## 4 Damage Detection Using TRM
### Damage Detection Using TRM  
The samples are divided into three groups to reduce the impact of machining error on the test results. Each group contains 5 galvanized steel wires with 7 mm diameter, approximate 1 m length and an artificial pitting corrosion in their respective middle position. The pitting gradually increases from 1 to 5 mm at 1 mm intervals, keeping 3 mm and 1 mm diameter on the surface and bottom respectively unchanged to highlight the influence of depth variation. The manufactured corrosive samples of one group and the sketch of configuration are shown in Figure 7.  
As the inevitable discrepancies due to the different coupling conditions between the specimen and the transducers, a direct comparison between the signals from different testing samples may lead to an incorrect conclusion. A factor based on the energy of the received signal \(V_{s}(t)\) is introduced to approximately normalize the amplitudes of \(V_{s}(t)\) and \(V_{AR}(t)\) after each time measurement for a more effective damage assessment. The factor is the Root-Mean-Square (RMS) of \(V_{s}(t)\), represented as  
\[RMS[V_{s}(t)]=\sqrt{\sum_{i=1}^{N}A_{i}^{2}/N} \tag{15}\]  
Figure 6: Truncation window for defect scatter signals extraction.  
Figure 7: Artificial pitting corrosion: (**a**) samples of one group; (**b**) configuration.  
where, \(N\) is the number of sampling points before the first boundary echo of mode \(L(0,2)\), \(A_{i}\) is amplitude of \(i\)th sampling point. The normalized received signal and reconstructed input signal are shown as follows:  
\[\overline{V}_{s}(t) =V_{s}(t)/RMS[V_{s}(t)] \tag{16}\] \[\overline{V}_{AR}(t) =V_{AR}(t)/RMS[V_{s}(t)]\]  
A 12-cycle Hanning-windowed tone burst is imposed on the actuator with a peak voltage of 8 V. The normalized received signals \(\overline{V}_{s}(t)\) of the second group are exhibited in Figure 8a. It is illustrated that a quantitative evaluation for damages depending on \(\overline{V}_{s}(t)\) is impossible, since the captured signals are extremely difficult to interpret in virtue of multimode, multipath and dispersion of guided waves propagation.  
The defect scattered signals included in the truncation window are reversed, normalized to 8 V as the original excitation and then relaunched. In Figure 8b, with reference to the wires with 1 mm to 5 mm corrosive depths, focusing packets of \(\overline{V}_{AR}(t)\) emerge at the trigger point and their amplitudes increase evidently along with the aggravation of corrosion. However, in terms of a compared intact wire, there is no distinct focusing packet at the trigger point, which indicates that the truncated signals are not the defect scattered ones, but the system noise which can not be focused. It can be seen from Figure 9 that the reconstructed signal amplitudes of the three test samples exhibit almost the same linearly increasing trend in line with the growth of corrosive depth. The amplitudes of the focused wave packets improved by TRM is about 10 times that of the defect echoes directly used for damage quantification in the conventional testing method described in Section 5. In conclusion, TRM is a technique of relatively higher resolution corresponding to the variation of corrosive defects.  
Figure 8: TRM process of defect assessment: (**a**) received signals before TRM; (**b**) received signals after TRM.