Resolution Enhancement Method of L(0,2) Ultrasonic Guided Wave Signal Based on Variational Mode Decomposition, Wavelet Transform and Improved Split Spectrum Processing
Round 1
Reviewer 1 Report
Reviewer’s suggestions and comments on the Manuscript entitled:
Resolution enhancement method of L(0,2) ultrasonic guided wave signal based on variational mode decomposition, wavelet transform and improved split spectrum processing
Manuscript ID: applsci-2032240
Pipeline systems are omnipresent in industry, shipbuilding, construction, petroleum, and other fields for transporting oil, gas, and petrochemical products. Because aging, stress concentration, and humid environment can provoke defects like cracks, corrosion, and notches of the pipeline system, non-destructive testing (NDT) can be used to confirm the reliability of operations avoiding possible failures. In this investigation, an advanced signal processing method was proposed. The method is based on variation mode decomposition (VMD), wavelet transform (WT), and improved split spectrum processing (ISSP). This was done in order to enhance the L(0,2) ultrasonic-guided wave (UGW) signals.
The authors have successfully analyzed the characteristics of UGWs .It was confirmed that the signal filter bank improved SSP. Moreover, all the pros and cons of ISSP were carefully examined. The signal processing method which is based on VMD, WT, and ISSP was found to be adequate to process the UGW signals. The L(0,2) UGW testing performed on aluminum and low-carbon steel pipes containing different types of defects was evaluated professionally.
This manuscript has citation potency. Therefore I recommend to the Editorial Office accept this manuscript for publication in its present form.
Author Response
Thank you for your recognition of my manuscript, which means a lot to me, I sincerely wish you good health, smooth work and harmonious family, and I will continue to conduct research in the direction of ultrasonic guided wave nondestructive testing to live up to your recognition.
Author Response File: 
Author Response.docx
Reviewer 2 Report
The manuscript " Resolution enhancement method of L(0,2) ultrasonic guided wave signal based on variational mode decomposition, wavelet transform and improved split spectrum processing" has the main objective of comparing which signal processing method had better accuracy and resolution processing effects with noisy multi-defect UGW signals. The results were compared and conclusions were drawn.
The introduction is presenting detailed information about the signal processing methods and containing recent literature citations.
The methodology is well described presenting details of the use of the method.
The results present rich discussions about the methods used with clear and detailed comparisons.
The conclusions present the items observed with the application of the proposed method, bringing closure to the findings of this research.
The paper can be approved as it is.
Author Response
Thank you for your recognition of my manuscript, which means a lot to me, I sincerely wish you good health, smooth work and harmonious family, and I will continue to conduct research in the direction of ultrasonic guided wave nondestructive testing to live up to your recognition.
Author Response File: Author Response.docx
Reviewer 3 Report
Dear authors,
I carefully checked your paper. It is suitable for publication. The respected authors followed a critical scientific way to represent their idea on the discussed topic. Please make some minor amendments before the publication of this paper.
1- Please summarize the introduction into three paragraphs with 10 to 12 references.
2- Please design a flowchart for your M&M section.
3- Please supplement the numerical data that used as input datasets for conducting analyses in this paper.
4- Please improve the figure captions and provide more details for each section of figures by interpreting the observed changes related to each plot.
5- Please highlight the novelty of this study in comparison to previously conducted studies in the literature.
6- Lines 194-208: Please provide citations for the given algorithm. If the authors developed this algorithm, please clearly elaborate on this case.
7- Figure 4: Please elaborate on the figure captions and provide more details on the applied filters.
8- How has your method improved the current knowledge of the discussed topic?
Author Response
Q1: Please summarize the introduction into three paragraphs with 10 to 12 references.
A1: According to your comment, I have summarized the introduction into three paragraphs with 10 to 12 references, which is shown as follows:
“Pipeline systems are omnipresent in industry, shipbuilding, construction, petroleum and other fields for transporting oil, gas and petrochemical products. Over time, due to the material aging, stress concentration, humid environment and other adverse factors, defects like cracks, corrosion and notches would like to appear in pipelines, which may compromise the safety and economy [1,2]. Hence, it is fundamental to apply nondestructive testing (NDT) on pipes to ensure reliable operation and avoid catastrophic failure. Ultrasonic guided wave (UGW) testing shows capabilities of high-efficiency, non-contact, long-distance and large-scale detection, which can be applied to check the structural integrity of buried, coated and liquid filled pipelines [3,4].
