitoring, a digital twin of the fabrication process can
be created and segments of the certification process can be conducted in
parallel7, 8, 9.

Laser powder bed fusion (LPBF), relies primarily on established process maps
10, 11, 12 to determine the optimal machine settings that minimize defects
within the finished part. Most commonly, these process maps explore the power
and velocity space to determine a combination of two that would result in a
sufficiently dense part. Informed control over these process parameters and
others such as hatch spacing 13, layer height 14, and raster pattern 15, can
greatly affect the part’s porosity, microstructure 16, and surface finish 14.
However, even within build conditions with nominal process parameters, defects
such as porosity remain an issue 17.

In-situ process monitoring offers a means to resolve this issue as information
obtained from the build process can assist in resolving many of the technical
challenges encountered during part fabrication 17, 18, 19. Many of these
defects and their precursors such as part distortions 20, surface roughness
21, or keyhole formation 22, 23 exhibit signals which with the appropriate
sensors can be detected before ex-situ sample analysis. These indicators can
be applied alongside the build process to analytical and machine learning
models in order to obtain the necessary feedback to adjust process parameters
for the build. This feedback loop would be optimized to reduce the number of
part defects through both preemptive and responsive measures. 24, 25. In
addition, reconstructing the porosity map can significantly accelerate the
part certification process as the knowledge of the porosity map can expedite
qualification through observations of statistics alone26, 27, 7, 28, 29.

Thermal imaging demonstrates effectiveness as an in-situ process monitoring
technique as evidenced by previous studies which have explored comparing melt
pool images to computational fluid dynamics simulations 30, mathematical
equations 31, and 3D surface maps32. Further exploration of this technique has
shown effectiveness in applications such as defect detection and correction
within the build process either indicating likely porosity given a thermal
image of a melt pool 33 or material extrusion correction in large scale
additive manufacturing34, 35.

Analytical solutions such as Rosenthal’s equation 36 provide a foundational
method to determine nominal process parameter regions within laser power and
scanning velocity space. This equation can be adapted to provide depth and
width estimates of the melt pool given specific process parameters such as
preheat temperature, power, and velocity which can be applied to the selection
of nominal parameters for hatch spacing and layer height. However, this method
poses limitations as solutions provided by Rosenthal’s equation are only
suitable for melt pools within the conduction regime 36, 37, 38. This leaves
areas out that are not captured through analytical models such as melt pool
behavior in the keyhole mode and process conditions such as scan strategies.

Much attention has been directed towards machine learning to fill this gap
between the projection of these analytical models and their applied results
some of which include process parameter optimizing 39, 40 and fatigue life
prediction 41. In this paper we explore the application of machine learning
towards the quantification and spatial localization of pores within a sample
given the in-situ monitoring data of thermal images. These predictions can
then be utilized to create a digital twin of the built sample and perform
qualification and certification tasks in parallel to the sample fabrication9,
8, 7.

For the task of pore quantification a three dimensional Convolutional Neural
Network (CNN) was utilized to extract features within a provided sequence of
thermal images and provide a singular scalar prediction of the expected number
of pores. Models such as ImageNet42 have shown the effectiveness of 2D CNNs
with image classification tasks and other models such as C3D43 have applied
this technique to extended over a sequence of images. Training a 3D CNN model
with the objective of pore quantification enables the identification of pore
counts within a build layer prior to any ex-situ sample analysis.

The task of pore localization utilizes a Video Vision Transformer (ViViT)44
which is suited to capture the spatial and temporal features within the
sequence of thermal images through subdividing the input into patches. The
original implementation of the ViViT model is structured to provide a
classification output44, however for the purposes of pore localization the
classification head is replaced with a dense prediction head which retains the
spatial information of the input sequence. Our network implementation utilizes
a dense output which directly correlates the spatial and temporal information
into a 2D pore localization prediction. This network builds off the work by
Ranftl et al.45 where fusion blocks and convolutional layers are added to a
vision transformer to provide depth predictions of a given image.

Additive manufacturing, specifically LPBF, relies on sample ex-situ post-build
inspection and testing to qualify parts and identify potential defects
encountered during the build process46, 47, 27, 48. This often includes
tedious processes such as cross-sectional imaging or x-ray computed micro-
tomography (CT) after the part fabrication. However, if similar information is
obtained earlier during the build process through the creation of a digital
twin, builds can be terminated earlier or dynamic adjustments can be applied
once the presence of defects is detected to reduce material waste and costs.
Applying machine learning techniques such as CNN or ViViT models on in-situ
data opens the possibility to acquire ex-situ sample insights during the build
process and fabricate parts within a closed feedback loop.

