## 5 Discussion
(5) The results of Case 8 and Case 9 indicate that the impact which the big hole exerts on the small one is related to their positions when the excitation source and multiple defects are in the same line. The direction and amplitude of the incident wave can be changed obviously when the big hole is in front of the small one. Hence, the wavenumber distributions located at the small hole also change. The impact that the big hole exerts on the small one comes mainly from the reflection wave when the big hole is behind the small one. However, it is the incident wave that plays a crucial role in changing the wavenumber distributions, because the incident wave has a larger amplitude than the reflection wave. Therefore, the test result for the small hole will only change a little when the big hole is behind it. (6) The depth errors for Case 10 and Case 11 are more than 10%. The length of the rectangular groove is larger than that of the spatial window. However, the width of the former is still far smaller than that of the latter. Hence, the local wavenumber is seriously affected by the window effect. (7) Several measures are adopted to improve the test quality when the proposed approach is applied for an unknown damage. In practice, both the damage size and its position are usually unknown. A large amount of data will be acquired if the entire structure is inspected. Thus, a preliminary step is desired. More specifically, it is easy to acquire the approximate location of a defect by using reliable methods, such as DAS or the compact phased array (CPA) method [40]. Then a small scanning region where the defect is likely to exist can be obtained. Under the circumstance, the local wavenumber approach can be conducted without consuming much time. The spatial window size is at least twice the wavelength of the excited mode. It should be noted that the best test result is not always obtained under the minimum size of the spatial window. In fact, the best test result is obtained under the optimum size due to the fact that the optimum size contributes to diminishing the spatial window effect. The optimum size is also fixed when the central frequency of the excitation signal and the excited mode are fixed. The optimum size can be attained by adjusting the size of the spatial window until the maximum wavenumber of the wavenumber map is acquired. Therefore, patience is important during the period of seeking the optimum size. The process of improving the test quality is shown as below. The excitation signal with a higher central frequency is adopted as the wavelength of the excited mode is small. Under this condition, the minimum size of the spatial window may be smaller than the optimum size. The wavelength of the A0 mode is about 5 mm when the central frequency of the excitation signal is 400 kHz. Hence, the minimum radius of the spatial window is 5 mm. The radius will be increased at an interval of 1 mm. The test results obtained under various window radii are shown in Figure 24. The maximum wavenumber obtained under various window radii is shown in Figure 25.  
Figure 24 shows that the identified damage region will expand with the increase of the window radius. It was found that the test results are poor when the radius is small. The identified damage region is almost equal to the actual size under a special window radius (8 mm). Figure 25 shows that the maximum wavenumber increases with the size of the spatial window and gradually approaches to the theoretical value at the early stage. The maximum wavenumber is very close to the theoretical value under a special window radius (8 mm). However, the maximum wavenumber will decrease when the size of the spatial window continues to be increased. It is worth that the wavelength of the excited mode is large when the central frequency of the excitation signal is low. Hence, it may lead to the minimum size of the spatial window being larger than the optimum size. Under this circumstance, a good test result is obtained at the minimum size of a spatial window.