## 5 Experimental Validation
### Experimental Results
#### 5.2.3 Results  
In this section, the statistical results of all methods under four working conditions are given, and their performance differences are comprehensively analyzed. 1. Dynamic range  
As shown in Table 5, the amplitude of Source A is the same as that of Source B, while the amplitude of Source C is relatively low, by 20 dB. The amplitude differences of the identified sources under the four conditions are plotted to analyze the dynamic range performance. According to Equation (31), \(D_{range}\) is calculated for different methods, and the closer to 20 dB, the better the dynamic range performance. If the source location in the vicinity of any of the three real sources cannot be successfully identified, it is labeled \"Failure.\"  
\[D_{range}=\left|\frac{SPL_{\text{SourceA}}^{\text{identified}}+SPL_{\text{ SourceB}}^{\text{identified}}}{2}-SPL_{\text{SourceC}}^{\text{identified}}\right| \tag{31}\]  
It should be noted that the dynamic range here refers to the difference in amplitude between the mean values of sources A and B, and the amplitude of source C, as identified by the method under the test condition, rather than the ability of the algorithm to identify the difference in amplitude between the largest and smallest sources. Since the true value of this value is 20 dB, the value of \"\(D_{\text{range}}\)\" in Figure 13 is calculated to be as close to 20 dB as possible, rather than as large as possible. As shown in Figure 13, the dynamic range of source identification of the VG-SBL method is overall closest to 20 dB, which demonstrates the ability of the method to accurately reconstruct the amplitude difference between the sources. This is of great significance for analyzing the source contribution amount, as well as for practical engineering guidance, such as in structural noise reduction design. For the method labeled \"Failure,\" it means that the method does not have the ability to identify noise sources with 20 dB amplitude difference at the same time. 2. Location distribution of sound sources  
The distribution of the three sources obtained by all methods under four working conditions is given. To more intuitively display the difference in location distribution, the real locations of Source A, Source B, and Source C and the source locations identified by different methods (represented as scatter points) are plotted in one figure. At the same time, take the real locations of Source A, Source B, and Source C as the center of the circle, and use dotted lines to draw multiple concentric circles with a radius of 0.2-1 m and a radius of 0.2 m apart, so that readers can more easily observe the distances between the identified source locations and the real source locations. When the distribution of scatter points is more concentrated near the center of the circle, the source location is identified  
Figure 13: Dynamic range of sound source identification. more accurately. When the method is not successful in identifying a source, the location of the scatter point is still plotted to standardize the number of points. Still, the scatter point is just randomly plotted outside of the circle with a radius of 1 m, which means failure of the method. The results are shown in Figure 14.  
As shown in Figure 14, among all methods, the sound source distributions of OMP and off-grid-\(GL_{1}\) clearly show apparent discrete character, while the RPCA-SBL and the VG-SBL method are the most consistent and concentrated with the actual position distribution. Among the three sound sources, there is no significant difference in the location identification errors between Source A and Source B. The OMP and off-grid-\(GL_{1}\) methods have more significant identification errors for these two sources than other methods. This is because they do not have enough resolution to accurately identify the two sources, resulting in the identified locations being significantly shifted to the outside.