Figure 1:  A sequence of 200 thermal pyrometry images (1c) providing absolute
temperature values of the build plate taken in-situ (1a) are provided as input
data for models for pore quantification (1d) and pore localization (1e). These
two separate models utilize a CNN and ViViT with dense output heads to produce
a scalar number of pores and 2D mapping of expected porosity regions
respectively. Metrics derived from ex-situ CT data for the corresponding build
layer are used as ground truth values for each model (1b).

##  2 Methodology

###  2.1 Spacing and Velocity Samples

####  2.1.1 Sample Fabrication and Data Acquisition

This paper analyzes two samples, one with variable hatch spacing (Spacing) and
the other with variable scan velocity (Velocity). Both of these samples were
manufactured using LPBF equipment (ProX DMP 200 from 3D Systems) with AISI
316L stainless steel powder and a constant laser power of 103 W49, 33. These
samples were designed with a staircase structure (Fig. 2(a)) with each sample
comprised of 10 separate steps and each step consisting of a 16 build layers
with a 30 µm layer height. Within each of these steps a different combination
of process parameters were implemented with changes to either hatch spacing
(Fig. 2(b)) or scanning velocity (Fig. 2(c)). The expected dimensions of each
sample are 4.80 mm × 2.80 mm × 1.00 mm in height, length, and width
respectively49. Each step consisted of dimensions 0.48 mm in height and ranged
from 1.00 mm to 2.80 mm in length, decreasing in length by 0.20 mm from the
top of the sample to the bottom. The Spacing sample with varying hatch spacing
was built with a constant 1.4 m/s scan velocity and the Velocity sample with
varying scan velocity was built with a constant 50 µm hatch spacing 49.A
normal rastering pattern consisting of line scans parallel to the build axes,
orthogonal to the previous layer was utilized as the scan strategy for both
samples.

(a) Sample Design

Step | Hatch Spacing
---|---
J | 25 µm
I | 30 µm
H | 35 µm
G | 40 µm
F | 45 µm
E | 75 µm
D | 70 µm
C | 65 µm
B | 60 µm
A | 55 µm
(b) Spacing Parameters

Step | Scan Velocity
---|---
J | 1.05 m/s
I | 1.12 m/s
H | 1.19 m/s
G | 1.26 m/s
F | 1.33 m/s
E | 1.75 m/s
D | 1.68 m/s
C | 1.61 m/s
B | 1.54 m/s
A | 1.47 m/s
(c) Velocity Parameters

Figure 2:  Each sample (2(a)) contains 10 different process parameter
combinations with the Spacing sample (2(b)) exhibiting varying hatch spacing
and the Velocity sample (2(c)) exhibiting varying scan velocity.

####  2.1.2 In-situ Pyrometry

Absolute temperature estimations were calculated from thermal radiation
captured by a Stratonics two-color pyrometer receptive to light emitted at 750
nm and 900 nm, a frame rate within 6 \- 7 kHz, and a 90 µs exposure.33
Synchronization between the LPBF equipment and pyrometer were achieved via
Transistor-Transistor Logic (TTL) triggering producing 1000 frames of 65 px ×
80 px images within each build layer33. This translated to a 1365 µm × 1680 µm
resolution with approximately 21 µm per px. This presented a total of 159,000
images taken for each sample and with initial screening applied to filter out
”empty” images, reducing the total number of frames down to 20,469 and 20,187
for Spacing and Velocity samples respectively.

####  2.1.3 Ex-situ Micro-computed Tomography (CT)

Micro-computed tomography analysis was performed using a Zeiss Xradia 520
Versa at the maximum output power of 10 W and tube voltage of 140 kV with the
sample positioned 11.1 mm from the source 49. Scans were taken at a cubic
voxel size of 3.63 µm and with a build layer height of 30 µm, this equated to
approximately 8.26 voxels per build layer. The obtained scans for the Spacing
and Velocity samples were bounded by 5.05 mm × 3.00 mm × 1.35 mm and 5.05 mm ×
3.17 mm × 1.44 mm respectively (Z × Y × X) 49. Both Spacing and Velocity
samples extended 1410 voxels × 900 voxels × 430 voxels along the Z, Y, and X
axes. The scanned tomography was further segmented to distinguish each pore
from the general sample with annotations denoting each of the labeled pore’s
centroid, equivalent diameter, number of voxels, and unique identifier.

