A Study on the Prediction of Mechanical Properties of Sheet Metal based on Deep Learning for Stamping Process

Kyungmin Lee; Charmgil Hong; WooHo Yang; Young-Dae Shim; Eun-Ho Lee

doi:10.57062/ijpem-st.2025.00045

Int. J. Precis. Eng. Manuf.-Smart Tech. > Volume 3(2); 2025 > Article

Lee, Hong, Yang, Shim, and Lee: A Study on the Prediction of Mechanical Properties of Sheet Metal based on Deep Learning for Stamping Process

Short Communication

International Journal of Precision Engineering and Manufacturing-Smart Technology 2025;3(2):193-200.

Published online: July 1, 2025

DOI: https://doi.org/10.57062/ijpem-st.2025.00045

A Study on the Prediction of Mechanical Properties of Sheet Metal based on Deep Learning for Stamping Process

Kyungmin Lee¹ · Charmgil Hong² · WooHo Yang³ · Young-Dae Shim^4.⁵ · Eun-Ho Lee^5.^6.⁷

¹Cell Development Team 1, Mobility & IT Battery Development Center, LG Energy Solution Ltd., Daejeon, 34122, Republic of Korea

²School of Computer Science and Electrical Engineering, Handong Global University, 558 Handong-ro Heunghae-eup, Buk-gu, Pohang-si, Gyeongsangbuk-do, 37554, Republic of Korea

³Manufacturing SI Engineering Research & Development Team 3, Hyundai Motor Group, Uiwang-si, Gyeonggi-do 16082, Republic of Korea

⁴George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA

⁵Department of Smart Fabrication Technology, Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon-si, Gyeonggi-do, 16419, Republic of Korea

⁶Department of Mechanical Engineering, Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon-si, Gyeonggi-do, 16419, Republic of Korea

⁷Department of Intelligent Robotics, Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon-si, Gyeonggi-do, 16419, Republic of Korea

Eun-Ho Lee, e.h.lee@skku.edu

Received March 5, 2025 Revised June 4, 2025 Accepted June 4, 2025

This is an Open Access journal distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In the manufacturing industry, efforts are being made to improve product quality by flexibly controlling processes based on material properties. Although several studies have developed methods considering material properties based on mechanics, these methods show insufficient accuracy due to assumptions involved in mechanics theory. Research utilizing artificial intelligence is needed to address these limitations. This work presents the feasibility of applying deep neural networks to predict the mechanical properties of metal sheets with limited data for real-time control of stamping processes. In a stamping process, the mechanical properties of a blank change due to plastic deformation, which can cause difficulties in quality control of products. Using a real-time control system with non-destructive material tests can improve product quality. This paper focused on improving the accuracy of real-time prediction for mechanical properties of blanks using a deep neural network algorithm when the data size is much smaller than that of general cases. Yield stress and plastic strain of metal sheets were predicted using a deep neural network-based approach from 27 features collected with an eddy-current material tester. By designing the model architecture with regularization, the deep learning-based solution provided results comparable to other machine learning approaches under limited sample conditions.

Keywords: Eddy-current · Mechanical property · Deep neural networks · Sheet metal forming · Machine learning

1 Introduction

In automobile manufacturing processes, sheet metal is one of the main materials for car bodies. Metal blanks are deformed in multi-stage stamping processes to build car body parts, and plastic deformation of the metal blank caused by press processes leads to mechanical property changes. Since the changes of mechanical properties are accumulated through all the stamping stages, an appropriate design of deformation path at each press stage is required. Conventional manufacturing processes have been designed based on ideal assumptions that all of the conditions are controlled, resulting in desired plastic strain and mechanical properties from the first to the final stage. However, in real engineering conditions, each stage includes unexpected variables leading to uncontrolled mechanical property changes. The undesired strain and property changes cause failures in the quality control of the products, such as large spring-back and necking in the manufactured product [1,2]. Attempting to completely control more manufacturing variables has been reported steadily [3]. However, as the level of the required product quality increases, the manufacturing process becomes more and more complicated, then the number of variables that need to be controlled increases.

