Wheel Impact Test by Deep Learning Prediction of Location and Magnitude of Maximum Stress Seungyeon Shin1a Ah-hyeon Jin1a Soyoung Yoo13 Sunghee Lee3

2025-04-29 0 0 2.49MB 28 页 10玖币

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Wheel Impact Test by Deep Learning: Prediction of Location and

Magnitude of Maximum Stress

Seungyeon Shin1,a, Ah-hyeon Jin1,a, Soyoung Yoo1,3, Sunghee Lee3,

ChangGon Kim2, Sungpil Heo2,

Namwoo Kang1,3,*

1Cho Chun Shik Graduate School of Mobility, KAIST, 34051, Daejeon, South Korea

2Hyundai Motor Company, 445706, Hwaseong-Si, Gyeonggi-Do, South Korea

3Narnia Labs, 34051, Daejeon, South Korea

*Corresponding author: nwkang@kaist.ac.kr

a Contributed equally to this work.

Abstract

For ensuring vehicle safety, the impact performance of wheels during wheel development must be

ensured through a wheel impact test. However, manufacturing and testing a real wheel requires a

significant time and money because developing an optimal wheel design requires numerous iterative

processes to modify the wheel design and verify the safety performance. Accordingly, wheel impact

tests have been replaced by computer simulations such as finite element analysis (FEA); however, it

still incurs high computational costs for modeling and analysis, and requires FEA experts. In this study,

we present an aluminum road wheel impact performance prediction model based on deep learning that

replaces computationally expensive and time-consuming 3D FEA. For this purpose, 2D disk-view

wheel image data, 3D wheel voxel data, and barrier mass values used for the wheel impact test were

utilized as the inputs to predict the magnitude of the maximum von Mises stress, corresponding location,

and the stress distribution of the 2D disk-view. The input data were first compressed into a latent space

with a 3D convolutional variational autoencoder (cVAE) and 2D convolutional autoencoder (cAE).

Subsequently, the fully connected layers were used to predict the impact performance, and a decoder

was used to predict the stress distribution heatmap of the 2D disk-view. The proposed model can replace

the impact test in the early wheel-development stage by predicting the impact performance in real-time

and can be used without domain knowledge. The time required for the wheel development process can

be reduced by using this mechanism.

1. Introduction

To ensure vehicle safety, vehicle wheels sufficiently durable to meet safety requirements need

to be developed. Accordingly, a strict impact test must be performed during wheel development to test

impact damage. However, completing a wheel design involves inspecting the wheel safety through the

wheel impact test, which takes significant time and money owing to trial and error during wheel

development. Therefore, vehicle manufacturing companies need a solution to reduce the time in the

wheel design and manufacturing stages through a rapid impact analysis of the various design proposals.

Although the actual wheel impact test has been replaced by computer simulations such as finite

element analysis (FEA), as proposed by Chang and Yang (2009), it is still time-consuming because the

computationally expensive simulation process needs to be repeatedly executed, and FEA experts are

required to inspect the wheel performance. Accordingly, recent studies have suggested methods for

replacing FEA through deep learning methodologies in various applications such as stress distribution

of the aorta (Liang et al., 2018), stress prediction for bottom-up SLA 3D printing processes (Khadilkar

et al., 2019), stress prediction of arterial walls (Madani et al., 2019), stress field prediction of

cantilevered structures (Nie et al., 2020), and natural frequency prediction of 2D wheel images (Yoo et

al., 2021). These approaches can considerably contribute to accelerating the analysis process. However,

there are still limitations to their use in real-world problems owing to the application domain. A more

detailed review is presented in Section 2.

In this study, we present a 3D wheel impact performance prediction model based on deep

learning that can replace 3D FEA of the aluminum road wheel impact test used in real-world product

development processes. The objective of this study is to replace the 3D FEA process for wheel impact

analysis, which requires high computational cost, to provide the impact performance of a wheel design

in the conceptual design stage, thereby reducing the time required for wheel development. Synthetic 3D

wheel data were generated through the 3D wheel CAD automation process (Oh et al., 2019; Yoo et al.,

2021; Jang et al., 2022) using 2D disk-view images (spoke designs) and rim cross-sections, and the

impact performance results were collected through FEA impact test simulation. Hence, we constructed

a real-time prediction model that predicts the magnitude of the maximum von Mises stress, the

corresponding location, and the overall stress distribution of the 2D disk-view using this mechanism.