Figure 3:  CT visualization of porosity segmented within overall sample for
Spacing (left) and Velocity (right) samples (3a). Pyrometry data is captured
within a subset of the built sample (3d) and initial alignment of image and CT
data occurs along the X and Y axes (3b), using the top left corner of both as
the origin. Alignment for a build layer is visually validated with an overlay
of the pyrometry data directly on top of a corresponding cropped CT voxel
layer (3c).

###  2.2 Dataset

####  2.2.1 Pyrometry and Micro-computed Tomography Alignment

Capture area was limited to 80 px × 65 px and lead to the raster patterns of
the lower build layers (steps A - F) to extend further than the camera’s
viewport 33. As mentioned, initial screening filtered out many of these empty
frames by applying a minimum threshold on each frame’s peak value from long
wavelength data33. This method removed the frames where the melt pool was out
of view, however still included some frames where spatter likely occurred.

In-situ thermal images and slices of ex-situ CT data shared the same origin at
the top left (Fig 3 b). Small offsets were then applied to align the X and Y
directions of CT to the thermal image. The provided Z direction offsets were
used as starting points to align the CT data to the corresponding build layer.
The Z alignment for both samples were visually verified through manual
alignment of the scan path of thermal images and the a top down view of the
corresponding CT layer. Step G (Fig. 2(a)) within both samples was the first
section of the sample where the entire scan path is in complete view of the
thermal camera and was used as a reference point to align the CT data. Both
samples (Spacing and Velocity) were offset by a total 5 build layers (~9
voxels per build layer) in total.

####  2.2.2 Pore Thresholding

A CT resolution of 3.63 µm per voxel allowed for the capture of distinct
shapes and contours associated with porosity, however this fine resolution
also resulted in recording scattered distributions of small voids. Accurately
predicting these small voids is a difficult task for a model as these defects
could be the result of gas porosity 50 or rogue flaws 51 and may have
precursors not visible to thermal imaging. To achieve greater correlation
between the pyrometry data and CT data, our attention focused on larger
diameter pores that can be attributed to factors such keyhole porosity or lack
of fusion porosity. In keyholing, pores generated by the vapor column during
builds resulted in an average diameter of 47 µm 52 and lack of fusion pores
with diameters dependent on the height and width of melt pool and
corresponding build layer 53.

Figure 4:  The Spacing sample on average consist of larger pores with a
standard deviation of 20.5 µm compared to the Velocity sample’s standard
deviation of 16.0 µm (4a). The tighter distribution of Velocity pores are
visible in the thresholded distribution of equivalent pore sizes (4b) within
the slices of the CT data. The segmentation of pores within the sample (4c)
relied on a minimum of 100 voxels (11.4 µm equivalent spherical diameter)33 in
order to register the contiguous cluster of voids as porosity (4d) and an
increase in the minimum size further removed smaller pores (4e).

The mean Equivalent Spherical Diameter (ESD) for each sample was compiled in
order to obtain minimum threshold values 1 standard deviation above the mean.
In the Spacing sample, pores exhibited an average diameter of 32.59 µm and a
standard deviation of 20.60 µm, resulting in a minimum ($\mu+\sigma$) ESD
threshold of 53.19 µm. In the Velocity sample, pores had an average diameter
of 30.78 µm and a smaller standard deviation of 16.01 µm resulting in a
minimum ($\mu+\sigma$) ESD thresholds of 46.79 (Fig. 4b).

##  3 Porosity Reconstruction

The quantity of pores and their position within the build layer was
reconstructed with machine learning inferencing upon a sequence of thermal
images. With the set of in-situ and ex-situ data, the tasks of predicting the
number of pores and the approximate location of these pores within the various
build layers were achieved using a CNN model and a ViViT model with dense
prediction heads respectively.

The number of pores corresponding to a sequence of thermal images were
predicted using a CNN model. In this task both the application of rotational
transforms on the input sequence and the volumetric depth utilized for pore
count were treated as variables. Labels were derived from counting the set of
unique pores within a specified volumetric depth corresponding to 1, 2 or 3
build layers and duplication was avoided by cross referencing each voxel’s
pore id. The quality of these predictions is measured using Root Mean Square
Error (RMSE) and $\text{R}^{2}$ score.

The localization of pores was predicted using the same sequence of thermal
images and utilized a ViViT model with a dense prediction head to indicate
sections expected to be porous. The labels for this task were obtained by
downsampling the CT data for the build layer equally along all axes in order
to provide a coarse porosity estimates for the model to train and predict. In
addition, the effect of applying rotational transforms on the input sequence
and minimum pore ESD thresholds for label compilation were investigated. The
quality of the predictions was measured using an Intersection over Union (IoU)
score, considering the overlap of the area of predicted porosity over that of
the label.

