# Out-of-Roundness Wheel Damage Identification in Railway Vehicles Using AutoEncoder Models
## 6 Conclusions  
In this study, three AE-based methodologies, combined with [PERSON]'s \(T^{2}\) statistics, were compared to detect and quantify structural changes in railway wheels. SAE-\(T^{2}\) stood out for its accurate anomaly detection and computational efficiency, outperforming VAE-\(T^{2}\) and CAE-\(T^{2}\). VAE, on the other hand, faced challenges in generalizing and correctly classifying data. While CAE-\(T^{2}\) produced promising results, SAE-\(T^{2}\) proved to be slightly more accurate in distinguishing between different levels of damage analyzed. Hyperparameter optimization proved to be important in enhancing models' performances, as evidenced by the variation in the results obtained for each model and structure. The choice between SAE and CAE methodologies depends on factors such as runtime and available computational resources. SAE-\(T^{2}\) is more accurate, while CAE-\(T^{2}\) is faster. Considering current technological advances and available data processing capacity, runtime does not necessarily constitute a significant impediment for SAE-\(T^{2}\). VAE, however, proved to be less effective due to difficulties in adjusting the suggestion range of its hyperparameters. For future research, we propose the development of real-time monitoring systems coupling the IoT (Internet of Things) with cloud computing to detect anomalies in an \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Accelerometer** & **CAE** & **SAE** & **VAE** \\ \hline
1 & 3 h 27 min 33 s & 5 h 28 min 17 s & 5 h 45 min 55 s \\
2 & 3 h 34 min 11 s & 5 h 27 min 52 s & 6 h 53 min 19 s \\
3 & 3 h 33 min 12 s & 5 h 35 min 50 s & 6 h 55 min 36 s \\
4 & 3 h 31 min 01 s & 5 h 19 min 23 s & 8 h 19 min 21 s \\
5 & 3 h 36 min 28 s & 5 h 45 min 34 s & 7 h 20 min 29 s \\
6 & 3 h 24 min 27 s & 5 h 15 min 52 s & 6 h 54 min 23 s \\ \hline Average Time & 3 h 31 min 9 s & 5 h 28 min 48 s & 7 h 01 min 21 s \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Individual time per accelerometer and average execution time for each AutoEncoder. automated manner. Additionally, exploring advanced Machine Learning techniques, such as reinforcement learning and Generative Adversarial Networks, may lead to significant advancements in SHM. Incorporating time-frequency analysis techniques may also enrich data analysis and enable the detection of subtle changes in structural behavior. Furthermore, to validate the methodology developed in this work, an experimental campaign will be planned, in which vehicles with wheel defects properly characterized will pass through an instrumented section of the track. Conceptualization, R.F., F.B., and A.C.; methodology, R.F., F.B., and A.C.; validation, R.M. ; formal analysis, R.M. and A.C.; investigation, A.M. and D.R. ; resources, D.R. ; data curation, A.M., A.G., and V.G. ; writing--original draft, R.M. ; writing--review and editing. F.B., A.C., R.F., and D.R. ; supervision, A.C.; project administration, F.B. and A.C.; funding acquisition, F.B., A.C., D.R., and A.M. All authors have read and agreed to the published version of the manuscript. This work was financed by CAPES (Finance Code 0001), Conselho Nacional de Desenvolvimento Cientifico e Tecnologico--CNPq (Brazil)--Grants CNPq/FNDCT/MCTI 407256/2022-9, 402533/2023-2, 303982/2022-5, and 308008/2021-9 and Fundacao de Amparo a Pesquisa do Estado de Minas Gerais--FAPEMIG--Grants BPD-00080-22 and APQ-00032-24.