## 4 Results and Performance Evaluation
### Effectiveness of the DLFBR Impulse Detection Algorithm  
For illustration purposes, this paper compared the proposed method with two other impulse detection methods found in the literature. The results of the proposed DLFBR algorithm and the other  
Figure 6: Performance of the DLFBR algorithm with different preprocessing: (**a**) Input with raw signal without any preprocessing; (**b**) input uses preprocessing based on envelope analysis; (**c**) and input uses the proposed shape extraction (SE) preprocessing. two methods, i.e., the soft threshold [21; 22] and constant fault alarm rate (CFAR) [24] methods, are considered by measuring the prediction performance of these methodologies based on the metric of the average precision, which is based on the intersection over union. To compute the precision, the overlap area between the output box from the algorithm and the ground truth box was first found. Then, the area of the union, which consisted of both the output box from the algorithm and the ground truth box, was also calculated. Dividing the area of overlap by the area of union gave the IOU proportion. Due to the variable AE signal and the fact that the impulses are transient and non-periodical, a complete match between the output boxes and ground truth boxes is unrealistic. This paper defines an evaluation metric that rewards output boxes for heavily overlapping with ground truth boxes. The ground truth box that bounds the impulse was generated by hand for each one-second sample signal, which contained the impulse. Then, the intersection over union was calculated between the output of the algorithm and the ground truth box. If the IOU was larger than a predetermined value, the algorithm detected a true positive impulse. Then, the precision was calculated as  
\[\text{Pre}=\frac{\#\text{{true}}\text{{positives}}}{\#\text{{true}}\text{{ positives}}+\#\text{{false}}\text{{positives}}}. \tag{6}\]  
The results of impulse detection for these three methods are shown in Figure 7. These results were obtained from the same sample for illustration purposes. The soft threshold method could not accurately detect the prominent impulse in the presence of background noise, as shown in Figure 7c; in fact, this method missed the second impulse of the sample. In addition, this method did not give good results for the width of the impulse when the predicted box did not cover the whole impulse, i.e., the trailing region of the impulse was cut off because its amplitude value was smaller than the threshold. Therefore, the threshold-based technique is appropriate when the level of the background noise is either unchanged or changes gradually. The CFAR detector's results showed better detection ability, as shown in Figure 7b. Because the threshold from the CFAR detector was more adaptive to the noise, it detected more true impulses. However, it did not perform well in terms of the box width when the signal consisted of strong temporal bursts of high AE activity. Such bursts were composed of overlapping transients with varying duration, strength, and shape. In this paper, in addition to determining the exact position, the width of the impulse is also important for defining the impulse box, which contains enough information related to the entire impulse to purify the leakage signal from the attack signal of the coal fuel stream. DLFBR was robust to different levels of noise and gave better width values for the boundary box of the impulse; it detected most of the impulses with a larger margin regression box relative to the CFAR detector, as shown in Figure 7a. This box covered the length of the impulse and ensured that there was only one box for each impulse. The calculated precision metrics used to evaluate the three algorithms for impulse detection with a boiler tube dataset are shown in Table 2. DLFBR yielded the best results, showing an average precision of 89.80% for the four datasets and higher IOU proportions of overlap between the predicted boxes and the ground truth boxes.