# Damage Imaging in Lamb Wave-Based Inspection of Adhesive Joints
## 3 Results and Discussion
### WRMS Imaging
#### 3.3.4 WRMS Histograms  
The WRMS method enables one to differentiate the areas of a properly prepared adhesive film and its defects. In addition to the visual assessment of prepared maps, a numerical analysis of its calculated values can be performed with the use of statistical analysis. The purpose is to prepare a histogram of calculated WRMS values that is expected to reveal the bimodal distribution of the sample population (concentrated on two values responding to disbonded and properly bonded areas). This presents the possibility for the quantitative determination of the optimal values of WRMS parameters. As observed from the images in Figures 10 and 11, higher WRMS values were obtained in the disbonded areas, whereas the lower ones occurred in the areas of good adhesion. To provide a clear interpretation of the WRMS histograms, the analysis was limited to the surface of the overlap (area of the adhesive joint). In the first step, the influence of the time window on WRMS histograms was considered. Figures 14 and 15 present the WRMS histograms for specimen #5 with different values of time window and different weighting factors \(w_{r}=r\) and \(w_{r}=r^{2}\), respectively. Additionally, to emphasize the characterization of the obtained distributions, each histogram was approximated by the probability density function with the use of the kernel smoother in a MATLAB(r) environment (shown as a red line). It was clear that, for higher time window values (0.50 ms and more), a population of WRMS values formed a bimodal distribution that was represented by a function with two conspicuous peaks values. As concluded before, the clearness of the defect image was related to the difference between the values that were obtained for health and poor adhesion areas of the overlap. For the histograms, this difference was interpreted as the distance between the peak values that were measured along the horizontal axis. For each diagram (if possible), peak values were localized. To compare the results that were obtained  
Figure 12: WRMS maps (values in (m/s)) with linear weighting factor (\(w_{r}=r\)), time window \(T=3.00\) ms and with different excitation frequencies \(f=200\) kHz (first column), \(f=100\) kHz (second column), \(f=50\) kHz (third column): (a) specimen #6; and (b) specimen #7. Figure 13: WRMS maps (values in (m/s)) with square weighting factor (\(w_{r}=r^{2}\)), time window \(T=3.00\) ms and with different excitation frequencies \(f=200\) kHz (first column), \(f=100\) kHz (second column), \(f=50\) kHz (third column): (a) specimen #6; and, (b) specimen #7. To move forward, histograms for all of the specimens were prepared with the time window \(T=3.00\) ms. Figure 16 presents the histograms with the linear weighting factor. For the intact joint (specimen #1), a common unimodal distribution was obtained. The calculated values were concentrated about a singular mode that represented the undamaged area of the adhesive joint. Typical bimodal distributions were obtained for specimens with a clear defect image (#2-#6). For specimens #7-#9, the distributions were likely to be unimodal, but when compared with specimen #1, their shapes were not that regular, and it was clear that their widths were greater than that of specimen #1. This may result in the conclusion that the defect was present, but it could not be clearly observable. Figure 17 shows the histograms with the square weighting factor. The conclusions from the analysis of each histogram were similar to ones based on Figure  
Figure 18 shows the relationships between the relative peak distance and the weighting factor that is represented by the power \(m\) for specimens #2-#6 that clearly presented bimodal distributions. It could be seen that for most of the specimens, higher values of power \(m\) resulted in the greater value of relative peaks distance. This means that the higher the value of \(m\), the clearer the image of the defect on the WRMS maps.