Two inherent characteristics of dispersion and multi-mode in UGW are inevitable, which are manifested in that the UGW velocity varies with the frequency and multiple modes of UGWs exist at a given frequency [5,6]. In this context, it is almost impossible to excite the pure UGW at desired mode, whilst UGWs at undesired modes may be excited for the imperfect experimental conditions and multi-mode characteristics. In addition, for the mode conversion caused by the interaction between non-axisymmetric defects and UGWs, dispersive flexural UGWs may arise, which may increase the interpretation complexity and further weaken the ability of defects detection [7]. In order to enhance the defect identification and classification of UGW testing, several signal processing methods based on time-frequency analysis have been introduced [8]. However, the improvement of UGW signal resolution processed by above methods is limited, and more effective signal processing methods need to be found. At present, signal processing methods aimed at improving the signal-to-noise ratio (SNR) of UGW signal are mainly through separation and elimination of dispersive UGWs, the former is typically represented by matching pursuit (MP), and the latter includes dispersion compensation (DC), pulse compression (PuC) and split spectrum processing (SSP), etc.
SSP can split the UGWs with multi-mode by separating the received signal into a sub-signal group in the frequency domain and recombining them in the time domain without the knowledge of dispersion and propagation distance [9,10]. It is rarely applied in the field of UGW testing, there are only a few studies on SSP processing T(0,1) UGW signals, whereas the studies about the SSP processing L(0,2) UGW signals cannot be found to the best of the authors’ knowledge. In addition, the processing effect of SSP is directly related to the SNR of unprocessed UGW signal, namely high noise level is harmful to the processing effect, and some defects may not be identified when SSP processes the UGW signal with multi-defect. In order to compensate the shortcomings, this paper proposed the improve SSP (ISSP) based on the raised cosine filter bank with varying bandwidth and spacing, and applied variational mode decomposition (VMD) and wavelet transform (WT) to UGW signals before ISSP. ”
Reference:
- Adegboye M. A., Fung W. K., Karnik A. Recent advances in pipeline monitoring and oil leakage detection technologies: Principles and approaches. Sensors, 2019, 19(11): 2548.
- Olisa S. C., Khan M. A., Starr A. Review of current guided wave ultrasonic testing (GWUT) limitations and future directions. Sensors, 2021, 21(3): 811-818.
- Wang Y. M., Yang B. Theory and method of magnetostrictive guided wave nondestructive testing. Science Press, Beijing, 2015.
- Guan R., Lu Y., Duan W., Wang X. Guided waves for damage identification in pipeline structures: A review. Structural Control and Health Monitoring, 2017, 24(11): e2007.
- Nakhli Mahal H., Yang K., Nandi A. Defect detection using power spectrum of torsional waves in guided-wave inspection of pipelines. Applied Sciences, 2019, 9(7): 1449.
- Rostami J., Tse P. W. T., Fang Z. Sparse and dispersion-based matching pursuit for minimizing the dispersion effect occurring when using guided wave for pipe inspection. Materials, 2017, 10(6): 622.
- Malo S., Fateri S., Livadas M., Mares Gan T. H. Wave mode discrimination of coded ultrasonic guided waves using two-dimensional compressed pulse analysis. IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 2017, 64(7): 1092-1101.
- Muñoz C. Q. G., Jiménez A. A., Márquez F. P. G. Wavelet transforms and pattern recognition on ultrasonic guides waves for frozen surface state diagnosis. Renewable Energy, 2018, 116: 42-54.
- Pedram S. K., Fateri S., Gan L., Haig A., Thornicroft K. Split-spectrum processing technique for SNR enhancement of ultrasonic guided wave. Ultrasonics, 2018, 83:48-59.
- Pedram S. K., Haig A., Lowe P. S., Thornicroft K., Gan L., Mudge P. Split-spectrum signal processing for reduction of the effect of dispersive wave modes in long-range ultrasonic testing. Physics Procedia, 2015, 70: 388-392.
In order to ensure the integrity of the introduction in the draft, I tend to properly integrate the introduction to 5 paragraphs and keep the original number of references, because the number of references only listed 10 to 12 is indeed a little small, and the specific modification is as shown in P 1 and 2 (annotation C1). I sincerely hope that the modification of the introduction can meet your requirements while retaining its original meaning
Q2: Please design a flowchart for your M&M section.