###  3.1 Porosity Count

This task investigates the extent in which sequences of thermal images can
quantify the number of pores that exist within the sample build layers. The
Spacing sample consists of 2069 pores and the Velocity sample consists of 1811
pores. The labels were obtained from slicing the CT sample data into the
appropriate dimensions that corresponding to the build layer and counting the
number of unique pore identifiers omitting the 0 value which represented the
background. Each build layer consisted of 9 voxels in depth and this volume
was extended to a depth of 18 and 27 voxels to obtain pore counts extending
down 2 and 3 build layers.

In this task a CNN model composed of 4 convolutional layers and 2 fully
connected layers reduce the input set of 200 64 × 64 pixel images into a
scalar value of the number of unique pores within the build layer (Fig. 5). A
3 × 3 pixel kernel is convolved on top each image with a stride of 2 and a
padding of 1. Within each layer the number of channels is reduced by a factor
of 2 and batch normalization and ReLU non-linearity activation function are
applied. The output of the CNN layers are reshaped into a 2 dimensional tensor
before they are passed to the two fully connected layers which output a single
scalar value which quantifies the number of pores within the build layer.

Figure 5:  A standard convolutional neural network with a kernel size of 3
pixels and a stride of 2 filters the features within an image down over 4
layers to a singular scalar value indicating the expected number of pores from
the sequence of thermal images.

A CNN operates by leveraging convolutional layers to extract features from
input images hierarchically. In the initial layers, low level features such as
edges and gradients are detected through convolutional operations where the
kernel moves across the input image, computing dot products and producing
feature maps 42, 43, 54, 55. Activation functions such as ReLU apply non-
linear transforms and allow for the capture of complex patterns. The following
layers then build upon these low level feature maps and repeat this task of
transforming the raw pixel values into the outputs for a specific task 42.
These tasks are determined by the final layers of the network which utilize
fully connected layers to shape the output to perform classification,
regression, or reconstruction.

Due to dataset size constraints, a 75 / 25 train test split of the data was
used for model training. The train test split occurred within the 16 build
layers of each of the 10 sample steps of either the Spacing or Velocity
sample. This split within sample steps was implemented to provide an equal
distribution of processing parameters between the train and test sets for the
model. This provided an input label set of 120 training pairs and 39 testing
pairs for the either of the samples. Our dataset implementation allowed for
the model to train on either the Spacing, Velocity, or on a combination of
both datasets with the All dataset. For this regression task, a mean squared
error was utilized as the loss function and the predicted value from the model
is rounded to the nearest integer. Each of the models were trained from 500
epochs with a learning rate of 0.0001 using the ADAM optimizer.

In addition, data augmentations of the input sequence in the form of
rotational transforms for the entire video sequence were applied. Data
augmentation provides a means to artificially expand an existing set of data
in order to improve the generalization ability and robustness of the model42.
Typical transformations change the input image applying one or a combination
of rotations, translations, flips, scaling, and cropping. In this application
we focus only on applying rotational transforms ranging between $0^{\circ}$ to
$180^{\circ}$ and avoid alterations to the contrast or brightness that would
affect the raw temperature value.

###  3.2 Porosity Localization

The localization task identifies areas within the build layer where pores are
likely to form through analyzing a sequence of thermal images. A video vision
transformer (ViViT) provides an applicable architecture to thoroughly analyze
the series of input frames to extract positional features through use of
spatial and temporal attention.44 In our model implementation a sequence of
thermal images is provided to the model to map to localized porosity labels
obtained through alignment and extraction of the CT data. These build layers
of initial size of 9 × 423 × 520 voxels are cropped and downsampled by a
factor of 24 to a coarser 2 dimensional 1 × 16 × 16 voxel shape to provide a
general area in which porosity is expected.

For this task a video vision transformer model with a dense prediction output
is utilized to localize pores within the sample space. This model is composed
of a spatial transformer layer with 4 sub-layers and a temporal transformer
layer with 5 sub-layers both with 8 heads and a dimension of 256 (Fig. 6).
Afterwards the class tokens resulting from each of the transformer layers are
removed and the output is passed into a feature fusion block which performs
residual convolution and provide a fine grain prediction. A series of 4
convolutional layers and ReLU non-linearity layers are applied before passing
to a sigmoid activation function to indicate whether porosity is expected at a
voxel location.

