## 4 Conclusions  
In this paper, a novel algorithm (IVMD-SVD) was proposed to automatically select the initial parameters for use in the VMD algorithm. Shannon entropy obtained from the proposed IVMD-SVD was used to categorise the significance of rail base corrosion.  
The statistical parameter distinction degree was used to compare the uniformity of distribution of both energy-based results obtained for particular rail conditions. Compared with the energy ratio results, the proposed entropy-based method was more robust regarding environmental interference, such as that caused by a change of impact location or force.  
A further index, based on maximum and minimum differences from the mean value, was applied to evaluate the capacity for identification of different track conditions. It  
\begin{table}
\begin{tabular}{c c} \hline \hline
**K-Value** & **Accuracy** \\ \hline
3 & 0.625 \\
4 & 0.931 \\
5 & 0.921 \\
6 & 0.949 \\
7 & 0.936 \\
8 & 0.873 \\
9 & 0.875 \\
10 & 0.845 \\
11 & 0.791 \\
12 & 0.764 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Accuracy results for different K-values.  
Figure 14: Accuracy results for different K-values.  
demonstrated that using the proposed method to select the K-value allowed effective identification of track conditions and faults from acoustic impact response signals.  
An RBF neural network was then used for fault classification. The results showed that the proposed method could effectively classify signals from different rail conditions and that the effectiveness was maximised when using the automatically selected K-value.  
In conclusion, this paper describes a new method (IVMD-SVD) and demonstrates its particular effectiveness in extraction of features from impact response signals. The proposed method efficiently selects the optimal K-value to be used in the initialisation of the VMD algorithm, thereby maximising its effectiveness for the decomposition of impact response signals. Furthermore, the results obtained from the algorithm were shown to be effective in the identification and classification of different extents of rail corrosion.  
Additionally, some work needs to be completed in the future. Firstly, the size of the dataset needs to be expanded. Secondly, the current algorithm is only specifically used for the impact response signal. The effectiveness of the proposed method on other signals needs further research.  
This paper was written by [PERSON] ([PERSON]), [PERSON], [PERSON] ([PERSON]), [PERSON] and [PERSON]. The algorithm (IVMD--SVD) was proposed by [PERSON] ([PERSON]). The experimental investigation was developed by [PERSON] ([PERSON]) and [PERSON] ([PERSON]). The result analysing were contributed by [PERSON] ([PERSON]) and [PERSON] Project supervision was provided by [PERSON], [PERSON] and [PERSON]. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the S-CODE project under Grant Agreement No. 730849.  
Not applicable.  
All relevant data are shown in the paper or could be recreated by following the methodology in the paper.  
The authors are deeply grateful to the Birmingham Centre for Railway Research and Education (BCRRE) for the resources provided.  
The authors declare no conflict of interest.