A2: According to your comment, a flowchart of M&M (materials and methods) section is necessary. In fact, I have designed a flowchart of the methods including VMD, WT and ISSP, which is shown in Figure 1.
Figure 1. Schematic diagram of VWISSP.
In addition, I have also plotted the schematic diagram of magnetostrictive UGW testing, which is shown in Figure 2, and I believe that the process of magnetostrictive UGW testing is easily understood graphically.
Figure 2. Schematic diagram of magnetostrictive UGW testing.
In my opinion, the main purpose of the manuscript is to introduce the signal processing method, and the specific experimental steps can be explained clearly. In this way, I think that the flowchart of the method is necessary, of which I have already designed in the manuscript, and the materials and experimental steps were also shown in the manuscript:
“The principle of magnetostrictive UGW testing is as follows [41]. Firstly, ensure that the magnetostrictive patch is in state of maximum magnetostriction rate by the pre-magnetization of magnetization coil. Secondly, the excitation siganl can be excited by GWNDT-Ⅲ platform, which generates dynamic magnetostriction in the form of UGW based on positive magnetostrictive effect. Finally, the induced voltage signal of receiving coil resulting from the variation of magnetic field strength near the magnetostrictive patch based on inverse magnetostrictive effect can be captured, which is processed and exhibited by GWNDT-Ⅲ platform.”
I hope my explanation can play some role. Of course, if you think my opinion is biased, please do not hesitate to point out that I will still humbly accept and revise.
Q3: Please supplement the numerical data that used as input datasets for conducting analyses in this paper.
A3: According to your comment, I have already provide the numerical data used as input in the excel form, which is named as “Input data.xlsx” and shown as follows:
Figure 3. Screen shots of the input data table.
Q4: Please improve the figure captions and provide more details for each section of figures by interpreting the observed changes related to each plot.
A4: Thank you for your comment, I have made some modifications, and the details are as follows:
Figure 1: In order to make the description of Figure 1 correspond to Figure 1, I have added the specific number of the figure in the explanation section (P3, annotation C2 and C4). In addition, I have changed the caption of Figure 1c to “normalized displacement distribution” to get a better description (P3, annotation C3).
Figure 2: The captions and interpretations of Figure 2 are suitable in my opinion (P3, annotation C5 and C6).
Figure 3: The captions and interpretations of Figure 3 are suitable in my opinion (P4, annotation C7).
Figure 4: The captions of Figure 4a is changed to “Comparison of GS and RC filters” (P7 annotation C10), and the interpretations of Figure 4 are suitable (P7 annotation C9, C11 and C12).
Figure 5: The captions of Figure 5 is changed to “Signals of (a) L(0,1)+F(n,1), (b) L(0,2)+F(n,3) UGWs in time domain, signals of (c) synthesized UGW signal in time and frequency domains” (P7 annotation C13), and the interpretations of Figure 5 are suitable (P8 annotation C14, and C15).
Figure 6: The captions of Figure 6 are suitable, and I have added some description of Figure 6 (P8 annotation C16 and C17).
Figure 7: The captions and interpretations of Figure 7 are suitable in my opinion (P9, annotation C18 and C19).
Figure 8: The captions and interpretations of Figure 8 are suitable in my opinion (P9, annotation C20).
Figure 9: The captions and interpretations of Figure 9 are suitable in my opinion (P10, annotation C21).
Figure 10: The captions and interpretations of Figure 10 are suitable in my opinion (P10, annotation C22-24).
Figure 11: The captions and interpretations of Figure 11 are suitable in my opinion (P12, annotation C25-26).
Figure 12: The captions of Figure 12 is changed to “Sparse signals of (a) single-defect NUS signals and (b) multi-defect N/PUS signals processed by EWISSP and VWISSP.” (P12 annotation C28), and the interpretations of Figure 12 are suitable (P12 annotation C27).
Figure 13: The captions and interpretations of Figure 13 are suitable in my opinion (P13, annotation C29).
Figure 14: The captions and interpretations of Figure 14 are suitable in my opinion (P13, annotation C30).
Figure 15: The captions and interpretations of Figure 15 are suitable in my opinion (P14, annotation C31).
