# Using artificial neural networks to model single bead geometries processed by laser-wire direct energy deposition

Reza Asadi, Antoine Queguineur, Aapo Ylä-Autio, Antti Martikkala, Olli

Wiikinkoski, Hossein Mokhtarian, Iñigo Flores Ituarte

► To cite this version:

Reza Asadi, Antoine Queguineur, Aapo Ylä-Autio, Antti Martikkala, Olli Wiikinkoski, et al. Using artificial neural networks to model single bead geometries processed by laser-wire direct energy deposition. IOP Conference Series: Materials Science and Engineering, 2023, 1296 (1), pp.012005. 10.1088/1757-899x/1296/1/012005. [hal-05094681](https://hal.science/hal-05094681v1)

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PAPER • OPEN ACCESS

Using artificial neural networks to model single
bead geometries processed by laser-wire direct
energy deposition

To cite this article: Reza Asadi et al 2023 IOP Conf. Ser.: Mater. Sci. Eng. 1296 012005

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# Using artificial neural networks to model single bead geometries processed by laser-wire direct energy deposition

Reza Asadi¹, Antoine Queguineur¹,², Aapo Ylä-Autio¹, Antti Martikkala¹,³ Olli Wiikinkoski¹, Hossein Mokhtarian¹, Iñigo Flores Ituarte¹

¹Department of Automation and Mechanical Engineering, Faculty of Engineering and Natural Sciences, Tampere University, Korkeakoulunkatu 6, 33014 Tampere, Finland

² Ecole Centrale Nantes, GeM - UMR CNRS 6183, 1 rue de la Noé, 44321 Nantes - France

³ Department of Mechanical and Industrial Engineering, Norwegian University of Science and Technology, Richard Birkelands Vei 2b, NO-7034, Trondheim, Norway

reza.asadi@tuni.fi

**Abstract.** Wire-feed laser additive manufacturing processes have gained researchers' attention because of their potential to reduce material waste, guarantee accuracy, increase material quality and density, and produce a wide dimensional range of final products. Nevertheless, printing materials with desired geometrical properties of the beads is still challenging in such processes. This might be attributed to the need for more sufficient experimental data and precise modeling approaches. In this study, an architecture based on Artificial Neural Networks (ANNs) is developed to model the bead geometries (width, height, and area), considering the wire feed rate, laser power, and travel speed as process parameters. A design-of-experiment based on full factorial design is considered for processing single beads with a Fraunhofer coaxial wire-feed laser system. Inconel 625 wire with a diameter of 1.14 mm and stainless steel substrate are utilized as the experimental materials. Geometrical data is obtained using a laser scanner model RA-7525 SE with 0.026mm volumetric accuracy. The beads' geometrical details are provided as the feeding data for the proposed ANN. For each bead, a length of 10 mm is considered to calculate the average geometrical parameters, which increases the accuracy of the dataset in comparison to the values acquired via a macroscopic picture of the cross-section of each weld bead. A variety of hyperparameters are chosen and compared regarding precision criteria, including Mean Square Error (MSE), to increase the model's accuracy. A train-test separation strategy is considered to evaluate the model's accuracy on independent data points. The outcome of this research is an ANN-based geometry prediction model that can be utilized to enhance the development of offline path planners and optimize process parameter selection for a precise geometry toward process control.

**Keywords:** Artificial neural networks, direct-energy deposition, additive manufacturing, bead geometry modeling, Inconel 625

## 1. Introduction

Metal Additive Manufacturing (AM) has become an increasingly interesting field of research due to its capacity to produce high-performance products, achieve high-level automation, and reduce materials waste [1]. There is an array of methods based on the deposition strategies, utilized materials and source of energy adopted in AM processes. Each method has its own specifications making them suitable for unique applications [2]. Wire-feed Laser Additive Manufacturing (WLAM) is an economical additive manufacturing method for complex geometries, good surface quality and near net shapes [3]. In

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Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
comparison to the AM methods using electric arc to melt and deposit the material, in WLAM processes energy coming from the laser can be more focused which results in smaller melt pools, smaller feature size, and more efficient energy consumption [4]. These characteristics of WLAM result in the final product with more controlled residual stresses and phase transformations [5]. However, the deposition rate in such methods is less than in wire arc additive manufacturing methods.

