Cold spray additive manufacturing is an emerging technology that offers unique advantages, including high production rate, unlimited product size and the ability to process oxygen-sensitive materials. However, dimensional control and accuracy in cold spray additive manufacturing are challenging, which limits its integration into commercial manufacturing systems. These problems originate from the poor understanding of the complex relationship between process parameters and the resulting deposit geometry. This knowledge gap motivated the development of an accurate predictive model for the geometry of a cold spray deposit profile to overcome the problems. Recently, a machine learning approach has gained interest in developing the predictive model of such a complex additive manufacturing process due to its superior nonlinear mapping capability, as seen in other manufacturing applications. Nevertheless, such a mapping capability can be realised only with a large amount of experimental data which is often impractical to collect in additive manufacturing applications. This data-scarcity issue has motivated the exploration of a data-efficient machine learning approach suitable for complex process modelling with limited data. Therefore, the objective of this study was to investigate a data-efficient machine learning approach to geometry prediction in cold spray additive manufacturing. The proposed modelling approach incorporated a conventional Gaussian mathematical model into the development and learning process of a data-driven model. We compared to purely mathematical and data-driven modelling results and showed that the proposed modelling approach provided improved predictive accuracy. The findings can contribute to the control and optimisation of the process for shorter production time and the development of build strategy for better as-fabricated surface and dimensional quality control. The approach in this study is also applicable in other deposition-based additive manufacturing technologies such as Wire and Arc Additive Manufacturing.

1. Australia’s National Science Agency
Data-efficient Machine Learning for
Geometry Prediction in Cold Spray
Additive Manufacturing
Daiki Ikeuchi, Alejandro Vargas-Uscategui, Xiaofeng Wu, Peter C. King | September 2020
For Further Information:
“Data-Driven Overlapping Track Profile
Modelling in Cold Spray Additive Manufacturing”
Citation: Ikeuchi,D.; Vargas-Uscategui, A.; King, P.C. Wu,
X., Data-Driven Overlapping Track Profile Modelling in
Cold Spray Additive Manufacturing. ITSC 2023. 15-21,
2023, https://doi.org/ 10.31399/asm.cp.itsc2023p0015
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
“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

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
• Physically consistent
• 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 an overlapping-track deposit profile in CSAM
Complete
overlapping-track
profile prediction
Include deposition
surface information
explicitly
Comparative study
against previously
proposed models
Data-efficiency
achieved without
more experiments

5. Method: Experimental
Fabrication of Two-Track Profiles:
• A commercial Impact Innovation 5/11 cold spray gun
• Purity grade-2 titanium feedstock
Design of Experiments:
• Traverse speed, and Standoff distance and Overlapping ratio
designed in a full factorial manner (48 overlapping tracks)
CSAM Overlapping Two-Track Profile

6. Method: Modelling Strategy (1)
𝑥 =
𝑇𝑟𝑎𝑣𝑒𝑟𝑠𝑒 𝑠𝑝𝑒𝑒𝑑
𝑃𝑜𝑙𝑎𝑟 𝑎𝑛𝑔𝑙𝑒
𝑆𝑢𝑏𝑠𝑡𝑟𝑎𝑡𝑒 𝑡𝑦𝑝𝑒
𝑃𝑜𝑙𝑎𝑟 𝑙𝑒𝑛𝑔𝑡ℎ
𝑦 = ∆ 𝑝𝑜𝑙𝑎𝑟 𝑙𝑒𝑛𝑔𝑡ℎ

7. Method: Modelling Strategy (2)
𝑦 𝑥 = 𝑓 𝑥 + ℎ 𝑥
Gaussian Process Regression (GPR) Explicit Mean Function
• 𝑚 𝑥 = 0
• Kernel: 3/2 Matern function
• K-fold cross validation (k = 5)
• 48 overlapping-track profiles
• 151 sampling points taken
between ± 5 mm around Tool
Centre Point
• Substrate type represented as -1
or 1
• Acts as an approximate solution
• Can be based on domain
knowledge or approximate model
• Mathematical Gaussian
superposing model used here
Simply added numerically

8. Result: Modelling Validation
Performance of ƒ (x):
• MSE = 0.003573
• Evaluated on testing dataset
• Cross-validated
Performance of y(x):
• MSE = 0.0002183
• Evaluated on testing dataset
• Cross-validated

9. Result: Analysis and Comparison
• Both pure GPR and data-
efficient GPR models
performing better than
mathematical Gaussian
model in mean error %
• The data-efficient GPR
model showed narrower
range up to 75% quartile
• Maximum error % lower for
GPR models than
mathematical Gaussian
model
Mean % 2.189 1.449 0.5748

10. Result: Visual Prediction Results

11. Conclusion
Complete
overlapping-track
profile prediction
Include deposition
surface information
explicitly
Comparative study
against previously
proposed models
Data-efficiency
achieved without
more experiments
Future works:
• Development of in-situ online sensing system to extend the modelling
approach for overlayer manufacturing
• Demonstration of the modelling approach on more complex
deposition scenarios (e.g., on curved or complex surface for repairing)

12. Australia’s National Science Agency
Daiki Ikeuchi
The University of Sydney
CSIRO Manufacturing
daiki.ikeuchi@sydney.edu.au
Thank you
For Further Information:
“Data-Driven Overlapping Track Profile
Modelling in Cold Spray Additive Manufacturing”
Citation: Ikeuchi,D.; Vargas-Uscategui, A.; King, P.C. Wu,
X., Data-Driven Overlapping Track Profile Modelling in
Cold Spray Additive Manufacturing. ITSC 2023. 15-21,
2023,
https://dl.asminternational.org/itsc/proceedings/ITSC2023/84
536/15/26283
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://www.mdpi.com/1996-1944/12/17/2827
“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://www.mdpi.com/2076-3417/11/4/1654