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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>AI-driven models for Cold Spray deposition: transforming additive manufacturing for sustainability</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Alessia Auriemma Citarella</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Luigi Carrino</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Fabiola De Marco</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Luigi Di Biasi</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Alessia Serena Perna</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Genovefa Tortora</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Antonio Viscusi</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Department of Chemical, Materials and Production Engineering, University of Naples Federico II</institution>
          ,
          <addr-line>Piazzale V. Tecchio 80, 80125 Napoli</addr-line>
          ,
          <country country="IT">Italy</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>University of Salerno, CAIS Lab, Department of Computer Science</institution>
          ,
          <country country="IT">Italy</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>The integration of Artificial Intelligence (AI) techniques holds promise for advancing the optimization of industrial processes, such as the use of Cold Spray (CS) in the field of Additive Manufacturing (AM). This paper explores the intersection of AI and Cold Spray technology, highlighting its potential to enhance various aspects of AM, including material deposition, surface properties, and process eficiency. Through the utilization of Machine Learning (ML) and Deep Learning (DL) techniques, AI facilitates the analysis of vast datasets encompassing parameters such as powder properties, substrate characteristics, and process conditions, thereby enabling the identification of optimal deposition strategies. Furthermore, AI-driven predictive models ofer insights into the complex interactions between process variables, leading to improved understanding and control of the CS process.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Artificial Intelligence</kwd>
        <kwd>Coldp Spray</kwd>
        <kwd>Manufacturing</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        eras embedded within AM systems, enabling real-time substrate, thereby ensuring the integrity of the coating
monitoring and proactive adjustments. Specifically, the [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ].
process of CS remains partially manual and uncontrolled. The CS process is governed by several factors. The
AI models ofer advantageous roads to overcome this size and composition of the powder particles determine
challenge by facilitating experimentation and expediting the characteristics of the deposited layer and its
adhethe integration of Low-Pressure CS into industrial work- sion to the substrate. Fine-tuning these parameters can
lfows. Additionally, AI-powered predictive maintenance optimize material properties and deposition eficiency.
can minimize downtime and maximize operational efi- The selection of gas type, flow rate, and pressure controls
ciency, further driving sustainability by reducing waste the acceleration and direction of the powder particles
and energy consumption. As such, the synergy between during spraying. Adjusting these parameters influences
AI and AM can revolutionize manufacturing practices coating density, adhesion strength, and deposition
qualand propel us toward a more sustainable future. ity. The design and geometry of the cold spray nozzle
play a vital role in directing the gas-particle mixture onto
the substrate [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]. Optimizing nozzle parameters such as
2. Research Fields diameter, shape, and exit velocity ensures precise
control over deposition conditions and coating morphology.
      </p>
      <p>
        The primary objective of our research is to design an The distance between the CS nozzle and the substrate,
innovative methodology for computer-aided manufactur- known as the standof distance, afects particle
velocing (CAM) systems by leveraging ML and DL approaches ity and impact energy. Adjusting this parameter
optito develop ad-hoc models. These models attempt to use mizes coating thickness, uniformity, and surface finish
cutting-edge technology to discover the best combina- [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ]. By carefully adjusting these input parameters,
mantion of factors for CS coating techniques. The advanced ufacturers can tailor the cold spray process to produce
parameter sensors used are several such as temperature, high-quality coatings with desired material properties
pressure, gas velocity, and optical and auditory sensors. and performance characteristics, all while optimizing for
Our research aims at the creation of automated decision- time-consuming and cost eficiency. Fine-tuning
parammaking systems for monitoring and control, allowing eters such as particle size, gas flow rate, nozzle design,
for the deployment of accurate spray strategies. By con- substrate temperature, standof distance, and powder
ducting experiments using a CS machine in real-world feed rate not only ensures the quality of the deposited
situations, our goal is to evaluate the efectiveness of layer but also minimizes production time and resource
our suggested ML approaches and obtain valuable input usage. This emphasis on eficiency is critical for meeting
to improve the accuracy of our forecasting results. The production schedules, reducing manufacturing costs, and
ifndings obtained from this research have the capacity to improving overall competitiveness in the market.
