## 3 Ultrasonic Guided Wave Signal Processing Methods
### Variational Mode Decomposition
The average SNRG, DNRG, and accuracy of VWISSP are 9.41 dB, 8.68 dB, and 100%, respectively, while the average SNRG, DNRG, and accuracy of ISSP are 7.07 dB, 6.77 dB, and 74.37%, respectively, which are improved by 32.97%, 28.25%, and 34.46%, respectively. To sum up, VWISSP has the promising ability to manifest the feature signals (defect and pipe end) in the form of obviously sparse signals, which solves the problems of the poor processing effect of ISSP on the UGW signals with high noise levels and multiple defects, and realizes the accurate recognition and location of defects. ## 7 Conclusions

An advanced signal processing method based on variational mode decomposition (VMD), wavelet transform (WT), and improved split spectrum processing (ISSP) was proposed to improve the signal interpretation accuracy of the L(0,2) ultrasonic guided wave

Figure 12:8 IMFs of VMD in the (**a**) time and (**b**) frequency domains; (**c**) VMD + WT and (**d**) VMD + WT + ISSP processing results of EUS 8. Figure 12:9 ISSP, EWISSP, and VWISSP processing results of EUS 5 to 8: (**a**) sparse signals, (**b**) SNRGs, DCRGs and accuraies. (UGW) signals, of which SSP may not achieve great pipe feature preservation on noisy multi-defect UGW signals. To begin with, it is essential to illustrate the UGW characteristics of dispersion and multi-mode, and UGW signals were divided into signals of features (desired UGW), coherent noise (undesired and non-axisymmetric UGWs), and incoherent noise (environmental noise). SSP was improved by replacing the Gaussian filter bank with cosine filters of constant frequency-to-bandwidth and frequency-to-filter spacing ratios (FSR-FBR-SSP), of which the pros and cons were revealed. The enhancement effects of VMD and WT on the signal to noise ratio (SNR) were exploited: combining them with ISSP is more beneficial to preserving features (defects and pipe end) and eliminating noise, which is inductive to obtain better signal interpretation accuracy. The L(0,2) UGW testing was performed on aluminum and low carbon steel pipes containing different types and numbers of defects, and the signal processing method based on VMD, WT, and ISSP (VWISP) was applied on the UGW signals. The signal-to-noise ratio gain (SNRG), defect-to-coherent noise gain (DNRG), and feature accuracy were introduced, and the results illustrated that VWISSP shows better capacity for obtaining the sparse UGW signals with high accuracy and resolution compared with ISSP, of which only feature signals are retained and noise signals are eliminated completely. Conceptualization, Y.W. and B.T. ; methodology, B.T. ; software, B.T. ; validation, B.T., A.C. and Y.W. ; formal analysis, R.G. ; investigation, Y.Z. and R.G. ; data curation, Y.Z. ; writing--original draft preparation, B.T. ; writing--review and editing, Y.W. and B.T. ; supervision, Y.W. ; project administration, Y.W. ; funding acquisition, Y.W. All authors have read and agreed to the published version of the manuscript. This research was funded by the Naval Engineering University, grant number 417214390. The authors would like to acknowledge the Nondestructive Testing Laboratory of Naval Engineering University School of Power Engineering for equipment support. The authors declare no conflict of interest. ## References

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