## 5 Conclusions  
The fault diagnosis of railway turnouts is critical for ensuring safe and reliable railway operations. This work developed an effective data-driven approach for diagnosing turnout faults using time-series monitoring data. An intelligent fault diagnosis method for railway turnouts with the support matrix machine was proposed. We have developed a data-driven intelligent method for diagnosing railway turnout faults, which considers the unique attributes of time series monitoring data. To address the noise sensitivity limitations inherent  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \(p\) & **0** & **0.1** & **0.2** & **0.3** & **0.4** & **0.5** & **0.6** & **0.7** & **0.8** & **0.9** \\ \hline Accuracy (\%) & 92.78 & 92.22 & 92.78 & 92.78 & 93.33 & 89.44 & 94.44 & 93.33 & 93.33 & 90.56 \\ \hline \hline \end{tabular}
\end{table}
Table 6: PL-MSMM performance with different parameter \(p\) values.  
Figure 8: Performance graph for the model according to parameter \(C\).  
Figure 9: Performance graph for the model according to parameter \(p\).  
in the multiclass support matrix machine (MSMM), we introduced the pinball loss-based multiclass support matrix machine (PL-MSMM), which is adept at handling noisy industrial data. First, the proposed method employed the original one-dimensional time-series signal to generate a two-dimensional image through data preprocessing. Subsequently, the two-dimensional image matrix was the feature matrix. Next, the proposed PL-MSMM was built by the feature matrix to realize the turnout fault diagnosis. We conducted validation experiments on the proposed method using a current real-world turnout dataset. The effectiveness of the proposed method was verified via a comparative analysis. The proposed method is useful for fault diagnosis of railway turnouts. The diagnostic capabilities developed in this work can enable the condition-based maintenance of turnouts, reducing failures and downtime. By supporting predictive analytics on railway assets, this research promotes sustainable and reliable transportation infrastructure.  
Although the proposed PL-MSMM approach has demonstrated proficiency in diagnosing railway turnout system failures, its reliance on extensive labeled data is a limitation, as such data are often scarce and demand considerable domain expertise for accurate annotation. Hence, the feasibility and expense of data labeling present a clear constraint. Future endeavors will explore semi-supervised or unsupervised learning strategies to diminish the reliance on labeled datasets, aiming to further enhance the efficiency and accuracy of fault diagnosis.  
Conceptualization, M.G. and Z.X.; methodology, M.G.; software, M.G.; validation, M.G.; formal analysis, M.G.; investigation, M.G. and M.M.; resources, Z.X.; writing--original draft preparation, M.G.; writing--review and editing, M.G.; supervision, Z.X.; project administration, M.M. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key Research and Development Program of China under Grant 2022 YFB4300504-4 and Special Fund Project supported by Shanghai Municipal Commission of Economy and Information Technology under Grant 202201034.  
Not applicable.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.  
The authors would like to thank the all-round rail transit control system integrator (CASCO) for providing research data and domain knowledge support.  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} CAE & Convolutional autoencoder \\ CNN & Convolutional neural network \\ MSMM & Multiclass support matrix machine \\ PHM & Prognostics and health management \\ PL-MSMM & Pinball loss-based multiclass support matrix machine \\ SMM & Support matrix machine \\ \end{tabular}