improve sustainability and make a valuable contribution However, achieving the ideal combination of parameters
to the scientific literature by increasing the efectiveness and selecting their right combinations can be a complex
and precision of cold spray coating processes. and time-intensive task. This is where the use of AI
mod
      </p>
      <p>These activities involve a multidisciplinary team from els comes into play. By leveraging AI algorithms and
the University of Salerno and the University of Naples machine learning techniques, manufacturers can analyze
Federico II. The CAIS Lab 1, laboratory from Computer the amounts of data to identify the most efective
parameScience Department of the University of Salerno, provides ter settings more quickly and accurately than traditional
important support in developing algorithms that require methods. This not only streamlines the optimization
prosignificant time and resources. Meanwhile, the University cess but also enhances the overall eficiency of the cold
of Naples Federico II focuses its eforts on the thorough spray deposition, leading to significant time and cost
savcollection and organization of data. ings while maintaining or even improving the quality of
the final product.</p>
    </sec>
    <sec id="sec-2">
      <title>3. Cold Spray</title>
      <p>CS is an emerging technology for micrometer-sized
powder deposition, increasingly utilized in additive
manufacturing for creating individual components and repairing
damaged parts. Among the advantages of CS is the fact
that it mitigates thermal degradation and facilitates
eficient deposition between the sprayed material and the</p>
      <sec id="sec-2-1">
        <title>1https://caislab.di.unisa.it</title>
        <sec id="sec-2-1-1">
          <title>3.1. ML models for CS process optimization</title>
          <p>CS, utilizing kinetic energy and operating at
temperatures well below the melting point of metallic particles,
presents a promising avenue for enhancing the surface
properties of polymers. While extensively explored and
utilized on metal substrates, the application of this
technology to polymers remains relatively uncharted
territory, and the underlying physics are not yet fully
elucidated. This is particularly significant because the charac- The output parameters under consideration are the
teristics of the final coating, such as powder deformation penetration depth of the particle and the degree of
flator penetration depth, crucial for coating adhesion, are tening. In CS, penetration depth refers to the distance
influenced by a multitude of factors. These factors in- into the substrate material that the sprayed particles can
clude the properties of both the metallic powder and penetrate and adhere to. This depth depends on various
the polymeric substrates, alongside the specific spray- factors such as particle velocity, temperature, and
maing parameters employed in the process. Consequently, terial properties. Flattening, on the other hand, refers
accurately predicting the behavior of metallic particles to the deformation of the sprayed particles upon impact
upon impact on various substrates remains a challenge. with the substrate surface. It describes how much the
Developing a physical model capable of accurately rep- particles spread out and flatten upon hitting the substrate.
resenting the deposition processes of metallic particles Flattening is influenced by parameters like particle
veonto nonmetallic substrates proved impractical. Validat- locity, temperature, particle size, and substrate material
ing such models would require the collection of extensive properties.
testing scenarios and outcomes using advanced tools, in- We employed three distinct ML models: Linear
Regrescluding sensors and high-speed cameras. sion (LR), Gaussian Process Regression (GPR), and Neural</p>
          <p>
            In this context, Machine Learning (ML) ofers the po- Networks (NNs). LR is a straightforward technique
utitential to reduce the number of necessary experimental lized to establish a linear relationship between variables.