A non-destructive material testing of mechanical properties with a real-time press control can introduce an alternative way to resolve the unpredictable strain and property change issues.

The concept of the way is to measure mechanical properties at the end of each press stage, and the next press process considers the measured properties to control the process variables to make the mechanical properties match the desired target property. Even though the conventional tension test is the most accurate method to measure the mechanical property, it cannot be used in a real-time production process because the tensile test results in the destruction of material; moreover, it is time-consuming. For metal sheets, the eddy-current based material test can be used to measure the material property [4]. A metal blank placed in a magnetic field that changes periodically leads to eddy-current near the surface of the material. Since eddy-current generation is affected by coupled electromagnetic and mechanical properties, eddy-current measuring can provide a prediction of mechanical properties. Some studies have reported predicting the average and variation of virgin material properties by using the eddy-current method [5]. In addition, a recent modeling showed that electrical resistivity is strongly affected by dislocation density, which can be detected by eddy current [6]. In the aforementioned papers, the traditional regression analyses were employed to fit the eddy-current data to the variation of the mechanical properties. While the traditional regression analysis is simple and effective in engineering applications, it has a limitation of accuracy and expandability.

As a subfield in machine learning, deep neural network (DNN) can be outlined as a general data modeling approaches that aim at learning features and underlying decision mechanisms directly from data. Using artificial neural networks as the representation of input data, DNN automatically deduces optimal feature sets and decision models for desired tasks. Accordingly, compared to traditional machine learning, DNN requires fewer human interventions in terms of data curation and feature extraction. Its adaptable and easily modifiable structures allow users to apply the models and methods to various types and domains of data. It is also able to effectively handle and learn from a large amount of data with an increased number of layers and parameters. Moreover, the recent success in deep learning research has influenced many areas, including manufacturing. Its technical breakthroughs resulted in a vast number of state-of-the-art solutions to virtually all data-driven problems, including image classification [7,8], object detection [9], natural language processing [10], human speech recognition [11], semantic video understanding [12,13], etc. These successes in turn are applied to create novel use-cases in many industrial areas, such as smart manufacturing [14], autonomous driving [15], semiconductor package design [16], trimming die inspection [17], synthetic chemistry [18], new drug discovery [19], game playing [20], etc.

This paper presents the feasibility of applying DNN to predict the mechanical properties of metal sheets for real-time control of stamping processes under a limited sample condition. Yield stress is changed according to plastic deformation, and it strongly affects springback and necking defects [21,22]. As yield stress increases, springback also increases; moreover, once the yield stress is over the ultimate tensile strength (UTS), necking defect starts resulting in stress concentration and unstable behavior. Plastic strain is another issue in the metal sheet because it is related to the forming limit. In this work, an eddy current testing machine measures an electrical signal of the blank, and then the DNN model predicts the mechanical properties of the stamping process. The eddy-current machine is specially built for a real-time control system for stamping processes. Since the integrated system of the real-time material testing and controlling required wide range of discussion, including mechanics, electronics, control, material engineering, etc., this paper focuses on improving the accuracy of the real-time prediction; design of the eddy-current testing machine and real-time control of the stamping press are outside the scope of this paper. In this work, 27 pre-strained steel specimens were generated to change the plastic strain and yield stress in the material; the yield stress and plastic strain were recorded during the pre-strain. With the specimens, the eddy-current testing was conducted to measure the current data. The collected data from the 27 specimens is considered insufficient for the DNN method. However, applying the DNN with a small amount of data is meaningful in the manufacturing process, because collecting data in the manufacturing engineering requires a lot of cost. This paper shows that by regularizing and building a model architecture, the DNN model can improve the prediction accuracy. The results show a possibility to apply the DNN to the prediction of the mechanical properties under limited data conditions.

