## 4 Results and Performance Evaluation
### Results for Leak Detection in Boiler Tubes  
To purify the leakage signal from the attack signal of the coal fuel stream, the detected impulses were removed from the AE recorded signals. Then, classification was performed on the impulse-removed signal between the normal and leakage conditions. During the experimental process of leakage detection, the leak stream along with the generated AE signal was continuous but nonstationary. Therefore, the transient impulse that appeared in the recorded AE signal contained less information about the leakage phenomenon. However, most of this was caused by the interaction between the coal fuel and the tube membrane. Removing these impulses helped increase the quality of the leakage  
Figure 7: Performance of impulse detection for different algorithms: (**a**) proposed DLFBR method, (**b**) constant fault alarm rate (CFAR) method, and (**c**) soft threshold method.  
signal component, which resulted in higher classification accuracy. This method helped to indirectly evaluate the effectiveness of the proposed DLFBR method. For this reason, the proposed method employs the 1D-CNN classifier to separate the normal and leakage signals in this study. The deep structure of the 1D-CNN architecture and the adaptation of the highly non-linear properties of the network allow this method to obtain salient information from the input data. To demonstrate the efficacy of the DLFBR impulse detection model, we obtained classification results for the leakage and normal signals when the input used the raw AE signal (without removing the impulse) and when the input had the impulse removed.  
The 1D-CNN used all four channels of each dataset as inputs for the neural network. The results of the classification accuracy are presented in the first column of Table 3. By using the input where the impulse had been removed, the classification accuracy was increased by 14.65%. However, this result shows low classification accuracy because the intrinsic information inside the signal is complex, and constructing an optimized neural network structure requires a huge effort. Alternatively, the frequency spectrum, which presents useful and stable details about the leak signal, can be utilized as an input for the 1D-CNN. In the frequency spectrum, normal noise is shown as low-frequency white noise (rumbling), while leaks display a higher frequency (hissing) signal. The classification results for the normal and leakage signals using the frequency spectrum as the input are shown in the second column of Table 3, and the confusion matrices are depicted in Figure 8. It can be seen that the classification model's average accuracy with the frequency spectrum input from the impulse-removed signal was 99.8%. This is an increase of 0.2% compared to using the signal without removing the impulse. This means that the employed classifier can accurately classify most of the testing samples. Specifically, the neural network can correctly classify 99.8% of the instances in the normal class; 99.8% of the instances belonging to the leakage state of the boiler tube were correctly predicted. Removing the attack impulses from the signal can yield enhanced classification performance.  
Figure 8: Confusion matrix of the one-dimensional convolution neural network (1D-CNN) classification results when the frequency spectrum input had (**a**) a signal with the impulse and (**b**) a signal where the impulse was removed.