trials. However, when we used ML solutions, achieving This relationship elucidates the functional link between
precise predictions requires feeding the model with ac- the independent and dependent variables within a given
curate and a large amount of data. Therefore, a viable dataset. Consequently, LR models the unknown or
deapproach could involve training the model with a com- pendent variable as a linear equation based on the known
bination of precise yet limited experimental data and or independent variable. Gaussian Process Regression
computational data obtained from Finite Element models (GPR), on the other hand, is a nonparametric Bayesian
(FEM), which, while less precise, do not sufer from the approach employed for regression tasks. It excels
parlimitations of experimental data. Consequently, in our ticularly with smaller datasets and infers a probability
work [
            <xref ref-type="bibr" rid="ref8">8</xref>
            ], we used a training dataset composed by 30% distribution model. The Neural Network (NN) used in our
of experimental data and 70% of FEM data (mixed data) study is a three-layer function-fitting model trained
comand a second dataset with only FEM data to train some prehensively on the entire dataset. Following training, it
ML models. The test dataset for both suggested models can adeptly generalize an input-output relationship. To
is fully made up of experimental data. Polyether-ether- assess the eficacy of the ML techniques employed, we
ketone (PEEK) and Acrylonitrile butadiene styrene (ABS) computed several performance metrics including
Rootsubstrates were chosen for the deposition process, includ- Mean-Square Error (RMSE), R-Squared, Mean Squared
ing both unreinforced and long carbon fiber-reinforced Error (MSE), and Mean Average Error (MAE). Figures 1-2
variants. Spherical powders of copper, aluminum, and report the results for penetration depth and flattening
steel were supplied by LPW South Europe for this pur- predictions. The top models for the penetration on the
pose. Depositions were carried out using low-pressure test set are NN and LR for the flattening prediction for
cold spray equipment (DYCOMET). The samples were po- the mixed data.
sitioned on a platform, with the spraying gun mounted on By examining the results derived from training the
a robot (HIGH-Z S-400/T-CNC-Technik), which operated model with FEM data, we were able to determine that
remotely and sprayed perpendicular to the substrates. the most accurate predictions on the test set for
penetraThese materials were chosen for their diverse properties tion and flattening were achieved using the GPR method.
and suitability for CS applications. Specifically, the GPR model demonstrated enhanced
pen
          </p>
          <p>The input parameters for the strategies employed can etration values while exhibiting a decrease in flattening
be categorized into three main groups: performance. Figure 3 depicted the comparison between
the performance of the models.
• impact velocity, which encompasses other process The conducted experiments indicate that the accuracy
parameters such as temperature and pressure; of the models improves with an increasing amount of
• powder parameters (Yp), representing the yield available data. Specifically, the models demonstrate
betstrength of the powder material; ter fit to the data when trained on the mixed dataset. By
• substrate parameters (Ys), indicating the yield ofering an initial insight into the influence of parameters
strength of the substrate material. afecting coating deposition, the integration of ML seems
to contribute to the optimization of the CS process.</p>
        </sec>
      </sec>
      <sec id="sec-2-2">
        <title>The latter also take into account the presence of fibers. When positioned appropriately beneath a matrix layer similar in size to the powders, these fibers reinforce the substrate, modifying its yield strength.</title>
        <sec id="sec-2-2-1">
          <title>3.2. Genetic Algorithm-Driven DL models:</title>
          <p>evolutionary approaches to improve</p>
        </sec>
        <sec id="sec-2-2-2">
          <title>CS deposition</title>
        </sec>
      </sec>
      <sec id="sec-2-3">
        <title>In our point of view to elevate the deposition eficiency of</title>
        <p>
          CS across a spectrum of materials and to explore the the
use of AI models, our attention focused on the integration
of DL models. Through the integration of DL models,
we aim to unlock new insights and capabilities that
propel the field of CS towards greater eficiency, eficacy,
and versatility. In this study [
          <xref ref-type="bibr" rid="ref9">9</xref>
          ], we had two primary
objectives:
• firstly, to investigate various DL models aimed at
augmenting automation capabilities within the
domain of CS;
• secondly, we explored the employment of a
genetic algorithm approach to refine the
aforementioned DL models, with the specific aim of
enhancing coating properties.
        </p>
        <p>
          In this scenario, when evaluating potential substrate
materials, our study examined a range of options
including ABS, PEEK, and Polyamide PA66 (PA66).