Among the nickel-based alloys, Inconel 625 is a superalloy widely used in the aerospace sector and especially the engines and turbines [6], [7]. This material is strengthened through solid solution hardening that enables the achievement of high mechanical properties. Hence, the addition of alloying elements such as chromium, molybdenum, and niobium to the nickel matrix lead to the formation of carbides and intermetallic [8] [9]. Inconel 625 has excellent characteristics, including high corrosion resistance, strength and good tensile properties at high and cryogenic temperatures [10]. The properties of Inconel 625 are well-suited in WLAM processes thanks to a high-energy-density laser used to fuse the wire and the near-net-shape required in aerospace applications. However, rapid melting and solidification as well as cyclic heating and cooling during the deposition of layers in WLAM impact the characteristics of the deposited materials and especially the risk of solidification cracking [11]. Therefore, a comprehensive study is essential for discovering the properties of final products.

There is a growing interest in laser-wire AM [12]–[15]. However, metal AM widespread acceptance is hindered by lack of knowledge in organizational structures and high costs [1], [16], [17], parts quality (i.e., geometry, defects, microstructure, mechanical properties, etc.) [18], lack of manufacturing robustness, stability, and repeatability in the process [19]. Therefore, modeling the geometrical details of the metal AM processes and specifically WLAM can have significant effect on the process control and stability. The impact of related process parameters on the product geometry [13], microstructure [14], and surface quality [15] have been considered. Ali Gökhan Demir [20] has studied the correlation between geometrical characteristics and process parameters. Naïve Bayes (NB) networks and Gaussian process regression (GPR) model were utilized to assess the quality of the model and predict the printed bead geometries [13].

Based on the literature review, more investigations are required in modeling and prediction of the bead geometrical details. To that end, modeling single bead geometry can be assumed as the basis and steppingstone for such details. Developing an accurate model considering the overlapping factors, weld pool details and geometrical details of layers is a prerequisite for developing an efficient process. Consequently, the adaption of a G-code generator to design and print multilayer complex parts is achievable. In this paper, a combination of different Design of Experiments (DoE) including, Full Factorial (FF) and Central Composite Design (CCD), is adopted to implement the experiments on WLAM of Inconel 625. The experimental data is fed to a Neural Network (NN) to model the geometrical properties, and finally the sensitivity of the process parameters to the geometrical properties and the accuracy of the utilized ANN is evaluated. This research endeavor makes contributions in the following areas: (a) developing ANNs by employing the most efficient hyperparameters, including activation functions. (b) utilizing and selecting the most suitable optimization algorithm for training ANNs specifically for WLAM experiments. (c) incorporating a comprehensive statistical analysis to evaluate the sensitivity of process parameters and their interactions with respect to variations in bead geometrical details.

## 2. Experimental setup and data acquisition plan

The experiments are conducted on a LW-DED device introduced in Figure 1 with predetermined sets of process parameters. Fraunhofer CoaxWire welding head is implemented on an Aerotech 3-axis CNC machine. The welding head feeds the wire from the central axis, while three laser beams converge at a common focal point to the wire to make the process direction independent. Dinse, FDE 100 L is utilized as the wire feeder and process control system. A 3 KW Coherent Corelase fiber laser is used as the energy resource of the process. A UTP A 6222Mo-3 is selected as alloy 625 wire feedstock material with a diameter of 1.14 mm. Table 1 presents the chemical composition of the selected wire. A 10 mm
plate of 316L stainless steel (SS) has been chosen as the substrate. Single beads of Inconel 625 with 35 mm length under various process parameter levels, without in-situ or ex-situ thermal treatment are printed and analyzed in this study. Laser Power (LP), Travel Speed (TS), and Wire Feed Rate (WFR) are used as process parameters, and bead height, width, and area are the response parameters.

<table><caption>**Table 1.** Chemical composition of the filler metal</caption><thead><tr><th colspan="14">Filler metal chemical composition - UTP A 6222Mo-3, wt%</th></tr><tr><th>C</th><th>Si</th><th>Mn</th><th>Ni</th><th>Cr</th><th>Mo</th><th>Cu</th><th>Ti</th><th>Al</th><th>Nb</th><th>P</th><th>S</th><th>Fe</th><th>Ta</th></tr></thead><tbody><tr><td>&lt;0.01</td><td>0.12</td><td>0.02</td><td>64.66</td><td>22.30</td><td>8.71</td><td>0.02</td><td>0.22</td><td>0.13</td><td>3.45</td><td>0.004</td><td>0.001</td><td>0.29</td><td>0.004</td></tr></tbody></table>

<figure><img src="image_7.png" /><figcaption>**Figure 1.** The utilized experimental setup for tests</figcaption></figure>

After the screening tests to determine the ranges of the process parameters, as provided in Table 2, three different Design of Experiments (DoE) were selected. Two different FF DoEs with small and large range of variables and a CCD DoE are chosen. All the experimental results obtained from the mentioned DoEs are collected and fed into the proposed network to predict the geometrical bead values. For each FF DoE and 3 levels for each factor, 27 experiments are required. Furthermore, 20 tests with 6 repetitions in center point for CCD DoE are required. With the reduction of common experimental points between different DoEs, in total there are 66 experiments needed to be conducted.