2 Eddy-current Testing

In order to build a deep-learning based model to predict the mechanical properties, specimens with different pre-strain levels were prepared. In the specimen preparation, the tensile test was conducted in order to create accurate pre-strain inside the material, as shown in Fig. 1. The target material of this work is SGACUD sheet, having a 0.7 mm thickness, which is one of the widely used materials in auto manufacturing. The tensile test specimens were built according to ASTM E8 with a 50 mm gauge length and 40 mm width. A universal testing machine (UTM) with 100kN capacity (made by SIMAZU company) was used in this work, as shown in Fig. 1(a), and the tension speed was 1mm/min in the test. Fig. 1(b) presents the 27 specimens with different plastic strain levels, and the yield stress and plastic strain were recorded for each specimen. With the specimens, the eddy-current measuring was conducted. Fig. 2(a) presents the eddy-current measuring machine, which was designed for use in stamping processes of the car body. As shown in Fig. 2(a), the machine can measure the eddy-current generated in the material and present the real-time eddy-current data on the monitor. In order to build the DNN model, the eddy-current was measured at the center of the gage length in this work. The principle of the eddy-current material test is presented in Fig. 2(b). In the probe of the machine, alternating current (AC) is generated through the primary coil, leading to a magnetic field having a frequency. If the target material is placed in the magnetic field, the eddy-current is generated, leading to a secondary magnetic field and the eddy-current in the material. The raw data of eddy-current includes the magnitude and phase of the signal, and they are used to calculate the real and imaginary parts of the impedance of the material. Since the impedance of the material is affected by mechanical properties [23], this work uses the measured impedance of the material of each specimen to predict the material’s properties based on the deep learning algorithm. This work conducted the eddy-current measuring at 1 kHz frequency.

3 Deep Learning-based Property Prediction under the Limited Sample Condition

The key component of this work is to acquire an effective set of feature representations from the eddy-current measurements to predict the mechanical properties of sheet metal specimens. In this work, a data-driven approach has been selected to build regressors based on the observations of the specimen. A common choice of regressor is the linear regression that makes predictions based on a linear weighted combination of observed attributes. This simple method, however, has limitations in many aspects, including accuracy and generalizability. To alleviate such issues and facilitate a more precise model, this work adopts the deep learning approach, which achieves state-of-the-art accuracy in many industrial domains. More specifically, a multi-layer neural network shown in Fig. 3 is applied to capture the relationship between the input eddy-current and target mechanical properties. The model is often referred to as the “universal approximator, emphasizing its powerful modeling capability and wide applicability.

3.1 Modeling a Building

The amount and quality of training data are crucial in building DNN models. In mechanical industries, however, it is often difficult to secure such a dataset, as doing so usually involves a large amount of time and budget. This work particularly considers a similar scenario and aims to obtain accurate predictive models under the small sample condition. When training a model with a limited number of data instances, a common concern is that the resulting model is susceptible to overfitting. That is, given a fixed number of training data, as the parameters (i.e., layers and neurons) of the model increase, it is more likely that the model overfits. Provided that the sample size is low, the chance gets even higher. The followings present how the model is constructed and trained to achieve accurate prediction in this work.

3.1.1 Model Architecture

In order to mitigate the effect of a limited data sample and avoid overfitting, this work first carefully explores and determines the architecture of the regressor. Neural networks are flexible in that the user can design and choose the network topology, which defines how the computation is conducted by the model. Four possible architectures are described below (Fig. 4): Reverse Triangle, Rectangle, Bowtie, and Diamond. Discussion of the four architectures is in section 4.