Furthermore, in selecting powders for the deposition process, we
incorporated a variety of metallic options such as copper,
aluminum, steel, and titanium. During the initial training
phase, we employed two distinct types of datasets to
develop our models. The first dataset, known as the mixed
dataset, comprised a blend of 30% experimental data and
70% FEM data. Additionally, we utilized a second dataset
consisting solely of FEM data, providing a more focused
exploration of simulated scenarios. Subsequently, during
the evaluation phase, our trained models tested using
exclusively experimental data. As input and output
parameters, we used the same of our previous work [
          <xref ref-type="bibr" rid="ref8">8</xref>
          ].
        </p>
        <p>We employed DL models, specifically focusing on neural
network models. These neural networks, inspired by the
structure and function of the human brain, are adept at
learning complex patterns and relationships in the data.</p>
        <p>In the development of these networks, we adopted a
genetic algorithm approach. Genetic algorithms (GAs) draw
inspiration from biological evolution, employing
principles of natural selection and genetic recombination to
ifnd optimal solutions for complex problems.
Traditionally, GAs are utilized to optimize algorithm parameters;
however, in our specific scenario, we employed GAs to
design the architecture of the networks. The process of GAs
requires several steps: , where potential
solutions are randomly selected; , which
identifies optimal parents based on their fitness; ,
where genetic material is recombined to generate new
solutions; mutation, introducing random changes to
generate genetic diversity; and , which assesses
the fitness of the solutions. Each of these steps plays a
crucial role in guiding the evolutionary process towards
identifying optimal solutions for complex problems. In
this work, we presented two NN as best solutions: Wide
Neural (WNN) and Trilayered Neural (TNN) Networks.</p>
        <p>WNN refers to an artificial neural network architecture
that typically has fewer hidden layers but a substantial
number of nodes in each layer. The TNN is a form of
artificial neural network, also known as a single-layer
perceptron, consisting of the input layer, one hidden
layer and the output layer. To assess the efectiveness of prior findings.
the DL approaches, we computed several performance
metrics, including the RMSE, R-squared, MSE, and MAE.</p>
        <p>For the flattening, the best results are obtained by the
WNN. For the penetration depth, TNN reached the best
values, but, except for the R-squared, all the values, on
the test set, are high. Overall, the DL models achieved
best performance for flattening (see Figure 4).</p>
        <p>In our previous study, we evaluated ML algorithms
using a mixed dataset. NN model excelled in
predicting penetration on the test set, while LR proved optimal
for prediction of flattening. To further comprehend our
approach, we compared the outcomes of our earlier
investigation with those obtained through the integration
of GAs and we reported these results in Table 1 and
graphically in Figure 1. Interestingly, the WNN
demonstrated exceptional performance in predicting flattening,
showcasing a marked improvement over previous results. Figure 5: Comparison between ML and DL models
However, it is important to note that for penetration
prediction, the TNN constructed with the use of GAs
exhibited a less favorable performance compared to our</p>
      </sec>
      <sec id="sec-2-4">
        <title>The conducted experiments underscore the potential</title>
        <p>of DL techniques in predicting optimal parameter
combinations, enhancing the eficiency and efectiveness of
the coating process. With the introduction of the GAs
to improve the design of networks, we can streamline
the optimization of model architectures, reducing the
need for manual hyperparameter tuning, which is often
time-consuming and suboptimal.</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>4. Acknowledgments</title>
      <sec id="sec-3-1">
        <title>This studies received funding from the European Union</title>
        <p>Next-GenerationEU - National Recovery and Resilience
Plan (NRRP) – MISSION 4 COMPONENT 2,
INVESTIMENT N. 1.1, CALL PRIN 2022 D.D. 104 02-02-2022 –
(OPTIMA: depOsition of cold sPray in the realm of green
addiTIve manufacturing through construction of
MAchine learning models) CUP N.D53D23017410001.</p>
      </sec>
    </sec>
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</article>