<table><caption>**Table 2.** WLAM process parameter ranges</caption><thead><tr><th>Process Parameters</th><th>Range</th></tr></thead><tbody><tr><td>A: WFR (m/min)</td><td>[0.4 – 1.1]</td></tr><tr><td>B: TS (mm/s)</td><td>[3 – 8]</td></tr><tr><td>E: LP (kW)</td><td>[1.4 – 2.1]</td></tr></tbody></table>

Bead geometrical details including the printed beads shapes, their height, width, and area are obtained from the laser scanning system model RA-7525 SE with volumetric accuracy of 0.026 mm (Figure 1). The obtained data are evaluated, and the bead geometries are calculated for 10 mm length in the middle of the beads. The overall length of printed beads is set to 35 mm. To validate the scanning measurements, the theoretical WFR is compared with the overall printed volume and if the difference is less than 5%, the values are accepted. Since the main aim of this study is evaluation of machine learning based methods, 20 random tests, which are not similar to the training data but are within the validated ranges of process parameters, are conducted and the results are fed to the developed networks.

### 3. Modeling approach

In this study, statistical analysis techniques and Deep Learning (DL) methods are utilized to assess the sensitivity of the response parameters to the process parameters and modeling the bead geometry respectively.
## 3.1. Statistical Analysis

In statistics, to evaluate the correlation between explanatory variables, which are process parameters in manufacturing, and response parameters, Response Surface Methodology (RSM) is the most popular method. RSM, which was introduced by P. Box and K. B. Wilson [21], deploys second-degree polynomial model on the sequence of DoEs data to attain such an aim. In this method, some criteria are provided to consider the sensitivity of the responses to the process parameters.

Coefficient of determination (R²) is the relationship between variations in one variable and differences in another. R² is defined as equation (1):

$$R^2 = 1 - \frac{\text{Sum of squared error (SSE)}}{\text{Total sum of squares(TSS)}} = 1 - \frac{\sum_{i=1}^{m}(y_i - f_i)^2}{\sum_{i=1}^{m}(\bar{y} - y_i)^2} \quad (1)$$

Which $y_i$ is the i-th target value, $f_i$ is the i-th modeled value and $\bar{y}$ is the mean of target values. The best case is when the model is exact, and SSE equals to 0. In this case, R² equals to one. However, R² values more than 0.85 is considered as a sign of significant correlation, and values more than 0.80 is acceptable. R²adj is a robust version of R² that is used for analysis and the acceptable value for this criterion is equivalent or smaller than R².

Pareto chart is a chart that visually depicts the most significant factors for modeling a specific response parameter. In the present study, all the mentioned criteria are utilized to assess the sensitivity of geometrical attributes including width, height, and bead to the variation of process parameters.

## 3.2. Artificial Neural Network (ANN)

Manufacturing processes signatures and expected outcomes behave non-linearly and containing many complex factors [22]. Consequently, mathematical modeling of the required phenomena is challenging and usually not accurate. The assumed phenomenon to be modeled is bead geometry (width, height and area) as it is introduced in Figure 2-a. ANNs are among the commonly used methods due to the simplicity of understanding their concept, and the ability to improve their performance by feeding them more experimental data. ANNs are bio-inspired methods based on the structure of neurons and neural system. As it is shown in Figure 2-b, an artificial neuron consists of input parameters multiplied by their dedicated weights ($W_i$). To handle the non-linearities, after adding a bias (b), an activation function ($\Psi$) is applied before getting the neuron’s output. The training process helps to adjust the weights, and bias (b) values [23].

<figure><img src="image_8.png" /><figcaption>Figure 2. Schematic representation of a) bead geometrical features and b) perceptron</figcaption></figure>

Due to the complexity of AM processes specially WLAM and existence of unknown parameters, modeling the geometrical phenomena cannot be implemented by a single perceptron. Consequently, multi-layer ANNs have been deployed. In this study, an ANN with three inputs and three outputs is utilized for the modeling of bead geometry (Figure 3-a). The specification of the network is as following: *Input layer:* The same as all ANNs, input layer is the layer for feeding the process parameters to the network. Here, WFR, TS, and LP are the input nodes.

