## 3 Ultrasonic Guided Wave Signal Processing Methods
### Variational Mode Decomposition
Therefore, VWISSP based on VMD, WT and ISSP can be considered as the most suitable method to gain the sparse UGW signals with high accuracy and resolution, of which only feature signals are retained and noise signals are eliminated completely. ## 6 Experiments of Ultrasonic Guided Wave Testing

UGWs can be excited and received based on the principles including, but not limited to, magnetostriction, piezoelectricity, and electromagnetism. Magnetostrictive UGW testing was chosen for the ease of implementation, low cost, and excellent sensitivity and durability, \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & \multicolumn{3}{c}{**SNRG(dB)**} & \multicolumn{3}{c}{**DNRG(dB)**} & \multicolumn{3}{c}{**Misjudments**} \\ \cline{2-10}  & **ISSP** & **EWISSP** & **WWISSP** & **ISSP** & **EWISSP** & **VWISSP** & **ISSP** & **EWISSP** & **VWISSP** \\ \hline NUS 1–1 & 7.32 & 7.73 & 7.9 & 6.57 & 6.67 & 7.32 & 0 & 0 & 0 \\ NUS 1–2 & 9.06 & 8.79 & 10.48 & 11.44 & 8.59 & 10.07 & 2 & 0 & 0 \\ NUS 1–3 & 8.83 & 9.01 & 11.04 & 8.83 & 8.91 & 10.54 & 3 & 1 & 0 \\ NUS 1–4 & 7.47 & 10.54 & 10.93 & 7.73 & 11.53 & 11.76 & 4 & 1 & 0 \\ NUS 1–5 & 8.86 & 12.05 & 12.48 & 6.81 & 8.65 & 9.43 & 4 & 2 & 0 \\ PUS 2 & 6.80 & 7.04 & 8.53 & 6.73 & 7.20 & 7.81 & 0 & 0 & 0 \\ PUS 3 & 6.05 & 6.72 & 7.61 & 5.72 & 6.18 & 7.12 & 0 & 0 & 0 \\ PUS 4 & 6.77 & 7.26 & 7.57 & 5.29 & 7.08 & 7.10 & 2 & 0 & 0 \\ NUS 2 & 7.56 & 8.73 & 9.67 & 5.75 & 5.45 & 6.84 & 1 & 2 & 0 \\ NUS 3 & 7.48 & 8.70 & 9.46 & 5.28 & 5.98 & 6.22 & 3 & 0 & 0 \\ NUS 4 & 7.31 & 8.48 & 9.49 & 5.85 & 7.38 & 8.34 & 4 & 1 & 0 \\ \hline \end{tabular}
\end{table} 
Table 1: SNRG, DNRG, and misjudments of N/PUS signals processed by ISSP, EWISSP, and VWISSP. Figure 12: Sparse signals of (**a**) single-defect NUS signals and (**b**) multi-defect N/PUS signals processed by EWISSP and VWISSP. of which the schematic diagram is shown in Figure 13. The magnetostrictive UGW testing system includes a self-made GWNDT-III platform, magnetizing coil, magnetostrictive patch (FeCo alloy), excitation/receiving coils and pipe; and the GWNDT-III platform integrates the modules of main control, excitation, data acquisition, and signal processing, which can realize the excitation and reception of UGW conveniently. The principle of magnetostrictive UGW testing is as follows [41]. Firstly, ensure that the magnetostrictive patch is in a state of maximum magnetostriction rate pre-magnetizing the magnetization coil. Secondly, excite the excitation signal using the GWNDT-III platform, which generates dynamic magnetostriction in the form of UGW based on positive magnetostrictive effect. Finally, the induced voltage signal of the receiving coil resulting from the variation of magnetic field strength near the magnetostrictive patch based on the inverse magnetostrictive effect can be captured, which is processed and exhibited by the GWNDT-III platform. ### Aluminum Pipe

The hole defects (H1, H2, H3, and H4) with diameters of 10 mm were artificially set on the surface of the aluminum pipe, of which their axial positions are illustrated in the upper Figure 14, and the L(0,2) UGW testing signals for the above aluminum pipes are shown in the middle Figure 14. It can be observed that UGW signals mainly comprise of direct echo, defect echo, end-reflected echo, and noise signal (coherent and incoherent noise). With the increase of the number of defects, the noise level, especially the coherent noise level, increases significantly, which can be attributed to the reflection, refraction, and mode conversion of UGWs, and it can be found that the defect resolution becomes poor in EUS 3 and 4. Removing the direct echo that is seriously affected by electromagnetic radiation, and applying the Chirplet transform to the residual signals, creates the results shown in the bottom Figure 14. Although Chirplet transform shows the defects clearly in time-frequency domain, the accurate localization of defects may not be achieved due to the interference of noise.