*3.2. Impact Localization Results*

A near-field impact at the point (200 mm, 90◦) is chosen as a typical case to be analyzed first. The impact signals extracted from each sensor of each IMF are shown in Figure 4. From Figure 4, the wave fronts cannot been seen in the high frequency region, including IMF1, IMF2, and IMF3. Additionally, much more noise signal, boundary reflection, and pattern aliasing appear in the IMF5, IMF6, IMF7, and IMF8. Only the wave fronts of impact signals can be easily found in the IMF4.

All the IMFs extracted from the impact signals are used to form the input vector of the near-field 2D-MUSIC model. The measured average velocity on this plate is 1154 m/s [11]. According to the structure dimension, the scanned area is set to be the distance from 0 to 450 mm and the direction from 0◦ to 180◦, and the scanning step length of the distance and direction is 1 mm and 1◦, respectively. The near-field impact obtained at the point (200 mm, 90◦) spatial spectrum **P**MUSIC(*r*, *θ*) is shown in Figure 5. The figure represents the spatial spectrum magnitudes of each scanned point (*r*, *θ*), and the highest pixel point of the figure represents the impact point localized by the presented 2D-MUSIC algorithm. Seen from Figure 5, the spatial spectrum of IMF4 located the impact source, and the direction and distance error are 0◦ and 0.4 cm, respectively.

**Figure 4.** The IMFs using the optimized EEMD to decompose the impact array signals.

Ten estimated results of impact points and the errors compared with actual impact points are listed in Table 1, including seven located results at the spatial spectrum of IMF4, and three located results at the spatial spectrum of IMF5. It shows that ten near-field impacts are in good agreement with the actual impacts. The maximum error is at the impact position (255 mm, 150◦), whose direction and distance error are 3◦and 2 cm, respectively.

**Figure 5.** The spatial spectrums of each IMF estimated by the 2D-MUSIC model.


**Table 1.** The localization results.