*Hidden layer 1:* This layer is the first computational layer. Each neuron gets the inputs to the neurons and apply the activation function on it to create the outputs for the next layer. The output of the j-th
neuron in layer k is calculated as it is shown in equation (2). Ψ is the assumed activation function. $w_{i,k}^j$ is the weight to be multiplied to the input from the i-th output of the previous layer. Each neuron j has its own bias and added is before applying Ψ.

$$y_k^j = \Psi \left( \sum_{i=1}^{n} w_{i,k}^j x_i + b_j \right) \qquad (2)$$

The utilized Ψ is Gaussian Error Linear Unit (GELU) and is calculated based on equation (3).

$$GELU(x) = xP(X \le x) \triangleq x\Phi(x) = x \cdot \frac{1}{2} [1 + \operatorname{erf}(\frac{x}{\sqrt{2}})] \qquad (3)$$

$x\Phi(x)$ is defined as GELU, and $\Phi(x)$ is the standard Gaussian cumulative distribution function. The term $\operatorname{erf}(z)$ is the "error function" and its function defined in equation (4):

$$\operatorname{erf}(z) = \frac{2}{\sqrt{\pi}} \int_{0}^{z} e^{-t^2} dt \qquad (4)$$

Based on the evaluations, GELU activation function performance proved to be better than others like Rectified Linear Unit (ReLU), tangent hyperbolic (Tanh) or sigmoid. This is attributed to the shape of such an activation function since it takes the advantage of linear function for positive values and opposite to ReLU it is not returning zero values abruptly for negative values. As it can be seen in Figure 3-b, it converges to zero smoothly and this is helpful for training the network for bead geometrical features. The number of neurons in this layer is set to 32, and all the neurons utilizes GELU as activation function. *Hidden layer 2*: Details for the second hidden layer including the activation function and the relation between inputs and outputs are the same as the previous layer. The number of neurons in this layer is set to 64 based on the assessment of different values for it.

<figure><img src="image_9.png" /><figcaption>Figure 3. a) Architecture of the proposed ANN, b) comparison between GELU and RELU</figcaption></figure>

*Output layer*: In this layer as the last layer of the architecture, the assumed response parameters including bead width, height, and area is obtained.

*ANN evaluation details*: The loss function to calculate the difference between ANN output and the target values is set to Mean Square Error (MSE) loss function (equation (5)).

$$\text{mean squared error (MSE)} = \frac{1}{m} \sum_{i=1}^{m} (y_i - f_i)^2 \qquad (5)$$

In DL, optimization method is one of the key parts of the architecture and determines the way by which the network tries to learn and make the model accurate. The optimization method utilized in this study is from Adaptive Moment Estimation (Adam) family. In Adam optimization method, which is an adaptive method for training the network, by combining the RMSprop and weighted average concept of momentum, it is tried to increase the speed and accuracy of training procedure. In the traditional Adam method, while adding the regularization term (as it can be seen in Table 3, step 7 yellow part), the algorithm is adding the regularization term to the cost function. As a result, it can easily track the
regularization term and affect the performance of training. To tackle this problem, AdamW method is introduced [24]. Instead of adding the L2 regularization to the gradient $g_t$, it is added to weight updated part as weight decay parameter (Table 3, step 10 green part). It is proved that this method has better performance than Adam, and weight decay coefficient is set to 0.01.

