## 3 Results and Discussion
### Case I: Numerical Simulation
#### 3.1.2 Damage Localization--Results  
The proposed examination procedure of vibration forms using statistic calculation consisted in determining a measure of similarity ratio between two given curves (damaged and intact). In the first stage of the investigation, the fit factors for all pairs of modes shapes were determined. Figure 5 presents results of these calculations for the blade with damage located in position 1 (10% of midspan measured from widest chord line of the profile) with the edges marked by vertical dashed lines.  
Figure 4: Damage pattern: (1–5)—numerical simulation; (a–c)—experiment.  
The length of the simulated damage was 6% of the total measurement line (12 samples). The data was normalized according to Equation (3). The size of the frame for determining the sliding window method was equal to four samples, which corresponds to 2% of the total number of samples. The optimal value of the window width was determined based on a series of calculations. Analysing the results of the above calculations, the thesis that various type of modes shapes, to a different extent, contain information about the damage, is confirmed. In this case, 1 st, 2 nd and 6 th form of vibrations include information that clearly allows for interpretation and directly indicates the limits of damage.  
Figure 5: Results of fit coefficient calculation as a function of normalized position (x/L) for modes order from 1 to 10 and the first case of damage localization: (**a**–**j**) consecutive modes; vertical dashed line—location of the damage; —length of the measuring line.  
In the case of the other modes, the understanding of the graph is more complicated and showing the place of damage is very difficult or even impossible. A similar relation can be seen for calculation of fit coefficient at other four locations of damage. Some examples of calculation results are presented in Figure 6.  
In the next step of the simulation study, the fit ratio was determined for all available mods using RMS averaging. The calculation results for the first case of delamination position (Figure 5) are shown in Figure 7. In the case of the first and the second damage location, the results were inconclusive. This effect was related to the relatively small impact of damage for total stiffness value of the cross-section near the blade root, where stiffness was high because of the widest chord line of the blade profile and the thickest coating, simultaneously. The visibility of the damage zone width on the graph increased with shifting damage position towards the tip of the blade. It is because the stiffness of the blade decreased in the blade tip direction and therefore, the relative effect of the delamination on the cross-section was more significant.  
Figure 6: Results comparison of _fit_ coefficient or individual modes (4 th, 6 th, 7 th and 9 th) for different cases of damage localization: (**a–d**) 1 st location; (**e–h**) 4 th location; vertical dashed line—location of the damage, \(\chi\)/L—normalized position; L—length of the measuring line.  
The results of the calculation for three values of the modelled damage zone in the same location (middle of the midspan) are shown in Figure 8.  
The length of the delamination was 4%, 5% and 6% of the total measurement line, respectively. It can be seen that as the size of the damage decreased, the maximum value of the characteristic peak at the location of the defect also decreased. This gave the possibility not only to detect the damage but also to estimate its size.  
Figure 8: Results of fit coefficient calculation for RMS value for all given modes shapes and three size of damage in one localization; x/L—normalized position.  
Figure 7: Results of fit coefficient calculation for averaged modes for all cases of damage localization: (**a**) 1 st location; (**b**) 2 nd location; (**c**) 3 rd location; (**d**) 4 th location; (**e**) 5 th location; dashed line—location of the damage; x/L—normalized position.