# 1D CNN Based Detection and Localisation of Defective Droppers in Railway Catenary
## 5 Results Analysis and Discussion  
The dataset was used to train the integrated 1D CNN model for fault classification. The optimal hyper-parameters of the two sub-models were obtained by the tuning technique using the training and validating dataset. The details of the simulated dataset and optimal hyper-parameters of the two sub-models along with the conventional CNN model are shown in Table 6. \begin{table}
\begin{tabular}{c c} \hline \hline CNN layers & 3 \\ Number of filters in the first convolutional layer & 64 \\ Number of filters in the second convolutional layer & 928 \\ Number of filters in the third convolutional layer & 896 \\ Optimal hyper-parameters of & Weight initialization & \(3.9753\times 10^{-5}\) \\ Sub-model 1 & Learning rate & \(1.0379\times 10^{-3}\) \\  & Number of filters in the dense layers & 150 \\  & Kernel initialiser & He normal initialiser \\  & Activation function & Relu \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Optimal hyper-parameters of CNN model. \begin{table}
\begin{tabular}{c c} \hline \hline
**CNN Hyper-Parameters** & **Selection Range** \\ \hline Number of filters in the convolutional layers & 64–1536 \\ CNN layers & 1–5 \\ Weight decay & \(1\times 10^{-7}\)–\(1\times 10^{-1}\) \\ Learning rate & \(1\times 10^{-6}\)–\(1\times 10^{-1}\) \\ Number of filters in the dense layers & 10–512 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Selection range of CNN hyper-parameters. The results of the two sub-models and integrated 1D CNN model through evaluating four metrics (accuracy, F1-score, precision and recall) are given in Figures 7-9. The performance in the four metrics is shown using the average values. Considering the metric values for all folds, the standard deviation of the results is small (all standard deviations are lower than 0.01); hence, the authenticity of the training and validating results is proven by using the K-fold cross-validation process. The average results trained by Sub-model 1, Sub-model 2 and the integrated 1D CNN model with different signal noise levels (dB) are presented in Table 7. The integrated 1D CNN model shows excellent classification performances in the four metrics (over 86%). \begin{table}
\begin{tabular}{c c c} \hline  & CNN layers & 2 \\  & Number of filters in the first convolutional layer & 128 \\  & Number of filters in the second convolutional layer & 1024 \\ Optimal hyper-parameter of & Weight initialization & \(1.1813\times 10^{-5}\) \\ Sub-model 2 & Learning rate & \(2.5224\times 10^{-4}\) \\  & Number of filters in the dense layers & 120 \\  & Kernel initialiser & Glorot uniform initialiser \\  & Activation function & Relu \\ \hline  & CNN layers & 5 \\  & Number of filters in the first convolutional layer & 320 \\  & Number of filters in the second convolutional layer & 288 \\  & Number of filters in the third convolutional layer & 704 \\ Optimal hyper-parameter of & Number of filters in the fourth convolutional layer & 864 \\  & Number of filters in the fifth convolutional layer & 576 \\ conventional 1D CNN & Weight initialization & \(1.3829\times 10^{-5}\) \\  & Learning rate & \(4.1412\times 10^{-3}\) \\  & Number of filters in the dense layers & 128 \\  & Kernel initialiser & Glorot uniform initialiser \\  & Activation function & Relu \\ \hline \end{tabular}
\end{table} 
Table 6: \(Cont.\)  
Figure 7: Results of Sub-model 1 through four metrics (25 dB). Figure 8: Results of Sub-model 2 through four metrics (25 dB). \begin{table}
\begin{tabular}{c c c c} \hline \hline Noise power & \multicolumn{2}{c}{Accuracy (\%)} \\  & Sub-model 1 & Sub-model 2 & Integrated model \\ \hline
5 dB & 96.33 & 100 & 96.33 \\
10 dB & 95.28 & 100 & 95.28 \\
15 dB & 95.00 & 100 & 95.00 \\
20 dB & 93.94 & 100 & 93.94 \\
25 dB & 88.76 & 97.7 & 86.72 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Accuracy of the first and second sub-models and the integrated 1D CNN model. Figure 9: Results of the integrated model through four metrics.