# Damage Imaging in Lamb Wave-Based Inspection of Adhesive Joints
## 3 Results and Discussion
### WRMS Imaging
#### 3.3.4 WRMS Histograms
It is worth noting that the value of the relative peaks distance stabilized at a specific value of \(m\) individually for each defect, so the increase in \(m\) could not infinitely the improve the quality of maps. Furthermore, specimen #4 provided a different relationship than the others where the relative distance between the peaks at the beginning increased with power \(m\) and then decreased. Maximal values were observed for the power \(m\) between 1 and 1.5. Based on the calculations presented above, it was concluded that the proposed analysis provides the opportunity to improve the process of determining the optimal value of the weighting factor (in fact, the power \(m\)) for damage imaging using WRMS. An attempt to quantitatively analyze the defects was performed based on the statistical analysis of the calculated WRMS values. Histograms and their approximations by probability density functions were prepared for different values of power \(m\) for specimens with a bimodal distribution (#2-#6). The limit point (here, the central point) in the peaks distance was determined as the mean value between peak values (along the horizontal axis). As previously mentioned, poor adhesion areas are related to higher values of WRMS. For that reason, the number of values that are above the central point value were counted, representing the number of points where the defect occurred. The percentage of points with higher values can be interpreted as the relative surface of the defect. Based on the relationships that are presented in Figure 19, it was clear that for most of the specimens, the relative defect surface did not vary significantly in relation to power \(m\) and it moderately decreased with its value. The exception was the defect in specimen #4 that presented the opposite relationship,  
Figure 17: Histogram of WRMS values for specimens #1–#9 (\(T=3.00\) ms, \(w_{r}=r^{2}\)). When comparing the results with measurements that were conducted on the real separated specimen (Table 1), it was clear that the good agreement of the proposed approach was obtained only for defect #3 (calculated mean value of relative surface is 68.5% and measured is 68.21%). For other specimens, the differences were much higher (calculated values ranged from 45% to 55% and measured between 33% and 37%). The reason for these discrepancies may possibly be related to the method of determining the limit point for counting the number of points that are related to the defect surface. Due to the complexity of bimodal distributions (e.g., different parameters of both modes), further analyses should be conducted. One additional aspect of this research included the statistical analysis of the influence of the excitation frequency. Figure 20 shows the WRMS histograms for specimen #6 with different excitation frequencies. For the lowest value (50 kHz), the unimodal (but asymmetric) distribution was obtained. Higher frequencies (100 kHz and 200 kHz) showed typical bimodal distributions with different  
Figure 19: Relationships between the relative defect surface and weighting factor (represented by power \(m\)) for specimens #2–#6. Figure 18: Relationships between the relative peak distance of WRMS histograms and weighting factor (represented by power \(m\)) for specimens #2–#6. characterization. To compare them, the relative peak distance was calculated. For 100 kHz, a value of 34.67% was obtained, whereas for 200 kHz, it was 27.33%. This meant that the 100 kHz frequency provided results with more differentiated WRMS values obtained in areas with good and poor quality (resulting in clearer defect image). Furthermore, the percentage of the defect surface was determined with the use of the above-presented method with the central limit point. For 100 kHz, the result was 35.67% and for 200 kHz, a value of 51.78% was achieved. When compared to the measured value (33.33%, Table 1), the nearest value was obtained for 100 kHz.