Figure 6:  The input sequence of thermal images are sliced into a set of
patches (6a) where 4 and 5 sublayers of the respective spatial and temporal
self attention are applied (6b). Each self attention block consisted of 8
attention heads (6c) of a dimension of 256\. A feature fusion block (6d)
applies residual convolution and a dense prediction head produces a 2
dimensional output indicating regions of expected porosity.

Attention within a transformer is comprised of three learnable components: The
query vector $\\{\textbf{q}_{i}\\}^{N_{q}}_{i=1}$, key vector
$\\{\textbf{k}_{i}\\}^{N_{k}}_{i=1}$, and the value vector
$\\{\textbf{v}_{i}\\}^{N_{v}}_{i=1}$ given that $N_{k}=N_{v}$56, 57, 58. In
the attention mechanism, the query vector retrieves contextual information
from the key vector and generates an output based on the weighted sum of
corresponding value vectors. Contextual information is retrieved in the form
of an attention score which is the scaled dot product between the query vector
and the key vector:
$\frac{\textbf{q}_{i}\cdot\textbf{k}_{j}^{T}}{\sqrt{d}}$57. The attention
score is then used in the calculation of weights ($\alpha_{ij}$) which apply a
Softmax over the individual contribution of each attention score (Eq. 1) 57,
56, 58.Each token’s numerical encoding along with its relevance to other
tokens is calculated from the cross product between the value vector and
weights resulting in the attention mechanism:
$Softmax\left(\frac{\textbf{Q}\cdot\textbf{K}^{\textbf{T}}}{\sqrt{d_{k}}}\right)\times
V$ 57, 56, 58.

$\alpha_{ij}=Softmax\left(\frac{e^{\frac{\textbf{q}_{i}\cdot\textbf{k}_{j}^{T}}{\sqrt{d}}}}{\sum^{N}_{k=1}e^{\frac{\textbf{q}_{i}\cdot\textbf{k}_{j}^{T}}{\sqrt{d}}}}\right)=Softmax\left(\frac{\textbf{Q}\cdot\textbf{K}^{\textbf{T}}}{\sqrt{d_{k}}}\right)$
(1)

In the case of a Vision Transformer (ViT), an image is divided up into self
attention patches via patch embedding, passed through the transformer encoder,
and utilized through a classification head59, 44. Within patch embedding, each
patch has a fixed pixel size in height and width and its embedding is derived
through flattening and linear projection59, 44. Class and position are applied
to the embedding before passed through the transformer encoder composed blocks
of layer norm, multi-head attention, and MLP layers after which a
classification head is attached.59

The dataset utilizes the same 75 / 25 train test split within the sample steps
for all the Spacing, Velocity, and All variants. The model was trained for
1000 epochs utilizing a binary cross entropy loss function for the binary
prediction of a voxel’s porosity classification. An ADAM optimizer along with
a cosine decay learning rate scheduler with an initial 10 epoch warm up period
from learning rates 0.00001 to 0.0001 is applied to help with regularization
and stabilization 60.

##  4 Results and Discussion

###  4.1 Porosity Count

The number of pores within a volume of the sample was predicted from a
sequence of thermal images using a CNN model trained on either the Spacing,
Velocity, or All dataset. Hyperparameters such as the utilization of
rotational transforms and the number of build layers involved in the
compilation of the pore count were investigated.

Table 1 outlines the model’s performance according to its training dataset and
indicates the data augmentation procedures that were applied and the various
depths used to calculate pore count. Models with datasets spanning 1 build
layer exhibited the lowest error and highest $\text{R}^{2}$ with a minimum
RMSE score of 7.84 from the Velocity sample and a maximum $\text{R}^{2}$ score
of 0.57 from the Spacing sample. The RMSE and $\text{R}^{2}$ score aim to
measure the average magnitude of errors and capture the proportion of variance
within the model respectively. The alignment of the prediction and the
corresponding target for each model (Fig. 7) shows a general trend where there
is a larger degree of porosity within the build layers ranging from 60 to 100
and to a lesser degree elsewhere. Notably, build layers greater than 100
display lower amounts of porosity for all models regardless of dataset or data
augmentation.

This is expected as both samples transition from off nominal process
parameters to nominal process parameters towards the middle of the sample
(Table 2(b), 2(c)) with the upper portion of each sample fabricated with ideal
process parameters. For all models, areas where the sample was fabricated with
nominal process parameters show a greater degree of clustering as pores are
sparse and few. In earlier build layers, specifically those closer towards the
middle of the sample a greater spread of predictions is seen (Fig. 7(b), 7(e),
7(f)).

