## 3 Results and Performance Evaluation
### Comparative Analysis of Fault Diagnosis Methods  
To evaluate the effectiveness of our proposed fault detection method, we compare it with three other methods: CWT-CNN [26], FFT-CNN [38], and STFT-CNN [39]. The performance of each method is assessed based on the matrices. The results obtained from the proposed and reference methods are presented in Table 5, while the per-class true positive rate is presented in Table 6.  
Figure 14: Fault components used during the experiment (**a**) BF, (**b**) GF, and (**c**) TF. In the proposed method, AE signals are first transformed into CWT scalograms, providing a detailed time-frequency representation. The CWT images are denoised using a Gaussian filter, which smooths the images and reduces noise. This step significantly improves the clarity of the CWT images, ensuring that the feature extraction process focuses on meaningful data for more accurate fault diagnosis. The denoised CWT scalograms are processed by the VGG16 model. The convolutional base of the VGG16 is used for feature extraction, helping its deep architecture and pre-trained weights. To assess the importance of each method within the model, additional experiments are conducted to compare results before and after applying key methods, such as Gaussian filtering and BiLSTM for temporal dependencies, as well as GA for optimized feature selection. The features extracted by the VGG16 are then processed by a BiLSTM network, which captures temporal dependencies in both forward and backward directions. This BiLSTM step enhances the model's ability to recognize sequential fault patterns, contributing to improved classification accuracy. A GA is added to optimize feature selection, reduce redundancy, and focus on selecting the most informative features. By selecting only the most discriminative features, the GA enhances the model's efficiency and classification accuracy. The optimized features are fed into a fully connected layer for final classification. The proposed method achieves an accuracy of 99.6%, outperforming the reference methods, as shown in Table 5. Additionally, the per-class true positive rate of the proposed method exceeds that of the reference methods, as detailed in Table 6.  
In the CWT-CNN method, AE signals are transformed into CWT scalograms, which are then fed into the CNN for feature extraction and classification. The CNN architecture includes convolutional layers, pooling layers, and a flattened layer, followed by fully connected layers for fault classification. The CWT-CNN method achieves an accuracy of 96.5%. The high accuracy of the CWT-CNN method demonstrates the superiority of CWT in obtaining important features of AE signals. However, the method does not explicitly capture temporal dependencies in the data, which results in lower accuracy as compared to the proposed method. The per-class true positive rate of the CWT-CNN is higher than 95% except for the GF, as can be seen in Table 6. Therefore, this method can be used for BF and TF detection in the milling machine. The FFT-CNN method involves transforming AE signals using fast Fourier transform (FFT) to obtain frequency-domain features. The FFT-CNN method achieves an accuracy of 87.5% with a per-class TPR lower than the proposed method, as presented in Tables 5 and 6. The FFT provides valuable frequency-domain insights, but it does not capture the transient and non-stationary nature of AE signals as effectively as CWT. This results in a loss of the most important information necessary for fault detection. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **BF** & **GF** & **TF** & **N** \\ \hline Proposed & 100 & 99 & 99.6 & 100 \\ \hline CWT-CNN & 100 & 87.50 & 100 & 100 \\ \hline STFT-CNN & 100 & 100 & 75 & 87.5 \\ \hline FFT-CNN & 100 & 100 & 87.5 & 62.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Per-class TPR of the proposed and reference techniques.