Data-driven Prediction of Temperature Evolution in Metallic Additive Manufacturing Process

Thinh Quy Duc Pham. Thu Dau Mot University, Vietnam. University of Liège, UEE Research Unit, MSM division, allée de la Découverte, 9 B52/3, B 4000 Liège, Belgium. Truong Vinh Hoang. RWTH-Aachen University, Germany. Quoc Tuan Pham. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Vietnam. Than Phuc Huynh. Thu Dau Mot University, Vietnam. Van Xuan Tran. Thu Dau Mot University, Vietnam. Corresponding author : xuantv@tdmu.edu.vn Seifallah Fetni. University of Liège, UEE Research Unit, MSM division, allée de la Découverte, 9 B52/3, B 4000 Liège, Belgium. Laurent Duchêne. University of Liège, UEE Research Unit, MSM division, allée de la Découverte, 9 B52/3, B 4000 Liège, Belgium. Hoang Son Tran. University of Liège, UEE Research Unit, MSM division, allée de la Découverte, 9 B52/3, B 4000 Liège, Belgium. Anne Marie Habraken. University of Liège, UEE Research Unit, MSM division, allée de la Découverte, 9 B52/3, B 4000 Liège, Belgium. Fund for Scientific Research F.R.S-FNRS


Intr Introduction oduction
Additive Manufacturing (AM) technology is a unique capability for building complex three-dimensional (3D) objects from computer-aided design models. Among many technologies used for metallic AM, Directed Energy Deposition (DED) is an interesting process that is flexible and adapted to repair operation. This method involves the deposition of metallic powder, which is melted via a focused heat source. DED is becoming widely used in industries such as aerospace [1], bio-design [2].
In order to identify optimal process parameters of AM, a design of experiments is often used [3]. However, performing the experiments of AM to find the optimal parameters is very expensive and time-consuming. The numerical approach, such as the Finite Element Method (FEM), is often employed to simulate the AM process [4]. However, the computing cost of these models remains excessively expensive when performing a large number of simulations. Therefore, it is ESAFORM 2021. MS13 (Additive Manufacturing), 10.25518/esaform21.2599 2599/1 not suitable to directly conduct uncertainty quantification and optimization of process parameters using these models to achieve a robust solution. To overcome this challenge, Machine Learning (ML) techniques are employed to construct surrogate models representing the complex relations between the process parameter and the temperature history defining the part quality [5]. Thanks to the predictive ML-based surrogate models, the simulations can be performed with a negligible computational cost. Recently, the application of ML to the AM field received significant attention from both the industrial and academic sectors [6,7,8]. A comprehensive review of this application can be found in [5].
In AM process, many physical phenomena occur at a short period of time and at a temperature above the melting point of materials. These temperature profiles strongly affect material properties related to the generated microstructures.
Some previous studies were performed to develop the ML-based surrogate model to predict the temperature evolution of the AM process. For instance, the Recurrent Neural Network (RNN) was developed to compute the temperature field for an arbitrary geometry with different scanning strategies 6]. Similarly, the temperature field is also predicted by the surrogate model with Bayesian loss function [7]. In addition, in [8], the temperature field was predicted directly by the Physics-Informed Neural Networks (PINNs) without numerical data.
Thus, it is essential to develop a simple ML-based model to directly predict the temperature field of the AM processes with a large number of layers. Based on this review, this study aims to develop a simple ML-based surrogate model to predict the temperature evolution as well as the melting pool size of a DED process of a cubic part with 36 layers. In this article, the data used to train the ML-based model are first generated using the Finite Element (FE) model, which has been validated with experimental data (see Section 2). In Section 3, the ML-based surrogate model is described with its results to predict the temperature evolution and melting pool size during the AM process.
2 ML-based surr 2 ML-based surrog ogat ate model f e model for the DED pr or the DED process ocess In this section, we describe the predictive ML-based model called also the surrogate model to predict the temperature evolution of the DED process. It is built using the following two-step process: (i) Data collection and data pre-processing, (ii) Evaluation of the surrogate model parameters.
For step (i), it is very important that the training data is physically representative. Note that this study focuses on bulk experiments of the M4 high-speed steel material powder. The material properties can be found in detail in [9].
Hereafter, the training data is generated by thermal simulations performed with the updated Lagrangian FE code Data-driven Prediction of Temperature Evolution in Metallic Additive Manufacturing Proc...

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Consequently, the FE model is able to provide high-quality structure data to the ML-based surrogate models described hereafter. Each data group contains 4.8 million data points (see details below). Consequently, a total of 19.9 million data points is used for the training of the FFNN-based model. For step (ii), a FFNN is chosen as it has advantages in approximating highly non-linear and high-dimensional functions. However, training the FFNN with such a small dataset might lead to the over-fitting problem. As a consequence, the training dataset is partitioned into a training dataset and a validation dataset. Beside the input energy, nodal coordinates and time, five additional features are considered as input features to boost the performance of the FFNN-based model including the laser head location in x-and y-direction, the distance from each sampling point to the laser head in x-and y-direction and the current printing layer at each time-step. Note that these additional features are also used in the work of Fetni et. al [11]. For any point of interest, the following 9 features are defined (see Fig. 2).
(i) The input energy (Qint)   Fig. 4), Val_Loss is the validation loss per each epoch (see Fig. 4). The converged value of the validate set is chosen to correspond to a MSE lower than 5×10 −5 as it is acceptable for the problem (see Fig. 4).  detail, the substrate point has a R2 value of 0.995. Fig. 5(b) and Fig. 5(c) show the comparison of the temperature evolution of the cladding P1 and P2 obtained from FE and FFNN-based models. Similar to substrate S point, the temperature evolution of the two cladding points is predicted well by the FFNN-based model with a high R 2 value of 0.991 and 0.999, respectively. As shown in Fig. 5, the oscillations of the temperature profiles as well as the temperature peaks are well captured by the FFNN-based model. Table 1 shows the computational cost and output data size of the FE and FFNN-based models. As observed in Table 1  groups of Section 2, and then they will become the validation data of the FFNN-based model. The value of Qint used to create FEM simulation data for training and validation of the FFNN-based model are described in Table 2. As shown in Fig. 7, the model predicts the other 18 FEM simulation data with a value of R 2 greater than 0.99 while the FFNN-based model is trained by only 5 FEM simulation data (see Table 2). Note that the datasets used in training are also used for validation. Accordingly, the FFNN-based model is able to predict the FEM simulation data created by the input energy  In this study, a simple FFNN-based surrogate model for the prediction of the temperature evolution and melting pool size in the DED process is developed. The numerical data of the evolution of the temperature fields under different process settings are obtained using a high-fidelity finite element model, which has been validated by experimental measurements. Beside the input energy, nodal coordinates and time, five additional features are considered as the input features of the FFNN-based model. Consequently, the surrogate model predicts the temperature evolution as well as the melting pool size of the DED process with excellent accuracies of 99% and 97%, respectively. In the future study, an optimization framework for the process parameters will be developed using Bayesian optimization.