Figure 16: The captions and interpretations of Figure 16 are suitable in my opinion (P14, annotation C32).
Figure 17: The captions and interpretations of Figure 17 are suitable in my opinion (P14, annotation C33).
Figure 18: The captions and interpretations of Figure 18 are suitable in my opinion (P15, annotation C34).
Figure 19: The captions and interpretations of Figure 19 are suitable in my opinion (P15, annotation C35).
Figure 20: The captions and interpretations of Figure 20 are suitable in my opinion (P15, annotation C36).
Q5: Please highlight the novelty of this study in comparison to previously conducted studies in the literature.
A5: Thank you for your comment. The previous studies in the literature are mainly conducted by Pedram et. al. The novelty of my manuscript in comparison to their studies are mainly consists of two parts.
Firstly, their studies are focused on the application of SSP on T(0,1) UGW signals, whereas the studies about the SSP processing L(0,2) UGW signals cannot be found to the best of the authors’ knowledge.
Secondly, their studies did not improve on the SSP and just apply SSP, and they also did not apply SSP on the UGW signals with high level noise and multi-defect, which is studied in my manuscript and the methods proposed in this manuscript has indeed achieved good results.
Q6: Lines 194-208: Please provide citations for the given algorithm. If the authors developed this algorithm, please clearly elaborate on this case.
A6: Thank you for your comment, and I have added the citation for the VMD algorithm (P5 annotation C7).
Q7: Figure 4: Please elaborate on the figure captions and provide more details on the applied filters.
A7: Thank you for your comment. As I have described in Q4, the captions of Figure 4a is changed to “Comparison of GS and RC filters” (P7 annotation C10), which illustrates that the raised cosine (RC) filters have transition bands in the shape of truncated raised cosine cycle and guarantee the energy contained is mostly concentrated around the center frequency for the design of flat top. Figure 4b-d show the frequency distributions of (b) RC, (c) FBR-RC and (d) FSR-FBR-RC filter bands. As the captions, the intentions of Figure 4 are revealed.
As I have described in P4, “The schematic diagram of SSP can be described as follows: First, the fast Fourier transform (FFT) is applied to transform an input signal x(t) in time domain into a frequency-domain signal X(f), which is split into a sub-band signal group Xi(f) (i= 1,2,…,N, N denotes the number of filters) in frequency domain by an intersecting bandpass filter bank. Then, employ the inverse FFT (IFFT) on Xi(f) and normalization to obtain a time-domain sub-band signal group yi(t). Finally, the nonlinear signal recombination methods are utilized to produce an output signal y(t).”. It can be found that it is by using filter banks to process frequency domain signals that sub-band signal banks can be obtained and nonlinear combinations can be performed, and the sparse signals revealing defect information can be obtained.
Figure 4. Schematic diagram of SSP.
Q8: How has your method improved the current knowledge of the discussed topic?
A8: Thank you for your comment. As I have mentioned in the introduction, “Two inherent characteristics of dispersion and multi-mode in UGW are inevitable, which are manifested in that the UGW velocity varies with the frequency and multiple modes of UGWs exist at a given frequency [8,9]. In this context, it is almost impossible to excite the pure UGW at desired mode, whilst UGWs at undesired modes may be excited for the imperfect experimental conditions and multi-mode characteristics. In addition, for the mode conversion caused by the interaction between non-axisymmetric defects and UGWs, dispersive flexural UGWs may arise, which may increase the interpretation complexity and further weaken the ability of defects detection [10,11].”
In order to reduce the complexity of signal interpretation, improve the resolution of signal and achieve accurate identification and location of defects, the manuscript proposed the improved SSP (ISSP) based on the raised cosine filter bank with varying bandwidth and spacing, and applied variational mode decomposition (VMD) and wavelet transform (WT) to UGW signals before ISSP. As discussed in the manuscript, the processing results only retained the pipe feature signals including the defects and end-reflected echoes, and we can easily distinguish the number and position of defects, which is hard to achieve with just time domain signals.
Author Response File: Author Response.docx
Reviewer 4 Report
The authors describe a signal processing scheme based on variational mode decomposition, wavelets, and improved spectrum split processing to improve the accuracy of detecting defects in pipes. For low carbon steel, both crack and hole defects could be accurately detected. However, detection of hole defects in aluminum pipe were limited to situations where only a few defects exist. The obvious question that should be addressed by the authors in their manuscript is why aluminum and carbon steel behave differently for detection of defects using ultrasonic guided wave signals.