The model trained with the Spacing dataset without rotational transforms (Fig.
7(a)) achieved the highest $\text{R}^{2}$ score of all models with a score of
0.57. This indicates that the more than half of the variance within this model
is able to be explained by the input data. However, the model trained with the
Velocity sample and rotational transforms achieved the lowest RMSE score of
7.84 of all models on input data with significantly less variability as
indicated with their lower $\text{R}^{2}$ scores. The model trained on the All
dataset produced RMSE and $\text{R}^{2}$ scores inbetween that of models
trained on either Spacing or Velocity datasets except in the situation for the
case where rotational transforms were applied where it yielded a $R^{2}$ score
of 0.07. The additional hyperparameter of various build layer depths displayed
worse RMSE and $\text{R}^{2}$ scores indicating that there exists a greater
correlation between the thermal images and the build layer directly underneath
it.

The RMSE and $\text{R}^{2}$ values align with what is expected of the two
Spacing and Velocity datasets as the hatch spacing and scan velocity are the
two variables that change between sample steps respectively. In the case of
Spacing sample, the hatch spacing produces a visible signal in the form total
rasters that is visible over the sequence of input frames. However, the
Velocity sample uses a consistent number of rasters traveling both vertically
and horizontally across the build plate. The most significant visual signal in
the Velocity sample is the distance the melt pool travels inbetween frames.

(a) Spacing

(b) Velocity

(c) All

(d) Spacing (with transforms)

(e) Velocity (with transforms)

(f) All (with transforms)

Figure 7:  CNN pore count predictions plotted alongside target pore values for Spacing, Velocity, and All (combination of both datasets) for a depth of 1 build layer. In all plots the pore counts for build layers 100 - 160 are clustered near the origin as the upper half of the sample is composed of nominal process conditions. Of all the various implementations, the CNN model trained on the Spacing (Fig. 7(a)) dataset without transforms shows the greatest level of alignment between the prediction and ground truth.  gray!30 |  | 1 Build Layer | 2 Build Layers | 3 Build Layers
---|---|---|---|---
gray!30 Dataset | Data Augmentation | RMSE | $\text{R}^{2}$ | RMSE | $\text{R}^{2}$ | RMSE | $\text{R}^{2}$
Spacing | Rotational | 12.60 | 0.33 | 19.04 | 0.18 | 22.94 | 0.17
| None | 10.14 | 0.57 | 18.46 | 0.23 | 19.75 | 0.39
gray!10 Velocity | Rotational | 7.84 | 0.09 | 11.41 | -0.04 | 14.74 | 0.03
gray!10 | None | 8.08 | 0.03 | 8.95 | 0.36 | 13.25 | 0.22
All | Rotational | 11.90 | 0.07 | 13.89 | 0.34 | 17.81 | 0.26
| None | 9.73 | 0.38 | 14.57 | 0.27 | 16.88 | 0.34
Table 1:  $\text{R}^{2}$ and RMSE prediction performance metrics for CNN model
trained on various datasets and build layer depths for 500 epochs.

###  4.2 Porosity Localization

During the training process, rotation transforms of the entire video sequence
were introduced as data augmentation methods and compared against models
trained without any rotational transformations. In addition to data
augmentations, the datasets were adjusted to allow for training on All Pores
and on pores with ESD 1 standard deviation above the mean ($\mu+\sigma$ Pores)
in an effort to investigate the model’s performance on identifying the larger
pores within the dataset.

The position of the pores within the build layer was predicting using a
sequence of thermal images with the ViViT Dense model trained on either the
Spacing, Velocity, and All dataset. The effect of data augmentation and
applying a threshold for minimum ESD for pores were investigated with the
training of this model as well. The Intersection over Union (IoU) also known
as the Jaccard Index was used to quantify the performance of each model’s
prediction. The intersection over union quantifies the prediction area overlap
onto the target with the highest metric of 1.0 occurring from an exact overlap
of the two sets. For the IoU calculation each set only includes the areas of
porosity and in the case where both the target and prediction exhibited no
porosity, a score of 1.0 was given as the prediction provided an exact match
of the ground truth.

(a) IoU Overlay with All Pores

(b) IoU Overlay with $\mu+\sigma$ Pores

Figure 8:  Comparison of prediction and label values for the model trained on
the All sample alongside the application of a minimum ESD pore threshold (Fig.
8(b)). The areas colored in yellow represent the intersection that is
considered for IoU calculations.

