Early Detection of Defects through the Identification of Distortion Characteristics in Ultrasonic Responses

Round 1

Reviewer 1 Report

• What is the significant of early detection
• Kindly define the criterion of early detection
• What is the level of early detection or incipient fault
• What is the time taken to detect the defect in the early?
• Compare the performance of the proposed approach w.r.t the available market- off-the-shelf solutions
• Generally, ultrasonic technique is costly. Then what is the main requirement to use this though other conventional techniques are available and provide a satisfactory results
• The state-of-the art is too short. If possible, kindly enhance it and tabulate the all possible research gape related the presented work
• If possible, kindly provide the indexing of the proposed work

Author Response

Dear Reviewer #1, attached you will find the file with the detailed answers to the individual questions you have posed

Pietro Burrascano

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper discusses the characteristics of a damage Index that has proved effective for the early detection of defects based on their nonlinear behavior. The proposed damage index is based on the Hammerstein model of the nonlinear physical system and is compared with the damage index that is defined as the ratio of the energy. The paper should be revised before further consideration.

1. The description style of the paper is a little too mathematical and non-mathematical readers in engineering fields find difficulties in following the paper. There are also some definitions and illustrations that are not clearly understood. The authors should provide as much information as possible for the readers.

(1) In Section 2.1, an illustrative figure(s) may be needed to show a nonlinear signal and how each step of Hammerstein decomposition is performed to find the necessary coefficients. It is also necessary to show how the decomposed second or higher harmonic component is different from that of Fourier transform.

(2) In Section 2, a signal of pulse compression and an exponential swept sign signal should be provided.

(3) In Section 3, define “early” in early damage detection.

(4) In Section 2.3.1, a relevant figure(s) may be helpful to show how to calculate energy-based damage index from a nonlinear signal in time domain.

(5) The denominator of Eq. (5) defining the energy-based damage index (DI) should be defined differently. It is not the sum of the responses of the non-linear branches of the Hammerstein model because it is before the Hammerstein model applied.

(6) In Section 3.3.2, the authors should present the figures of function g₁(t) and g_k(t).

(7) A time-domain signal and other relevant signal(s) obtained from Figure 2 in connection with the Hammerstein model should be provided.

2. The authors should clearly describe the main difference of their paper from the paper of Ref [22]. The general approach and the example nonlinear system is almost the same as Ref [22].
3. The authors emphasize the proposed damage index (HI) is better (or higher) in assessing early detection of damage compared to the energy-based damage index (DI). The reviewer does not see any parameter describing early stage of damage process and cannot find much higher value of SI compared to DI for given damage state in Fig. 3 thru Fig. 7.
4. The same y-axis scale should be used in Fig. 3 thru Fig. 7. I do not see a much higher damage index of SI compared to DI for the same damage level. Please explain why the authors insist that the SI is more sensitive to the damage than DI for the same damage level. Please explain.

Author Response

Dear Reviewer #2, attached you will find the file with the detailed answers to the individual questions you have posed
Pietro Burrascano

Author Response File: Author Response.pdf

Reviewer 3 Report

Thank you for sharing your work. My question/comments are as follows:

1. Please add a reference scale with their respective techniques in introduction section. For example, in line 61, what is the size of the crack that is possible to detect with the technique?
2. Line 123 – 124: Not sure why this is a disadvantage?
3. Line 338: What is meant by “measurement noise” ?
4. What is the rationale behind selecting 2sigma in the results?
5. Section 3, Fig. 3 to Fig. 7: From the experimental results shown for different SNR, it appears that the mean value of HI performed well as compared to DI. However, if we consider the 2sigma variation along with the mean value, they appears to overlap significant position specially in low SNR and low alpha values. Please provide strong argument to justify why HI is indicator is better than DI ?

Author Response

Dear Reviewer #3, attached you will find the file with the detailed answers to the individual questions you have posed
Pietro Burrascano

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

I think the paper has been revised according to the reviewer's comments and can be accepted for publication in Mathematics.

Reviewer 3 Report

Thank you for your responses. I don't have any further question.