Author Response
Firstly, I would like to explain why aluminum and low carbon steel pipes were chosen to apply ultrasonic guided wave testing. The magnetostrictive ultrasonic guided wave sensor used in this manuscript is very suitable for the detection of ferromagnetic materials (low carbon steel), and if non-ferromagnetic materials (aluminum) are to be detected, a magnetostrictive patch (FeCo alloy is used in this paper) needs to be applied to the pipe surface. As shown in the schematic diagram of magnetostrictive ultrasonic guided wave detection (Figure 5), we attached a magnetostrictive patch to the surface of each pipe, so both low carbon steel and aluminum pipes can be tested by ultrasonic guided wave testing, and we do applied ultrasonic guided wave testing to low carbon steel and aluminum pipes to demonstrate that ultrasonic guided waves can be applied to pipeline detection of a variety of materials.
Figure 5. Schematic diagram of magnetostrictive UGW testing.
Secondly, I would like to explain that why aluminum pipes are only considered to be set with hole defects, while low carbon steel pipes are set with hole and crack defects. In the manuscript, we artificially set 1 to 4 holes on the surface of the aluminum pipe, of which the purpose is to study the variation of ultrasonic guided wave signals with different number of defects, and it was found that the coherent noise increases with the increase of the number of defects (Figure 6). Then, we artificially set 4 to 5 defects including holes and cracks on the surface of low carbon steel pipes (Figure 7), of which the purpose is to study the variation of ultrasonic guided wave signals with multiple quantity and type defects, and it showed more complex signals than those in Figure 6. It is obvious that it is difficult to distinguish the defect signals only through the time domain signal diagrams, so we apply VMD, WT, and ISSP on these signals to improve their resolution. It is not important to set a variety of defects for aluminum pipe or low carbon steel pipe. What is important is to use the signal processing method proposed in this manuscript to solve the problem of low resolution of ultrasonic guided wave signals in the case of single type, multi-type, single and multiple defects. In other words, it is not necessary that aluminum pipes are set with hole defects and low carbon steel pipes are set with defects including holes and cracks, aluminum pipes can also be set with crack defects, and low carbon steel pipes can also be set with only hole defects.
Figure 6. Experimental UGW signals : (a) EUS 1, (b) EUS 2, (c) EUS 3, (d) EUS 4.
Figure 7. Experimental UGW signals : (a) EUS 5, (b) EUS 6, (c) EUS 7, (d) EUS 8.
Finally, I would like to explain that why aluminum and carbon steel behave differently for detection of defects using ultrasonic guided wave signals. As I described in the manuscript: “Outer diameter, wall thickness and material of pipe are the influence factors for dispersion”, aluminum pipes with an outer diameter of 56 mm, a wall thickness of 3.5 mm and a length of 4 m and low- carbon steel pipe with an outer diameter of 48 mm, a wall thickness of 5 mm and a length of 5.5 m were used, so their dispersion characteristic are quite different. Their dispersion curves are shown in Figure 8 and 9, of which Figure 9 was also shown in my previous work “Split-spectrum processing with raised cosine filters of constant frequency-to-bandwidth ratio for L(0,2) ultrasonic guided wave testing in pipeline”. The ultrasonic guided waves in them travel at different speeds even at the same frequency, aluminum and low carbon steel pipes have different length and defect settings, and neither does the process of ultrasonic guided wave interaction with defects. In this way, the signals of aluminum and low carbon steel pipes after ultrasonic guided wave testing are quite different.
Figure 8. Dispersion curves of axisymmetric UGWs: (a) phase velocity and (b) group velocity in aluminum pipes.
Figure 9. Dispersion curves of axisymmetric UGWs: (a) phase velocity and (b) group velocity in low carbon steel pipes.
The corrections in the paper and the responds to the comments are described above, we have tried our best to improve the manuscript and made some changes in the manuscript, and hope the correction will meet with approval.
Once again, thank you for your comments and suggestions.
Author Response File: Author Response.docx
Round 2
Reviewer 4 Report
Publish as the authors have adequately responded to the previous criticisms raised.
