# Detection and Quantification of Damage in Metallic Structures by Laser-Generated Ultrasonics
## 4 Artificial Damage Detection and Quantification for Aluminum Alloy Plates
### Damage Visualization and Quantification  
As mentioned in Section 2.3, the excitation laser pulse scans over both the damaged area and the comparison undamaged area while the ultrasonic responses from the excitation point are recorded by a transducer placed at a fixed point. The scanning area covering the damage was 5 \(\times\) 5 mm\({}^{2}\) in this experiment. The scanning process continues until the whole area is covered. The calculated NNPE values can be used to visualize the entire scanned area, and the spatial distribution of the values is expected to help in detecting the damage. Furthermore, because the pitch between two adjacent points in the scanned area is known before scanning (0.02 mm for this experiment), the size of the damage can be quantified by counting the number of points that contain damage in the visualization picture. The results are summarized in Figure 11. For simplicity's sake, only the visualization pictures for specimens (c) and (d) with the smallest damage widths are plotted. One thing deserves to be mentioned is that when the laser beam spot irradiates in the front of the damage, the focal distance of the laser beam will change and result in a varying diameter of the laser beam spot. It means that the presence of the damage changes the characteristics of the structure as well as the laser beam. However, we should notice that the changing in the received signal caused by a varying laser beam spot is very limited. According to the work conducted by [PERSON] et al. [PERSON] et al. (2018), the diameter of the laser beam spot mainly affects the pulse duration of the surface waves. Compared with the nonlinear modulation caused by the damage as shown in Figure 2, the effects caused by a varying laser beam spot is almost negligible. From another perspective, the state-space predictive model mainly focuses on the changing of the received signal. Generally speaking, the changing of the laser beam spot caused by damage is helpful for the damage detection. From Figure 11 we can see that a strongest nonlinearity was observed when damage appeared. Thus, the damage could be localized by the proposed technique successfully. Notably, the distribution of the damage is uniform through the Y direction. This is caused by the limitation of the transducer. When the laser pulse irradiates at the edge of the transducer, the laser generated ultrasonic waves will be propagating to the transducer obliquely. Some of the signals may be missed in this situation. So the calculated NNPE values are not uniformly distributed, especially at the edge of the scanning area. By extracting the coordinate values of the damage in Figure 11, the damage size can be quantified too. In Figure 11a, the longest distance of the damage width along the \(X\) direction was 59.7 \(-\) 57.1 = 2.6. The width of the damage was then 2.6 \(\times\) 0.02 = 0.052 mm, which matched the actual width. Similarly, the width of the damage to structure (d) was 5.1 \(\times\) 0.02 = 0.102 mm. Using this method, the damage was not only localized, but its size was quantified too. Especially noteworthy is the number of scanning points and the pitches between two adjacent points being adjustable, which means, proper visualization parameters can be chosen to detect the different damage dimensions to obtain the best visualization results. For example, a larger distance between the scanning points should be chosen to visualize lager dimensioned damage. In the above damage detection process, the crack is contained in the scanning area. However, if the damage is located between the scanning area and the transducer, the damage detection process is relatively cumbersome. In this situation, the detection process is as follows:  
Three plates are needed, as shown in Figure 6a-c. Plates (a) and (b) are undamaged and plate (c) is a damaged plate with a crack. First of all, we make plate (a) the reference undamaged plate and plate (b) the current undamaged plate to be detected. Calculate the NNPE values in the scan area for plate (b).