3.1.2 Regularizing the Model Complexity

Another model-building technique applied in this work is regularization. Regularization is a widely adopted approach to curb overfitting of the training data. Regularization of neural networks can be done in various ways. One method is to add a penalty term to the objective function that suppresses the model, with commonly used types of penalty term shown in Eq. (1): L₂ (also referred to as weight decay or ridge). For the sake of explanation, consider a linear regression model that optimizes the squared error between the prediction and the true target value: ||y − Xθ||², where X and y are respectively the observed input and output values; and θ denotes the parameters of linear regression. An L₂ penalty is defined as:

(1)

θ^ridge=argminθ‖y-Xθ‖2+λ‖θ‖2

(2)

‖θ‖2=θ12+θ22

where ||θ||₂ denotes the p-norm expressed in the unit circle of Eq. (2) and λ is referred to as the regularization coefficient, which controls the effect of the regularization. Practically, the L₂ penalty shrinks those parameters on unimportant features close to zero (Fig. 5).

4 Empirical Study

4.1 Modeling a Building

In order to compare deep neural networks to other machine learning models, regularized Linear Regression (LR), Support Vector Regression (SVR), and Random Forest (RF) are implemented with the Scikit-Learn package. Hyperparameter optimization is executed with Scikit-learn’s ‘GridSearchCV’ function with 10 folds. Since the dataset is limited to 27 data points, dividing the data into a training, test dataset is not appropriate. This work incorporates K-fold cross validation with the help of the Scikit-Learn package. K-fold cross validation tests with the first fold and trains with the other folds. Testing fold changes to the last fold, and the final result averages outputs from every fold. To justifiably assess the significance of DNN, this work includes the prediction with other models. The described model, including DNN, is implemented and optimized through iterative grid search. The machine learning models, including the DNN, are introduced to the eddy-current data so as to establish a representative feature map. Mean and standard deviation from 10-fold cross validation are also appended.

4.2 Metrics

Root mean squared error (RMSE), normalized root mean squared error (NRMSE), and R-squared value (R²) are used for the assessment. RMSE measures the prediction errors on the test data in the original scale of the target values. NRMSE normalizes the RMSE value by the average target value; Hence, NRMSE can be useful when comparing predictions on multiple targets in different scales. The R² describes how accurately the regression model explains the test data.

4.3 Determining the Model Architecture

The candidates of optimal structures are constructed by the PyTorch package. The results of the four possible architectures are in Table 1. Reverse triangle architecture is the most renowned Multi-Layer Perceptron architecture. Its diminishing size of the inside neuron compresses the input information consecutively, and a higher dimension of the feature map will provide a prediction at the end. The rectangle architecture is to transport input data to the output layer without losing the contained information. Bowtie architecture is derived from the shape of the Autoencoder [24]. Autoencoder is used to extract the core feature map and deliver the original shape at the end. It is likely to transmit significant information and gradually converge into the feature map on which is optimized for the task.

A mere triangular-shaped deep neural network architecture is not able to properly describe the I/O relationship. Thus, diamond-shaped architecture is more advantageous in shaping nonlinear relationships by increasing the number of model parameters and complexity effectively. Optimal weight decay hyperparameter and learning rate are investigated empirically. The DNN models are implemented through the PyTorch package.

Fig. 6 illustrates the research plots on diverse weight decay parameters with respect to each architecture candidates. According to Fig. 6, diamond architecture has shown the lowest RMSE trend compared to the other three architectures. For yield stress, the weight decay lambda range that has the lowest RMSE occurs between 9e-7 and 3e-6. Rectangle, bowtie, and reverse triangle architecture are followed. For plastic strain, the weight decay range that has the lowest RMSE occurs between 1e-6 and 3e-5. Bowtie, rectangle, and reverse triangle architecture are followed. Finally, as shown in Fig. 7, a DNN model architecture was formed in a diamond shape.