The effect of training on the various Spacing, Velocity, and All datasets were
investigated for this task as well the impact of rotational transforms on the
input sequence. In addition, the prediction performance of the model upon
applying a threshold to hide pores smaller than 1 standard deviation above the
mean was applied. The prediction results of these models measured for each
input label pair within the test dataset with the overall average and maximum
IoU scores recorded on Table 2. Within the datasets that included All Pores,
models trained on the Spacing datasets performed the best on average IoU
scores when trained without rotational transforms. A maximum IoU score of 0.85
was achieved within the model trained on the dataset for All samples with
rotational transforms applied. Without the applied threshold for minimum pore
ESD, the model trained on the Velocity produces the lowest IoU score of the
three models. However, after a minimum pore ESD threshold is applied, the
Velocity dataset model performs on par to that of the model trained with the
Spacing dataset. In all of the cases there was a greater trend in overlap
within the lower layers of the sample (Fig. 8(a)) likely due to the higher
porosity resulting from the off nominal process conditions used within those
sample steps.

With a minimum pore threshold of 1 standard deviation above the mean pore
equivalent diameter ($\mu+\sigma$ Pores), all models were able to achieve
maximum IoU scores of 1. These results were achieved towards the top of each
sample where nominal process conditions were used and correctly predicted the
ground truth of no pores above the threshold were present. (Fig. 8(b)) In some
cases, areas with higher levels of porosity produced lower IoU scores after
thresholding as the previously larger regions associated with porosity are
reduced in size (Fig. 8). Overall, the mean IoU increased for all models after
the application of a minimum pore ESD threshold. The greatest of these
increases is seen in the models trained with the All dataset of which scored
the highest average IoU of any other models. Rotational transforms did not
prove to have a significant impact on improving training as the resulting
metrics were often within a percent error from each other.

(a) Spacing

(b) Velocity

(c) All

(d) Spacing (with transforms)

(e) Velocity (with transforms)

(f) All (with transforms)

Figure 9:  IoU trends by build layer for various datasets with and without rotational transforms.  gray!30 |  | All Pores |  $\mu+\sigma$ Pores
---|---|---|---
gray!30 Dataset | Data Augmentation | Average IoU | Max IoU | Average IoU | Max IoU
Spacing | Rotational | 0.25 | 0.75 | 0.29 | 1.0
| None | 0.28 | 0.77 | 0.28 | 1.0
gray!10 Velocity | Rotational | 0.16 | 0.42 | 0.24 | 1.0
gray!10 | None | 0.17 | 0.44 | 0.29 | 1.0
All | Rotational | 0.22 | 0.85 | 0.32 | 1.0
| None | 0.21 | 0.72 | 0.32 | 1.0
Table 2:  Pore localization prediction performance metrics for ViViT Dense
model trained on Spacing, Velocity, and All sample datasets for 1000 epochs on
both all segmented pores and pores with equivalent diameters greater than 1
standard deviation above the mean. The adjusted threshold to consider only
pores with larger equivalent diameters improved prediction results in build
layers with nominal process parameter and low resulting porosity.

##  5 Conclusion and Future Work

In this work we investigate the application of machine learning to in-situ
thermal image process monitoring for the prediction of pore count and pore
localization. For this we utilized a CNN architecture and a modified ViViT
model with dense prediction heads for various dataset such as Spacing,
Velocity, and All. For the task of pore quantification, we have found that the
Spacing dataset provides the greatest amount of signal within and models
trained on the Velocity dataset produces the least amount of error. The pore
localization task displayed a similar trend with models trained on the Spacing
dataset achieving the best overlap when evaluating All Pores. The model
trained on the All dataset showed better performance when evaluating on
$\mu+\sigma$ Pores.

In both tasks, the effect of rotational transforms were minimal resulting in a
negligible difference in prediction outcomes. Our pore localization model
experienced improved performance with the application of a minimum pore ESD
threshold as it achieved higher average IoU scores, especially within areas of
the sample built with nominal processing parameters. These works show the
potential of utilizing in-situ process monitoring techniques for faster ex-
situ part certification and future work would aim to develop a more robust
digital twin achieving greater defect quantification and localization
precision over the entire sample.

Sandia National Laboratories is a multimission laboratory managed and operated
by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned
subsidiary of Honeywell International Inc., for the U.S. Department of
Energy’s National Nuclear Security Administration under contract DE-NA0003525.
This paper describes objective technical results and analysis. Any subjective
views or opinions that might be expressed in the paper do not necessarily
represent the views of the U.S. Department of Energy or the United States
Government.

