# Out-of-Roundness Wheel Damage Identification in Railway Vehicles Using AutoEncoder Models
###### Abstract
Specifically, a significant amount of recent research focuses on the application of ML-assisted data-driven SHM techniques for railway wheel polygonalization detection [3; 20; 21; 22; 23]. Unsupervised Machine Learning techniques, particularly Physics-Informed Generative Adversarial Networks (PI-GANs), have shown significant promise in Structural Health Monitoring (SHM) of Vehicle-Bridge Interaction (VBI) systems. For instance, [PERSON] et al. (2025) [24] proposed a Physics-Constrained Generative Adversarial Network (PC-GAN) for accurately estimating bridge surface roughness from vehicle vibration responses, demonstrating its adequacy under challenging conditions and its potential for rapid bridge pavement inspection. Moreover, [PERSON] et al. (2025) [25] proposed an image-to-image Generative Adversarial Network (GAN) to estimate temporal frequency variations in Vehicle-Bridge Interaction systems, with validation through experiments confirming its effectiveness for bridge condition assessment. Among those, AutoEncoders (AEs) [13; 26] in particular have shown significant promise. AEs are a type of unsupervised ANN that learns efficient data representations by compressing input into a lower-dimensional space and subsequently reconstructing it. By employing AEs as dimensionality reduction techniques and combining them with appropriate metrics, it becomes possible to identify structural behaviors indicative of damage. According to [PERSON] et al. (2024) [27], the three most prominent AE approaches in SHM problems are Sparse AutoEncoders (SAEs) [28], characterized by sparsity constraints; Variational AutoEncoders (VAEs) [29], featuring probabilistic representations of the data; and Convolutional AutoEncoders (CAEs) [30], which incorporate convolutional layers. In their work, [PERSON] et al. (2024) [27] compared the performance of these AEs in SHM problems applied to structures such as frames and bridges, concluding that VAEs exhibited superior performance for the analyzed structural types. This paper presents a comprehensive comparative study of the main AutoEncoder models for OOR wheel damage identification. Our primary goal is to provide researchers with a clear reference for selecting the most suitable model for this type of application. While numerous studies have explored individual AutoEncoder models, there is a lack of direct comparisons among them, making it challenging for researchers and practitioners to determine the most effective approach. To address this gap, this study evaluates the effectiveness of SAE, VAE, and CAE for detecting stages of polygonization. Furthermore, to enhance the detection capabilities, this paper employs an approach that combines these AE models with [PERSON]'s \(T^{2}\) Control Chart to capture and quantify structural variations in railway wheels at different stages of polygonization. This paper utilizes simulated data generated using computational models implemented in ANSYS(r) (version 2022 R2) [31], based on the Finite Element Method (FEM). This methodology is commonly adopted in research [3; 32; 33] due to the significant challenges associated with instrumenting trains with sensors such as accelerometers. As highlighted by [PERSON] et al. (2020) [34], the harsh railway environment, characterized by vibrations, temperature fluctuations, humidity, and dust, poses significant challenges to the deployment and reliable operation of electronic sensors. Moreover, the installation of these sensors often requires access to difficult-to-reach locations and necessitates robust mounting mechanisms to ensure their integrity. Considering this scenario, numerical studies can also provide valuable insights into the robustness of the methodology at different levels of damage or noise in the data.