<table><caption>**Table 3.** The steps of implementing Adam and AdamW algorithms</caption><caption>Adam and AdamW optimization algorithms</caption><tbody><tr><td>1.</td><td>Given α<sub>t</sub> (learning rate), β<sub>1</sub> (momentum), β<sub>2</sub> (RMSprop factor), ω (weight decay), and ε (constant equals to 10<sup>-8</sup>)</td></tr><tr><td>2.</td><td>Initialization η (learning rate), m and v (first and second momentum vector), time t</td></tr><tr><td colspan="2"><strong>Loop:</strong></td></tr><tr><td>3.</td><td>t → t+1</td></tr><tr><td>4.</td><td>Applying the gradient on batch: ∇f<sub>t</sub>(x<sub>t-1</sub>)</td></tr><tr><td>5.</td><td>Calculation of g<sub>t</sub>: ∇f<sub>t</sub>(x<sub>t-1</sub>) + w<sub>t</sub>x<sub>t-1</sub></td></tr><tr><td>6.</td><td>Calculation of 1<sup>st</sup> momentum: m<sub>t</sub> → β<sub>1</sub>m<sub>t-1</sub> + (1 - β<sub>1</sub>) g<sub>t</sub></td></tr><tr><td>7.</td><td>Calculation of 2<sup>nd</sup> momentum: v<sub>t</sub> → β<sub>2</sub>v<sub>t-1</sub> + (1 - β<sub>2</sub>) g<sub>t</sub><sup>2</sup></td></tr><tr><td>8.</td><td>Bias correction of m<sub>t</sub> and v<sub>t</sub>: m<sub>t</sub> → m<sub>t</sub>/(1-β<sub>1</sub><sup>t</sup>) , v<sub>t</sub> → v<sub>t</sub>/(1-β<sub>2</sub><sup>t</sup>)</td></tr><tr><td>9.</td><td>readjust η if any decay is needed</td></tr><tr><td>10.</td><td>Weight update: x<sub>t</sub> → x<sub>t-1</sub> - η(α<sub>t</sub>m<sub>t</sub>/√v<sub>t</sub>+ ε + w<sub>t</sub>x<sub>t-1</sub>)</td></tr></tbody></table>

# 4. Results and discussion

## 4.1. Statistical analysis of experimental data

In the present study, CCD DoE is selected to evaluate the sensitivity of the response parameters (width, height, and area of a single bead) to a variation of process parameters. Due to the specification of the selected DoE, all the interaction terms and quadratic terms can be considered for statistical analysis. Pareto charts, which introduce the most influencing parameters to the geometrical features, are illustrated in Figure 4. It is worth mentioning that p-values less than 0.05 is considered as the criteria for considering a parameter as sensitive term. Whereas all the response parameters are sensitive to WFR and TS, there are trivial differences in the sensitivity of other terms, including individual LP, quadratic or interaction terms.

For bead height, quadratic terms of TS (BB), and WFR (AA) are among the parameters that are affecting the output. Bead width is the response parameter with the highest number of effective factors. As can be seen in Figure 4-b, along with AA and BB as the quadratic terms of WFR and TS, LP is a sensitive term to the variation of bead width as the output. Bead area is the parameter with TS, WFR, quadratic term of TS (BB), and the interaction term of WFR and TS (AB) as the most sensitive parameters. While all the geometrical features have their own sets of sensitive parameters, WFR, TS, and quadratic term of TS are their common factors as the effective parameters to model them.

<figure><img src="image_10.png" /><figcaption>**Figure 4.** Pareto charts for a) bead height, b) bead width, and c) bead area based on p-values less than 0.05 as the sensitivity line</figcaption></figure>
After specifying the most sensitive parameters to the assumed geometrical features, the degree of correlation between all the process parameters and each response parameter is essential for modeling the bead geometry. Table 4 provides the values for the criteria including R² and R²<sub>adj</sub> for each response parameter. All the values are over 90%, and as a result the inputs-outputs correlation is satisfying. However, the lowest R² and R²<sub>adj</sub> are attributed to width and should be considered for ANN modeling.

<table><caption>**Table 4.** R² and R²<sub>adj</sub> for geometrical features</caption><thead><tr><td>Response parameter</td><td>R<sup>2</sup></td><td>R<sup>2</sup><sub>adj</sub></td></tr></thead><tbody><tr><td>Bead height (mm)</td><td>98.45</td><td>97.05</td></tr><tr><td>Bead width (mm)</td><td>96.00</td><td>92.41</td></tr><tr><td>Bead area (mm<sup>2</sup>)</td><td>99.51</td><td>99.08</td></tr></tbody></table>

## 4.2. ANN-based modeling of geometrical parameters

The introduced ANN is utilized to model bead geometries, including width, height, and area. To ensure the accuracy of the training process and prevent over or underfitting, 15% of training dataset was separated and utilized as the validation data. Whereas the training process is initialized with 2000 epochs, it stops as soon as the validation dataset loss increases continuously. The best model coefficients and specification in terms of validation results are saved and loaded for evaluation of testing data.

The training and validation loss reduction and the stopping epochs are presented in Figure 5. The best epochs for training bead height, width, and area are 790, 280, and 295, respectively. It can be observed that after rapid fluctuations and decrease of MSE as the loss function for the considered response parameters, the improvement rate decreases and stops with less than 1000 epochs.

