The document describes research into developing a data-efficient neural network model to predict the track profile geometry in cold spray additive manufacturing using limited experimental data. Researchers trained an artificial neural network on profile data from 36 experiments and tested it on 12 additional experiments. The neural network was able to accurately predict both symmetric and asymmetric track profiles using less data than previous mathematical models, demonstrating the potential for data-efficient machine learning in additive manufacturing applications with scarce training data.

1. Australia’s National Science Agency
Hybrid Predictive Modelling of Geometry
with Limited Data in Cold Spray Additive
Manufacturing
Daiki Ikeuchi, Alejandro Vargas-Uscategui, Xiaofeng Wu, Peter C. King | August 2020
For Further Information (Open Access):
“Data-Efficient Neural Network for Track Profile
Modelling in Cold Spray Additive Manufacturing”
Citation: Ikeuchi,D.; Vargas-Uscategui, A.; Wu, X.; King,
P.C. Data-Efficient Neural Network for Track Profile
Modelling in Cold Spray Additive Manufacturing. Appl. Sci.
2021, 11, 1654. https://doi.org/ 10.3390/app11041654
Our Related Work (Open Access):
“Neural Network Modelling of Track Profile in
Cold Spray Additive Manufacturing”
Citation: Ikeuchi, D.; Vargas-Uscategui, A.; Wu, X.; King,
P.C. Neural Network Modelling of Track Profile in Cold
Spray Additive Manufacturing. Materials 2019, 12, 2827.
https://doi.org/10.3390/ma12172827

2. Introduction
osition – The basic concept
Additive Manufacturing | Dr. Alejandro Vargas-Uscategui
ted, high pressure gas is accelerated to supersonic velocities through a de Laval
zle.
allic Particles (< 50 µm) are fed into the gas stream.
particles impact onto a substrate, forming a deposit.
Why Cold Spray Additive Manufacturing (CSAM)?
• Solid-state deposition with low-oxygen contents
• Avoidance of melting-induced microstructure changes
• Stable fabrication with high deposition rate with robotic system
• Large-scale manufacturing without a protective atmosphere

3. Background and Challenge
Challenge: Geometric Modelling and Control
Approach Mathematical Data-driven
Advantage
• Complete profile prediction
• Asymmetric profile can be
predicted
• Potential for higher
predictive accuracy
• Learning capability
Disadvantage
• Limited predictive accuracy
• May require multiple forms
of underlying math models.
• Limited to prediction of
geometric features only
• Need large dataset
Question: Can we address the problem of data-
scarcity in CSAM for data-driven modelling?

4. Objectives
Investigate data-efficient machine learning modelling
for a single-track deposit profile in CSAM
Complete single-track
profile prediction
Predict both
symmetric and
asymmetric profiles
Comparative study
against previously
proposed models
Data-efficiency
achieved without
more experiments

5. Method: Experimental
-8 -6 -4 -2 0 2 4 6
-0.5
0
0.5
1
1.5
2
Number of output sampling points
Normalised
area
Fabrication of Track Profiles:
• A commercial Impact Innovation
5/11 cold spray gun
• Purity grade-2 titanium feedstock
Design of Experiments:
• Traverse speed, Spray angle and
Standoff distance designed in a full
factorial manner (48 tracks)
Profile Geometry Sampling:
• Geometric points sampled from
each track profile
• The sufficient number of sampling
points determined by area
validation method (67 points)
CSAM Single-Track Profile

6. Method: Modelling
Input Layer ∈ ℝ⁵ Hidden Layer ∈ ℝ¹¹ Hidden Layer ∈ ℝ⁴ Output Layer ∈ ℝ¹
NN-SVG
Publication-ready NN-architecture schematics.
Download SVG
FCNN style LeNet style AlexNet style
Input layer:
• # of input neurons = # of relevant
features based on domain
knowledge in CSAM
Hybrid layer:
• # of neurons and layers found by
iterative investigations with mean
square error (MSE) minimised
Output layer:
• # of output neurons = # of
predictive variable of interest
Original Dataset:
• Training – 36 CSAM profiles
• Testing – 12 CSAM profiles
Training data Testing data
Evaluate
Learn
Artificial Neural Network (ANN)

7. Method: Data-efficiency Strategy
Previously built math model

8. Result: Modelling Validation
5 11 4 1
0 100 200 300 400
Epoch
10
-4
10-2
10
0
Normalised
Mean
Squared
Error
(MSE)
Train performance
Test performance
Best
Architecture and Performance:
• [5 11 4 1] architecture
• MSE = 0.0001032
• Evaluated on testing dataset
Training process:
• 445 iterations (or epochs)
• No evidence of overfitting and
underfitting

9. Result: Analysis and Comparison
Tech. 1 Tech. 2 Tech. 1+2
Gaussian curve fitting
ANN
0
5
10
15
20
25
30
Absolute
Error
%
Mean
Tech. 1 Tech. 2 Tech. 1+2
Gaussian
curve fitting
ANN
Data-efficient ANN modelling
• Both Tech. 1 and 2
shown effective
• Tech. 1 found more
effective than Tech. 2
• Data-efficient ANN
performed better than
purely data-driven ANN
and mathematical
Gaussian model.
Mean % 2.060 4.040 1.230 1.873 7.174

10. Result: Visual Prediction Results
0
0.2
0.4
0.6
0.8
1.0
1.2
Sample 48
Gaussian
ANN
Data-efficient
ANN
Sample 39
Gaussian
ANN
Data-efficient
ANN
-5 -4 -3 -2 -1 0 1 2 3 4 5
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14 Gaussian
ANN
Data-efficient
ANN
-5 -4 -3 -2 -1 0 1 2 3 4 5
Gaussian
ANN
Data-efficient
ANN
(a) (b)
Horizontal location on substrate (mm)
Absolute
Error
(mm)
Deposit
height
(mm)

11. Conclusion
Complete single-track
profile prediction
Predict both
symmetric and
asymmetric profiles
Comparative study
against previously
proposed models
Data-efficiency
achieved without
more experiments
Future works:
• A more adaptive toolpath planning algorithm to be explored
• Implementation of the proposed model into user-friendly software
• Further investigation into data-efficiency side of research in CSAM

12. Australia’s National Science Agency
Daiki Ikeuchi
The University of Sydney
CSIRO Manufacturing
Thank you
For Further Information (Open Access):
“Data-Efficient Neural Network for Track Profile
Modelling in Cold Spray Additive Manufacturing”
Citation: Ikeuchi,D.; Vargas-Uscategui, A.; Wu, X.; King,
P.C. Data-Efficient Neural Network for Track Profile
Modelling in Cold Spray Additive Manufacturing. Appl. Sci.
2021, 11, 1654. https://doi.org/ 10.3390/app11041654
Our Related Work (Open Access):
“Neural Network Modelling of Track Profile in
Cold Spray Additive Manufacturing”
Citation: Ikeuchi, D.; Vargas-Uscategui, A.; Wu, X.; King,
P.C. Neural Network Modelling of Track Profile in Cold
Spray Additive Manufacturing. Materials 2019, 12, 2827.
https://doi.org/10.3390/ma12172827