The novelty of this study is as follows. This is the first study to apply deep learning to vehicle

system impact tests. Second, various types of data were used as input and output through the multimodal

autoencoder architecture to improve prediction accuracy. Third, to overcome the data shortage problem,

a 3D convolutional variational autoencoder (cVAE) is used for transfer learning to extract important

features of the 3D wheels. Through the proposed model, the impact performance of a wheel design can

be checked in real-time, even in the conceptual design stage, by predicting the magnitude of the

maximum von Mises stress, and the location of the maximum stress can also be known, informing the

parts to be supplemented in the wheel design. The overall von Mises stress distribution of the 2D disk-

view was also predicted, providing more information to the designer. Accordingly, this method can be

easily utilized by general designers without engineering expertise, thereby enabling rapid impact

performance inspection of various design proposals. The same process can be applied to any product

that requires an impact test in addition to the wheels.

The remainder of this paper is organized as follows. Section 2 summarizes the related studies,

and Section 3 presents the data collection and preprocessing steps for training the model and the

architecture of the proposed model. The prediction results are discussed in Section 4. Finally, Section

5 presents conclusions, limitations, and directions for future work.

2. Related Work

Recently, studies to solve various real-world engineering problems using deep learning are

being conducted, such as autonomous driving (Grigorescu et al., 2020), smart factories (Essien and

Giannetti, 2020), and environmental engineering (Ostad‑Ali‑Askari et al., 2017; Ostad‑Ali‑Askari and

Shayan, 2021). In addition, deep learning can be used in engineering problems to efficiently develop

various products as the product development process requires repetitive iterations to obtain an optimal

design (Kim et al., 2022; Shin et al., 2022; Yoo and Kang, 2021). In particular, design optimization for

product development is time-consuming and computationally costly owing to repeated simulations such

as FEA and computational fluid dynamics (CFD), which are essential for inspecting the safety of a

product. Therefore, studies have recently emerged to replace the simulation process by applying various

deep learning methodologies (Deng et al., 2020; Lee et al., 2020; Qian & Ye, 2021; Zheng et al., 2021).

This section focuses on deep learning studies that predict the stress distribution in structures.

Liang et al. (2018), which is an early study that applied deep learning to replace FEA, predicted the

aortic wall stress distribution according to the shape of thoracic aorta. Shape encoding of the aorta shape

was performed through principal component analysis (PCA) for this purpose, and the stress distribution

of the aorta was predicted through a neural network. Madani et al. (2019) predicted the maximum von

Mises stress value and the corresponding location for 2D arterial cross-sectional images to replace finite

element simulation using machine learning. Nie et al. (2020) predicted the stress distribution of a 2D

linear elastic cantilevered structure subjected to a static load to accelerate structural analysis. In this

study, two networks—SCSNet and StressNet—were proposed, and the von Mises stress distribution

was predicted by inputting various structures, external forces, and displacement boundary conditions.

However, the aforementioned studies are predictions for the 2D domain and have limitations when

applied to actual product development. In real-world problems, high-dimensional data such as 3D data

must be considered. However, high-dimensional data are difficult to train and require considerable

training data. Therefore, appropriate data representation and training methods for high-dimensional data

must be devised to replace 3D simulations with deep learning.

Similar to our study, Khadilkar et al. (2019) proposed two CNN-based networks to predict the

stress distribution by layer for the bottom-up SLA printing process among manufacturing methods. In

particular, the 2-stream CNN network, which exhibits the highest performance among them, uses a

binary image of the cross-section and a 3D model up to the previous layer as input, in the form of a

point cloud, to predict the stress distribution of a layer cross-section. The 2D image passes through the

convolutional layer, and the 3D point cloud enters the network by adding each feature vector that passes

through PointNet (Qi et al., 2017). This method has an input similar to that of our method. However,

our proposed method predicts the maximum von Mises stress value and the corresponding location as

well as the 2D stress distribution using voxel-based 3D data. Khadilkar et al. (2019) predicted the stress

distribution for 2D domains, whereas our proposed methodology could predict the 3D coordinates of

the maximum von Mises stress location for the 3D domain, enabling the replacement of the existing 3D

FEA.

Two major issues must be considered for deep learning in the 3D domain. A considerable

problem in the field of 3D deep learning is that it requires a large amount of training data. However,

collecting a sufficient amount of 3D data in practice is difficult; therefore, we need to construct a model

with high accuracy, even with limited data. Second, the representation of the 3D data is important when

dealing with 3D data. In the field of 3D deep learning, representation methods such as point clouds,

meshes, and voxels are commonly used.

