Ultrasonic Guided Wave Health Monitoring of High-Temperature Aircraft Structures Based on Variational Mode Decomposition and Fuzzy Entropy

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this paper, the authors propose the application of zirconia ceramics as a thermal buffer layer for the health monitoring of aircraft structures using guided waves, which is suitable for high temperature inspections. Furthermore, the authors proposed the approach for analysis of inspection results based on the application of Variational Mode Decomposition and Fuzzy Entropy. According to the performed in-situ experiments the authors reported that the proposed apporoaches demonstrate the efficiency on the temperatures up to 150 оС. Unfortunately, the range of experiments is very limited and it is difficult to draw a definite conclusion about the efficiency of proposed approaches and their limitations.

In my opinion, the paper is in dire need of revision. Authors are therefore encouraged to respond to the following comments:

1. One of the novelties of this research is the new approach to the analysis of structural health monitoring results. This rather hot topic in current researches. However, the review of the current state of research and development in this field provided by the authors in the introduction is extremely limited. Why are existing approaches not suitable for the task that has been solved?

2. What is the reason for the choice of 2 cm diameter holes as model defects in the experiments? It is worth considering the limitations of proposed approaches in the area of flaw size. What size defects cannot be detected with the proposed approach? How does the sensitivity (ability to detect defects of small size) decrease due to the application of zirconia ceramic heat buffers?

3. The numbering of the figures is broken. Please check.

4. There are also some formatting problems. The format of references (numbers in the text referring to the cited publication), figure captions and equations does not meet the requirements of the journal. Please check these requirements and make appropriate changes in the paper.

Author Response

Comment 1. One of the novelties of this research is the new approach to the analysis of structural health monitoring results. This rather hot topic in current researches. However, the review of the current state of research and development in this field provided by the authors in the introduction is extremely limited. Why are existing approaches not suitable for the task that has been solved?

Response 1. We appreciate your recognition of the novelty in our approach to structural health monitoring (SHM) analysis and your feedback on the introduction.

You are correct in noting that our initial review of the current state of research and development in the field was limited. We have now rewrote the introduction to provide a more comprehensive overview of existing approaches and clearly articulate their limitations. Specifically, we have included a subsection detailing why existing methods may not be fully suitable for the high-temperature SHM task addressed in our study. What new problems have been brought by the transplantation of guided wave monitoring technology from high temperature pipe thickness to guided wave damage monitoring method of aircraft, and how to solve these problems by means of signal mode decomposition and damage characterization methods.

We believe that these additions provide a clearer context for our research and underscore its novelty and significance in the field.

Comment 2. What is the reason for the choice of 2 cm diameter holes as model defects in the experiments? It is worth considering the limitations of proposed approaches in the area of flaw size. What size defects cannot be detected with the proposed approach? How does the sensitivity (ability to detect defects of small size) decrease due to the application of zirconia ceramic heat buffers?

Response 2. We thank the reviewer for their insightful question regarding the choice of 2 cm diameter holes as model defects and the implications for our approach's sensitivity and limitations.

The author is not clear here, so there is a misunderstanding. We want to monitor a process of gradual damage expansion, starting at 2cm, and we do not want to explore the accuracy limits of the methods proposed in this paper. A hole with a diameter of 2cm is a typical damage size that many researchers have used as a starting point for damage identification, such as “Gorgin R, Wu Z, Zheng Y. A Novel Complementary Method for the Point‐Scan Nondestructive Tests Based on Lamb Waves [J]. International Journal of Aerospace Engineering, 2014, 2014(1): 351840.

Zielińska M, Rucka M. Imaging of increasing damage in steel plates using Lamb waves and ultrasound computed tomography[J]. Materials, 2021, 14(17): 5114.”

Regarding the application of zirconia ceramic thermal buffers, we found that while thermal buffers provide the necessary insulation for high-temperature operation, they introduce some signal attenuation, which affects the detection of smaller defects. We will try to come up with possible solutions to mitigate this effect in follow-up studies.

Comment 3. The numbering of the figures is broken. Please check. 

Response 3. We apologize for the oversight in figure numbering. We have carefully reviewed the manuscript and corrected the figure numbering to ensure consistency and clarity.

Comment 4. There are also some formatting problems. The format of references (numbers in the text referring to the cited publication), figure captions and equations does not meet the requirements of the journal. Please check these requirements and make appropriate changes in the paper.

Response 4. We appreciate the reviewer's attention to detail regarding the formatting of the manuscript. We have reviewed the journal's formatting requirements and made the necessary adjustments to the references, figure captions, and equations to comply with the guidelines.

