# Adaptive Sensor Array Error Calibration Based Impact Localization on Composite Structure
## 4 Evaluation on Carbon-Fiber Composite Panel
### Impact Localization Results  
In this section, four different impact cases are evaluated which list in Table 2. To compare the proposed method, classical 1D-MUSIC algorithm [8], adaptive error calibration based 1D-MUSIC, and standard 2D-MUSIC [11] are applied for locating the four impact cases.  
Figure 5: Spatial spectrum estimated by (**a**) standard 2D-MUSIC and (**b**) 2D-MUSIC after error calibration  
Figure 6: (**a**) Experimental setup and (**b**) imprecise PZT sensors array bonded on the aircraft oil tank structure.  
Figure 7 shows the respond array signals of case #1, and its narrow band signals extracted with a center frequency of 20 kHz. From figure, the direct waves between two dashed lines were intercepted as observed signal vectors and entered into the 1D-MUSIC and 2D-MUSIC model. The spatial spectrum of case #1 at the point (131 mm, 108\({}^{\circ}\)) are shown in Figure 8, obtained by classical 1D-MUSIC algorithm, 1D-MUSIC algorithm after error calibration, standard 2D-MUSIC method and the proposed method. The peak of Figure 8a,b represents the direction of impact (1D-MUSIC localization); the highest pixel point of Figure 8c,d represents the distance and direction of impact (2D-MUSIC localization). From figures, both the beam-formings of 1D-MUSIC and 2D-MUSIC algorithm are getting better after sensor array error calibration. The other three spatial spectra obtained are shown in Figures 9  
Figure 8: Spatial spectrum of case #1 estimated by **(a)** classical 1D-MUSIC algorithm, **(b)** error calibration based 1D-MUSIC algorithm, **(c)** standard 2D-MUSIC method and **(d)** the proposed method.  
Figure 9: Spatial spectrum of case #2 at (189 mm, 102°) estimated by **(a)** classical 1D-MUSIC algorithm, **(b)** error calibration based 1D-MUSIC algorithm, **(c)** standard 2D-MUSIC method and **(d)** the proposed method.  
Figure 11: Spatial spectrum of case #2 at (190 mm, 76\({}^{\circ}\)) estimated by (**a**) classical 1D-MUSIC algorithm, (**b**) error calibration based 1D-MUSIC algorithm, (**c**) standard 2D-MUSIC method and (**d**) the proposed method.  
Figure 10: Spatial spectrum of case #2 at (76 mm, 121\({}^{\circ}\)) estimated by (**a**) classical 1D-MUSIC algorithm, (**b**) error calibration based 1D-MUSIC algorithm, (**c**) standard 2D-MUSIC method and (**d**) the proposed method.  
The results of four impact cases and their errors estimated by classical 1D-MUSIC, standard 2D-MUSIC and the proposed method are summarized in Table 3. Compared with the actual impact points, the maximum error of direction estimated by classical 1D-MUSIC is 9\({}^{\circ}\) and all of the direction estimated errors decrease after error calibration. Table 3 also gives a comparison between the standard 2D-MUSIC in ref. [11] and the proposed method. The maximum direction and distance estimation error of standard 2D-MUSIC method is 4\({}^{\circ}\) and 2.2 cm, respectively. The maximum direction and distance estimation error of the proposed method is 2\({}^{\circ}\) and 2.2 cm, respectively. The results show that the proposed adaptive sensor array error calibration based 2D-MUSIC method is effective for impact localization on a real composite structure, which have more accurate localization results than standard 2D-MUSIC when sensors array is imprecise. In addition, the beam-formings both of 1D-MUSIC and 2D-MUSIC algorithm are getting better after sensor array error calibration.