4.4 Results

4.4.1 Prediction on Yield Stress

Table 2 summarizes the prediction results of the four models on yield stress, and Fig. 8 demonstrates the predicted results. According to the results, the DNN model shows good results even compared to other models under the limited data condition. This result supports the effectiveness of the DNN model in prediction task with an insufficient amount of data. Specifically, the DNN model has resulted in a mean RMSE = 5.12 [MPa] with an acceptable range of standard deviation. Taking the mean of yield stress on dataset 270.82 [MPa] into account, RMSE with mean normalization is 0.0208. R² implicates that the DNN prediction represents 93.72% of the feature map between the input eddy-current and yield stress mechanical property. The SVR shows second second-best prediction results. The traditional data ensemble method, RF, is not able to exhibit its power because of an extremely small dataset.

4.4.2 Prediction on Plastic Strain

Table 3 summarizes the prediction results of the four models on plastic strain. The feature map of plastic strain is more linear than the map of yield stress, so that accurate prediction is attainable from a relatively plain DNN architecture. Fig. 9 shows that the DNN model succeeds in predicting plastic strain with both absolute and relative scale, compared to other models, thereby supporting the idea that the DNN approach with the weight decay is an efficient way to build an I/O feature map with an inadequate dataset. Specifically, the DNN model has resulted in mean RMSE = 0.0096 [mm] with a tolerable amount of standard deviation. Taking the mean of plastic strain on dataset 0.195 [mm] into account, the RMSE with mean normalization is 0.0692. R² implies the DNN prediction represents 91.36% of the feature map between the input eddy-current and plastic strain mechanical property. Although the SVR shows second second-best prediction results, the LR is not able to be applied to practical application. The RF with the bagging data gathering method is also not able to approximate an accurate feature map.

5 Conclusions

This work attempted to apply a deep learning approach to the material property prediction problem that aims to predict the yield stress and plastic strain from the eddy-current measurement. It shows the effectiveness of layer arrangements and weight decay in a small dataset from eddy-current data to be used in real-time control of stamping processes. The result demonstrates that the DNN method with optimized architecture and weight decay can attain proper accuracy even though the input dataset size is insufficient. Moreover, the DNN layer arrangement affects the information learning procedure; for example, an expanding number of neurons seems to learn more information even from a lacking dataset, and a consecutive diminishing layer size exploits customized information for the task. Furthermore, the weight decay parameter also contributes to mitigating overfitting effects. L₂ weight decay prevents excessive increase of neuron weights so that the network does not focus on specific input data. Thus, appropriate usage of layer arrangements and weight decay supports optimization of DNN with a small dataset, allowing the mechanical industry to utilize DNN with less burden from overfitting.

According to the results in Section 4.3–4.4, the DNN model shows its efficiency in predicting the output variable with respect to the deficit of input data. The DNN model successfully accomplishes the practical accuracy in terms of both absolute and relative perspectives, in which traditional models cannot easily achieve. These models’ architecture is fixed with several hyperparameters, so they cannot present enough flexibility in architecture grid research. Hence, exploiting DNN in a complex regression task can be a reasonable choice, in which the task is complicated with specific reasons, such as a lack of data.

DNN’s effectiveness is heavily dependent on an appropriate form of neural network architecture. Nevertheless, the most effective architecture of DNN is different according to the different data. Moreover, specific guideline for neural network architecture is not firmly established, so an extensive iterative grid search is recommended. Moreover, weight decay is also an effective way to alleviate the effect of overfitting. By restricting the range of weight, DNN is able to learn more solidly. Through augmenting dataset with data sampling models, improving generalizability of DNN prediction model is pursued. Various overfitting mitigation techniques such as batch normalization [25] or attention mechanism [26] will be adapted to enhance prediction accuracy.

Declarations

Acknowledgement(s)

This work was supported by Hyundai Motor Group through Hyundai NGV, and by the Technology Innovation Program (K-CHIPS: Public-private joint investment semiconductor R&D program to foster high-quality human resources), No. RS-2024-00403256, funded by the Ministry of Trade, Industry and Energy (MOTIE) of Korea.