Reviewer 2 Report

Comments and Suggestions for Authors

The authors presented an approach for high-temperature health monitoring of plates based on variational mode decomposition and fuzzy entropy. Considering the novelty and quality of this paper, I have decided to reject it. The main reasons are as follows:

(1)  The proposed waveguide design has been explored by many researchers. For example, this paper (Liao Z., Zhang, X., Liu, T., Jia, J. and Tu, S. 2020, Characteristics of high-temperature equipment monitoring using dry-coupled ultrasonic waveguided transducers, Ultrasonics, 108, 106236) proposed a very similar waveguide transducer for health monitoring of high-temperature structures. Therefore, I do not find the approach presented in this paper to be novel.

(2)  The authors do not provide evidence that only the longitudinal wave was generated by the transmitter. Besides, the signals under different frequency excitations were not shown in the paper.

 

(3)  The authors claim that the IMF8 corresponded to SH0, and IMF2 corresponded to SH1. Are these Lamb waves? What criteria are used to classify these wave types? Is it appropriate to distinguish them only by comparing their amplitudes? Can variational mode decomposition be effectively used for decomposing wave modes?

Comments on the Quality of English Language

English writing can be improved.

Author Response

Comment 1.  The proposed waveguide design has been explored by many researchers. For example, this paper (Liao Z., Zhang, X., Liu, T., Jia, J. and Tu, S. 2020, Characteristics of high-temperature equipment monitoring using dry-coupled ultrasonic waveguided transducers, Ultrasonics, 108, 106236) proposed a very similar waveguide transducer for health monitoring of high-temperature structures. Therefore, I do not find the approach presented in this paper to be novel.

Response 1. We understand the reviewer's concern regarding the novelty of our proposed approach. It is true that waveguide designs for high-temperature monitoring have been explored by other researchers. However, our paper presents an innovative integration of a zirconia thermal buffer layer with an ultrasonic waveguide wave system and an accompanying signal feature extraction method, which differs from previous work by Liao Zhen et al. (2020). This integration is critical for addressing the challenges of environmental thermal noise and structural nonlinearities, which are not fully addressed in the dry-coupled approach. We have revised the manuscript to clarify how our approach advances the state of the art in high-temperature structural health monitoring.

Comment 2.  The authors do not provide evidence that only the longitudinal wave was generated by the transmitter. Besides, the signals under different frequency excitations were not shown in the paper.

Response 2. The ceramic heat buffer layer is considered as a rod structure, and the vibration generated by the sensor d33 is equivalent to striking one end of the rod. At this time, energy mainly propagates in the form of longitudinal waves along the length direction of the rod structure.

In another article that is about to be published, the correlation between excitation frequency, signal energy, and temperature repeatability was discussed, and it was concluded that 350 kHz is the most suitable excitation frequency. Due to intellectual property issues, this part of the content was not involved in this article. To avoid misunderstandings, the authors have made a brief explanation in the manuscript.

Comment 3.  The authors claim that the IMF8 corresponded to SH0, and IMF2 corresponded to SH1. Are these Lamb waves? What criteria are used to classify these wave types? Is it appropriate to distinguish them only by comparing their amplitudes? Can variational mode decomposition be effectively used for decomposing wave modes?

Response 3. Upon reevaluation of our data and analysis, we have identified the error in correlating IMF8 and IMF2 with the SH0 and SH1 modes, respectively.    We have taken immediate action to remove this incorrect association from the manuscript.    We understand the importance of accurate wave mode identification in our research and the implications it has for the reliability of our findings.   This reevaluation will involve a detailed examination of the modal characteristics, energy distribution, and central frequencies to ensure that our conclusions are well-founded and supported by the data.     We are grateful for the reviewer's vigilance in maintaining the scientific rigor of our work.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

There is still room for improvement in the paper. The authors did not explain the motivation for choosing Variational Mode Decomposition (VMD) and Fuzzy Entropy (FEN) for the analysis of the test results. Why were these approaches chosen? What are their advantages over other approaches? Authors are encouraged to add this discussion to the introduction. 

Author Response

There is still room for improvement in the paper. The authors did not explain the motivation for choosing Variational Mode Decomposition (VMD) and Fuzzy Entropy (FEN) for the analysis of the test results. Why were these approaches chosen? What are their advantages over other approaches? Authors are encouraged to add this discussion to the introduction. 

Response: We appreciate the reviewers' attention to the integrity of the manuscript argument. The guided wave excitation mode based on thermal buffer layer has the problem of strong noise interference and mode aliasing, and the traditional signal analysis method is difficult to effectively characterize the structural damage. The VMD method can be used to separate useful signals from noise signals by non-recursive variational decomposition and suitable for the noise reduction of received signals in complex environments.

The fault detection algorithm based on fuzzy entropy is robust to strong noise environment and is an objective fault detection algorithm in low SNR environment. The VMD method is commonly used in the diagnosis of guided wave damage in low SNR ultrasound. The innovation of this paper is to use fuzzy entropy to characterize the damage severity.

We have added this discussion to the introduction.

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript well addressed my concerns. It can be published in the current version.

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

In general, the note has been addressed. The paper can be published.