After training and validating the performance of the model, the testing process is required to be accomplished. The best approach is to plot the fit line between model output as the predicted values and the target values as ground truth data. Figure 6 provides the fit line and the line y=x as the best results with R² equals to 1. As it can be observed, the fitted lines for bead height and area are perfectly matching the model outputs with R² more than 0.98 and 0.99 respectively. R² for bead width is less than other two features and is slightly over 0.82. As it was shown in Table 4, R² values for width based on statistical analysis of CCD DoE is less than R² for height and area. However, this value for our ANN model is even lower and it is due to two main reasons: a) In general, the bead width is more challenging for modeling based on statistical analysis, and b) in the modeling approach, all the conducted DoEs are utilized to create the model. As a result, while it is more generalized and reliable model, the variations of parameters are higher in comparison to a single CCD DoE and modeling the bead geometry based on the whole data is more sophisticated.

<figure><img src="image_11.png" /><figcaption>**Figure 5.** Validation and training loss for modeling a) bead height, b) bead width, and c) bead area, and their best validation epoch</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Figure 6.** ANN model fit line for a) bead height, b) bead width, and c) bead area, and comparison of them with line y=x</figcaption></figure>

As the last analysis, Table 5 provides the values for MSE and RMSE of training and testing datasets as the criteria for assessing the accuracy of the ANN model. Since the model is built and trained based on training dataset, it is obvious that MSE and RMSE values are higher for testing data. Bead height has the lowest MSE and RMSE for both training and testing datasets, approving that the model for height is the most accurate model. In addition, the values of the MSE and RMSE loss functions for the bead area are quite close to those for height with less than 0.00005 and 0.00123 differences, respectively for training. However, the same criteria for bead width are higher in comparison to values for height and area. MSE and RMSE for testing data in modeling of bead width are 0.01642 and 0.12817, respectively.

<table><caption>**Table 5.** MSE and RMSE for training and testing datasets in terms of bead geometrical features</caption><thead><tr><th rowspan="2">Response parameter</th><th colspan="2">Training</th><th colspan="2">Testing</th></tr><tr><th>MSE</th><th>RMSE</th><th>MSE</th><th>RMSE</th></tr></thead><tbody><tr><td>Bead height (mm)</td><td>0.00037</td><td>0.01939</td><td>0.00155</td><td>0.03939</td></tr><tr><td>Bead width (mm)</td><td>0.00305</td><td>0.05523</td><td>0.01642</td><td>0.12817</td></tr><tr><td>Bead area (mm²)</td><td>0.00042</td><td>0.02062</td><td>0.00730</td><td>0.08546</td></tr></tbody></table>

**5. Conclusion**

In this study aimed to model bead geometries of WLAM processes on an Inconel 625 wire based on ANN. Three different DoEs and statistical analysis are deployed to consider the correlation between process and response parameters and model the geometrical features. A length of 10 mm in the middle of printed beads is considered for geometrical details. The main inferred conclusions are:

* The best performance is attributed to an ANN with two hidden layers including 32 and 64 neurons, respectively. The assumed activation function is GELU which takes advantage of linear function for positive values and opposite to ReLU it is not returning zero values abruptly for negative values. These specifications are proved to be effective in the training process. 15% of training data was separated and fed to the network as the validation data. It is proved that for all the response parameters, the required epoch numbers were less than 1000.

* Based on statistical analysis, wire feed rate, travel speed and the quadratic term of travel speed are common influencing parameters to all geometrical features. However, quadratic term of wire feed rate is a sensitive factor to height, and laser power and quadratic term of wire feed rate is other sensitive terms for bead width. For bead area, the interaction between wire feed rate and travel speed is an additional sensitive factor.
* While the ANN models R² for response parameters are acceptable (0.988, 0.824, and 0.993 for height, width, and area), the values for height and area are more significant. As a result, MSE values for height and area are less than 0.0004 and 0.007 for training and testing data, respectively.

* While MSE and R² values for bead width were acceptable, they were lower in comparison to the statistics for other response parameters. There are reasons for that. The statistics obtained from RSM with lower values for beads width approve that modeling the bead width is more challenging than height and area. In addition, some instabilities in the process including the wobbling of wire can make the printed bead weaving and complicated to model.

The future research plan includes improving the stability and accuracy of the WLAM process. Additionally, investigating the printing of walls and thermal management challenges during the process.

## Acknowledgements

This research has been supported by the project TANDEM (4056/31/2021) Business Finland under the SMART EUREKA cluster on Advance manufacturing program and partially supported by the project Multi-disciplinary Digital Design and Manufacturing - D2M (346874) Academy of Finland / Academy Research Fellow.

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