The point-cloud-based method represents the shape through a set of points distributed near the

surface of a 3D shape (Bello et al., 2020). However, the point cloud method has the disadvantage that

expressing the details of a shape is difficult because it is sparse. The mesh-based method represents a

3D shape using a polygon-shaped face made of vertices. However, this method is sensitive to the quality

of the input mesh and the surface patch of the shape may not be stitched. The voxel-based method uses

volumetric data to express a 3D shape in a cube form. However, the voxel method requires a large

amount of memory storage because it expresses the occupied and non-occupied parts (Ahmed et al.,

2018). The resolution of the voxel needs to be increased to express the 3D shape in more detail, but the

problem is that the higher the resolution, the more the parameters increase. Several studies have been

conducted to solve the computational cost problem of the voxel method. For example, some studies

have been performed to express 3D shapes with high resolution using an octree-based method (Häne et

al., 2017; Riegler et al., 2017; Tatarchenko et al., 2017).

In this study, we propose a multimodal autoencoder architecture that uses multiple modalities

in parallel as input and output. As in Bachmann et al. (2022), it is typically used to handle multiple

sources such as images, text, and audio. We constructed a prediction model based on a multimodal

autoencoder architecture that uses various dimensions of inputs and outputs in parallel to overcome the

data shortage problem and reduce the computational cost by utilizing a latent vector of the input to

reduce the dimension of the high-dimensional data. To this end, we used voxel-based 3D wheel data to

extract the features of the 3D CAD data using a 3D CNN-based convolutional variational autoencoder

(cVAE). Training was carried out using the latent vector of 3D CAD data and 2D wheel image data

through the pretrained 3D cVAE model and the 2D convolutional autoencoder (cAE) model, and

accurate results were derived even with 2,501 3D CAD data.

3. Deep Learning Framework for Wheel Impact Test

3.1. Overall Framework

The entire study process comprises four steps. In Stage 1, the 3D road wheel CAD datasets

were automatically generated. Spoke designs were first collected from the Internet, provided by

Hyundai Motors, and then generated using topology optimization. The rim cross-sections of the 3D

wheels were also collected, and six representative designs were selected for use in 3D CAD generation.

In Stage 2, wheel impact analysis was performed using the generated 3D wheel data. Based on the

analysis results, post-processing was performed to remove outliers, and the magnitude of the maximum

von Mises stress and its location coordinates were extracted. Stage 3 involves developing 3D cVAE

and 2D cAE, which are dimensionality reduction models used to improve the performance of the

proposed model. These models were used to reduce the dimensions of the input data. Finally, Stage 4

is the phase of developing a deep learning model that predicts the magnitude of the maximum von Mises

stress, the corresponding location coordinates (x, y, and z), and the overall von Mises stress distribution

in the 2D disk-view. The proposed model architecture and hyperparameters were selected by conducting

various experiments while varying the input and output of the model. Finally, the performance of the

proposed model was confirmed by conducting transfer learning using an actual wheel used in real life.

The overall process proposed in this study is illustrated in Figure 1.

3.2. Stage 1: Generating 3D Wheel Data

Several detailed 3D wheel models used in reality are needed to construct an accurate wheel

impact performance prediction model. However, considerable synthetic concept wheel data was

generated and used for training because sufficiently detailed 3D wheel data are difficult to obtain. The

3D CAD automation framework proposed by Yoo et al. (2021) was used herein. The framework

comprises a stage that handles 2D spoke designs (disk-view images) and rim cross-sections and a stage

that creates these into 3D CAD. This process automatically generated a large amount of 3D roadwheel

CAD. First, 2D work dealing with spoke designs and rim cross-sectional images was performed.

Accordingly, spoke designs and rim-cross-section images were collected for this purpose, as explained

in Sections 3.2.1 and 3.2.2.

3.2.1 Disk-view spoke design data collection and preprocessing

First, 2D disk-view spoke design images for 3D CAD generation are collected in various ways.

The three main collection methods were as follows. First, 603 binary wheel images available on the

Internet were collected, and topology optimization using the collected images as the reference design

was performed to collect 177 generative design piece wheels. Topology optimization was performed

on the wheel pieces, as shown in Figure 2, and they were rotated to make a complete wheel, solving the

conventional problem of generative design wherein the symmetry of the generation result is not

guaranteed. Here, 10 types of equal wheel pieces from 4 to 13 pieces were used, and generative design

Figure 1. Overall framework of the proposed method

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WheelImpactTestbyDeepLearning:PredictionofLocationandMagnitudeofMaximumStressSeungyeonShin1,a,Ah-hyeonJin1,a,SoyoungYoo1,3,SungheeLee3,ChangGonKim2,SungpilHeo2,NamwooKang1,3,*1ChoChunShikGraduateSchoolofMobility,KAIST,34051,Daejeon,SouthKorea2HyundaiMotorCompany,445706,Hwaseong-Si,Gyeonggi-Do,SouthK...

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Wheel Impact Test by Deep Learning Prediction of Location and Magnitude of Maximum Stress Seungyeon Shin1a Ah-hyeon Jin1a Soyoung Yoo13 Sunghee Lee3

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