*3.2. WRMS-Based Damage Identification and Imaging*

The non-destructive diagnostics of specimens #1–#5 was conducted in two stages: identification and imaging. The aim of the damage identification was to detect, whether there are any defects in the adhesive joint between the concrete beam and the steel plate. The root mean squares values were calculated for the time signals excited by the actuator located in point P5 and measured by the sensor located in point P3 (see Figure 3c). This means that the wave propagated through the whole length of the specimen. The calculations were performed for the time of averaging assumed as *ta* = 1 ms, with a linear weighting factor (*m* = 1, *wr* = *r*). The results for all specimens are presented in Figure 8a. It is clearly visible that the WRMS value for specimen #5 (single-layer steel plate) is significantly higher than in others. In the case of specimen #5, the point of excitation was located on the free steel plate, characterized by the relatively small material damping. For specimens #1–#4, the wave was excited on the area where the steel plate had a good connection with the adhesive layer and concrete part (i.e., materials with higher damping) what resulted in the instantaneous leak and dissipation of energy in the bottom part of the specimen. For this reason, a close-up of the chart for the specimens #1–#4 is shown in Figure 8b. The correlation between WRMS value and the size of the defect is clearly visible, with the greater the damaged area, the higher WRMS value. This relationship occurs because the wave energy is magnified by the multiple reflections of propagating waves at the boundaries of defects. It is also worth noticing that the WRMS increased significantly between intact #1 and damaged #2 specimen (71%) but the further growth of defect surface did not result in the significant growth of WRMS. The damaged area of specimen #4 was 2.5 times bigger than in specimen #3 but the growths in comparison with #1 were equal to 116% and 129%, respectively. Concluding, the comparative analysis of WRMS values gave the answer about the presence of the defect, however, it did not provide the information about the size and location of damaged areas.

**Figure 8.** Weighted root mean square (WRMS) values of experimental signals collected in P5 point: (**a**) specimens #1–#5 and (**b**) specimens #1–#4.

The second stage, i.e., damage imaging, was performed to identify the exact position and size of the damaged area of each specimen. The WRMS map in the form of the two-dimensional defect representation over the scanned area was prepared based on the experimental investigations and numerical simulations on 3-D FEM models (see Figures 3c and 4b). The parameters of the calculations were assumed to be the same as for damage identification stage (*ta* = 1 ms, *wr* = *r*). The results for specimens #1–#5 are presented below. Figure 9 shows the WRMS maps for the intact composite beam (specimen #1). Regardless of the location of the excitation point, the visualizations reveal that no internal defects were detected inside the analyzed adhesive joint. The values in each experimental and numerical map are concentrated over a certain value. The horizontal lines with magnified values in images for excitation P3 (Figure 9a), such as the vertical lines for excitation P4 (Figure 9b) are the effects of the specimen and the load symmetry. Some interesting conclusions can be derived from the analysis of the results for specimen #2 with a partial debonding (Figure 10). It is clearly visible that the map obtained for the excitation applied in point P3 (Figure 10a) results in the moderate defect imaging when compared with the excitation in point P4 (Figure 10b). The reason is that the wave excited in point P3 (in the area of good adhesion) strongly leaks into concrete, so the wave energy is damped significantly before meeting the boundaries of the defect, thus it has no possibility to be clearly visualized. It was already possible to conclude in the stage of damage identification (the high WRMS value for specimen #5 indicated on this effect, see Figure 8a). However, the damaged area is somehow detectable and it is characterized by slightly smaller WRMS values than the remaining part of the sample. The energy of the wave excited by the actuator P4 is concentrated in the damaged area and the damage map has a high quality. The properly boded areas have much lower WRMS values because the waves transmitted to the three-layer medium are highly damped.

**Figure 9.** Experimental and numerical WRMS damage maps for specimen #1: (**a**) Excitation P3 and (**b**) Excitation P4.

**Figure 10.** Experimental and numerical WRMS damage maps for specimen #2: (**a**) excitation P3 and (**b**) excitation P4.

A good agreement of experimental and numerical results is observed, however, the quality of the numerical visualization for the excitation in point R3 is richer compared with the experimental one. This may be caused by the noise present in the experimental signals. Similar conclusions can be derived from the analysis of damage maps of scanning for the two other partially damaged beams: #3 (Figure 11) and #4 (Figure 12). The WRMS maps for the fully debonded joint #5 (Figure 13) are similar to the ones obtained for the intact composite beam #1 (cf. Figure 9). This convergence allows stating that the damage visualization is possible only when the area of scanning covers both areas of good adhesion and debonding. The only difference between both specimens is that the value of WRMS is significantly higher for the steel plate (see color bars in Figures 9 and 13).

**Figure 11.** Experimental and numerical WRMS damage maps for specimen #3: (**a**) excitation P3 and (**b**) excitation P4.

**Figure 12.** Experimental and numerical WRMS damage maps for specimen #4: (**a**) excitation P3 and (**b**) excitation P4.

**Figure 13.** Experimental and numerical WRMS damage maps for specimen #5: (**a**) excitation P3 and (**b**) excitation P4.