##  6 Input Cropping and Label Downsampling

The input thermal images were cropped from the original 85 px × 60 px shape
down to a 64 px × 64 px shape to fit the desired input shape of the network.
To achieve this 8 pixels (188.8 µm) were cropped from both the top and bottom
of the image and 1 pixel (23.6 µm) was removed from the left hand side of the
image. To match the cropped input, the corresponding CT label was first
cropped then downscaled to align with the expected 64 px × 64 px input. The
crops of 8 pixels and 1 pixel were converted to their voxel equivalents and
rounded to 52 voxels and 7 voxels respectively. This reduced the CT label a
size of 520 voxels × 423 voxels down to 416 voxels × 416 voxels (Fig. 10a).
The resulting cropped CT was downscaled by a factor of 24 down to 18 voxels ×
18 voxels along the x and y directions and 1 voxel along the z direction.
Further cropping was applied to the x and y directions by 1 voxel on each side
to reduce the label down to 16 voxels × 16 voxels× 1 voxel (Fig. 10b).

Figure 10:  Relative porosity locations are derived from the raw CT data which
are cropped to capture a consistent area to match the input thermal data (Fig.
10a). The CT data is further downsampled factor of 24 and cropped to provide a
16 x 16 label shape (Fig. 10b).

##  7 Calculating absolute temperature estimations with data obtained through
Stratonics pyrometer

The estimation of absolute temperature was achieved with grey-body assumption
where the emissivity remains constant at various wavelengths. Thus, with
proper calibration using a NIST-traceable tungsten lamp, the pyrometer was
able to read out a temperature estimation within 4% accuracy for stainless
steel. 33. This temperature is estimated with the following formula for hybrid
mode temperature estimation (Eq. 2) where $p_{2}$ is a constant held at 14388
nm-K. Wien’s approximation 61 of Planck’s law is used to evaluate
$A_{\lambda}$ (Eq. 3) which takes into consideration emissivity and the
instrument’s detection factor with $\bar{I_{1}}$ representing the average
intensity calculated over region $\Omega_{p}$. $I_{1}$ and $I_{2}$ here
represent the the radiance from images over $\Omega_{p}$, for
$\lambda_{1}=750\text{nm}$ and $\lambda_{2}=900\text{nm}$ respectively. The
temperature ratio $T_{R}$ (Eq. 4) is calculated with $R$, the average of
radiance from images $I_{1}$ and $I_{2}$ over $\Omega_{p}$, and hardware
constants for contour levels $c_{1}$ and $c_{2}$ obtained from least squares
fitting over calibration data62. Contour level defines the region $\Omega_{p}$
with a $\beta$ value between 0 and 1 through means of marching squares (Eq.
5). Our dataset utilizes images taken at $\beta=0.7$ for its most accurate
approximation of the meltpool by single contour as opposed to the multiple
contours that appear at $\beta=0.3$.

$T_{H}=\frac{p_{2}}{\lambda_{2}\ln\left({A_{\lambda}/I_{2}}\right)}$ (2)
$A_{\lambda}=\bar{I}_{1}e^{p_{2}/\lambda_{1}T_{R}}$ (3)
$T_{R}=\frac{1}{c_{1}\ln R+c_{2}}$ (4) $c=\beta\times\text{max}\left(I\right)$
(5)

###  7.1  Sample alignment of thermal images to CT data along the X and Y axes

CT data for both samples had a shape of 1410 × 900 × 430 voxels with values
ranging from 0 - 255 depending on data selection type of pore, sample, or pore
segmented sample. Common alignment between the in-situ pyrometry data and ex-
situ CT data was established by converting the pyrometry data into voxels and
applying a consistent offset. The in-situ pyrometry data was converted from
pixels (80 px × 65 px) to microns (1680 µm × 1365 µm) to voxels (462.81 voxels
× 376.03 voxels). The CT data was then shifted to align with the pyrometry
data by -18 voxels × 0 voxels × 63 voxels for the Spacing dataset and -14
voxels × -2 voxels × 73 voxels for the Velocity dataset.

###  7.2  IoU scores of models trained on equivalent sphere diameter pores 1
standard deviation above the mean ($\mu+\sigma$ Pores)

(a) Spacing

(b) Velocity

(c) All

(d) Spacing (with transforms)

(e) Velocity (with transforms)

(f) All (with transforms)

Figure 11:  IoU trends by build layer for various datasets with and without
rotational transforms with the application of minimum equivalent diameter pore
threshold.

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