Fig. 1

Material testing setting: (a) Tensile test setting and (b) Specimens with different strain levels for eddy-current measuring

Fig. 2

Eddy-current measuring setting: (a) Eddy current measuring setting and (b) Conceptual drawing of the principle

Fig. 3

Conceptual drawing of the neural networks: (a) Abstract description of basic neural network and (b) Multi-layer perceptron

Fig. 4

Model architecture: (a) Reverse Triangle, (b) Rectangle, (c) Bowtie, and (d) Diamond

Fig. 5

Conceptual drawing of L₂ regularization

Fig. 6

Weight decay parameter with respect to each architecture candidate: (a) Architecture research on Yield Stress and (b) Architecture research on Plastic Strain

Fig. 7

DNN model architecture

Fig. 8

Prediction of yield stress

Fig. 9

Prediction of plastic strain

Table 1

Hidden layer description of architecture research candidates

Architectures	Yield stress	Plastic strain
Reverse triangle	16d→16d→8d→8d→4d→4d→2d→2d→2d→d	16d→8d→4d→2d→d
Rectangle	d→d→d→d→d→d→d→d→d→d	d→d→d→d→d
Bowtie	8d→4d→4d→4d→2d→2d→d→2d→2d→4d	4d→2d→d→2d→4d
Diamond	2d→4d→8d→8d→16d→8d→8d→4d→2d→d	2d→4d→8d→8d→4d

Table 2

RMSE, NRMSE, and R² on the prediction of yield stress

	DNN	LR	SVR	RF
RMSE [MPa]	5.1222±1.8928	19.2974±6.5471	12.3949±9.6913	18.5805±7.4906
NRMSE	0.0208±0.0115	0.0737±0.0313	0.0502±0.0434	0.0709±0.0416
R²	0.9372±0.0737	0.1499±0.3492	0.7359±0.2442	0.0383±0.0596

Table 3

RMSE, NRMSE and R² on the prediction of plastic strain

	DNN	LR	SVR	RF
RMSE [MPa]	0.0093±0.0034	0.0336±0.0241	0.0186±0.0167	0.0508±0.0204
NRMSE	0.0472±0.0363	0.2333±0.2374	0.1267±0.0113	0.3376±0.2765
R²	0.9324±0.1424	0.6060±0.3433	0.8598±0.1844	0.1666±0.6392

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Biography

Kyungmin Lee worked as a process engineer at Winder Process Technology team and is currently a research engineer at Mobile Cell Development team, LG Energy Solution (South Korea). His research interests include intelligent manufacturing and electrochemical battery cell design optimization.

Biography

Charmgil Hong received the Ph.D. degree at the University of Pittsburgh, USA. He is an associate professor of the School of Computer Science and Electrical Engineering in Handong Global University, Korea. His research interests include machine learning and data mining techniques to solve large and complex data-driven problems

Biography

WooHo Yang received the Ph.D. degree at the department of Mechanical Engineering, Oackland University (MI, USA). He is currently working as senior manager at E-FOREST Center of Hyundai Motor Company, South Korea. His research interests include sheet metal forming analysis, confluence manufacturing system, autonomous design and manufacturing system.

Biography

Young-Dae Shim received the Ph.D. degree in the department of Smart Fab. Technology, Sungkyunkwan University, South Korea, in 2024. He is currently a Postdoctoral Fellow in the Department of Mechanical Engineering at the Georgia Institute of Technology, Atlanta, USA. His research interests include the development of smart sensing systems using continuum mechanics and electromagnetic-mechanical coupled physics.

Biography

Eun-Ho Lee previously worked as an Engineer at General Motors Research and Development (MI, USA) and at the Samsung Electronics package team (South Korea). He is currently an Associate Professor with the School of Mechanical Engineering, Sungkyunkwan University, South Korea. His research interests include intelligent manufacturing, semiconductor/packaging manufacturing, and multiphysics system design.