## 4 Experimental Application  
In this section, a couple of experiments including single sound source and plate were carried out to compare the reconstruction performances of the four methods. The experiments were performed in an ordinary room where both sound reflection and random disturbing sources exist. The first experimental setup is shown in Figure 9a. A loudspeaker was used as the sparse sound source. Three microphones with a uniform interspacing of 10 cm were used to measure the pressure on the hologram plane. Another microphone was used as a reference to address the problem that the pressure on all grids points could not be measured simultaneously. The relative phase was preserved by a fixed reference microphone. The pressure was measured on the plane 0.2 m from the loudspeaker with a grid of 6 \(\times\) 6 and an interspacing of 10 cm. The reconstruction plane and the equivalent source plane shared the same dimensions of 0.5 m \(\times\) 0.5 m, a grid of 21 \(\times\) 21, and a uniform interspacing of 0.025 m.  
Figure 8: Pressure distributions of **(a)** ERDCESM with \(\
u=0\), **(b)** ERDCESM with \(\
u=1\), **(c)** ERDCESM with \(\
u=3\) and **(d)** ERDCESM with \(\
u=5\) for a simply supported plate at 500 Hz. The two planes were located 0.02 m (reconstruction plane) and 0.001 m (equivalent source plane) from the loudspeaker. The second experimental setup is shown in Figure 9. A steel plate with dimensions of 0.35 m \(\times\) 0.3 m\(\times\) 2 mm was used as the sound source. The plate was fixed by G-type clamps, and it was excited at (0.1 m, 0.1 m) by a vibration exciter. Three microphones with a uniform interspacing of 5 cm were used to measure the pressure on the hologram plane. Another microphone was used as a reference to address the problem that the pressure on all grid points could not be measured simultaneously. The pressure was measured on the plane 5 cm above the plate with a grid of 7 \(\times\) 6 and an interspacing of 5 cm. The reconstruction plane and the equivalent source plane shared the same dimensions of 0.3 m \(\times\) 0.25 m, a grid of 31 \(\times\) 26 and a uniform interspacing of 0.01 m. The two planes were located 0.02 m (reconstruction plane) and 0.001 m (equivalent source plane) above the plate. To evaluate the reconstruction, the pressure on the reconstruction plane was also measured to serve as the reference value. The source maps for a single source based on the four methods are shown in Figure 10. The results showed that for the single source at 500 Hz, it was identified as a large spot in the sound maps of TRESM and CMESM. Compared with the results based on ERDCESM, the resolution of TRESM and CMESM was not satisfactory. For the single source at 2000 Hz, all four methods could detect the position of the target source. However, the accuracy of ERDCESM and CESM was better than that of CMESM and TRESM. Figure 11 shows contour maps of the reconstructed sound pressure at 500 Hz and 2000 Hz. It shows the results based on ERDCESM-\(\
u\) on the reconstruction plane. It can be found that all of them identified the peak of the reconstructed sound pressure at the loudspeaker's location. However, the source map of ERDCESM with order \(\
u=3\) (see Figures 11 and 11f) covered a relatively small area, which demonstrated that it could detect the location of the actual source more accurately. Although there was a position deviation at 500 Hz due to the influence from other interferences, it did not affect the identification of the source localization. Therefore, similar to the simulation, the experimental results also suggested that ERDCESM-\(\
u\) could identify the source with high accuracy and wide dynamic range. Figure 9: Experimental setup: (**a**) Single source; (**b**) Plate sound source. Figure 10: The Experimental results of (**a**) TRESH map at 500 Hz, (**b**) CESM map at 500 Hz, (**c**) CMESM map at 500 Hz, (**d**) ERDCESM map at 500 Hz, (**e**) TRESH map at 2000 Hz, (**f**) CESM map at 2000 Hz, (**g**) CMESM map at 2000 Hz and (**h**) ERDCESM map at 2000 Hz for a single source.