Research on the Indirect Solution Optimization Regularization Method for Ship Mechanical Excitation Force

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have investigated the topic “Research on the Indirect Solution Optimization Regularization Method for Ship Mechanical Excitation Force”. Though the subject has gained increasing relevance considering global sustainability objectives and optimization of different systems, however, I have few comments that can improve the manuscript.

 

1. Although the authors in the introduction section of the study established the importance of excitation force identification, however, the motivation for proposing specifically the Q-O and BL-curve methods could not be made clear and have to be highlighted and made clearer. This can be achieved if the authors can expand on why these two were chosen over other advanced approaches.
2. Interestingly, the authors compare Q-O and BL-curve against TSVD, GCV, and L-curve. However, the study would be stronger if additional recent advanced techniques (e.g., hybrid adaptive regularization, machine learning–based methods) are not only benchmarked but discussed in this study.
3. Looking at equations (1)–(7), it appears that some intermediate steps are missing, which may reduce reproducibility. The authors are encouraged to clarify these derivations with more explanation or an appendix.
4. In the parameter sensitivity, the authors reported that the Q-O method expands the parameter search space by 7.3x, but did not specify how this was quantified or validated. The authors are recommended to provide more detail on the sensitivity analysis for the regularization parameters.
5. Considering the experimental reproducibility, the scaled 1:4 cabin model experiment is well described, but more detail on boundary conditions (e.g., how the mounting conditions replicate real ship environments) should be added to the manuscript to ensure reproducibility for other researchers.
6. The authors reported that the simulations and experiments use noise levels up to 20 dB. However, it is not clear if these values reflect actual ship operating conditions and the viability of the noise condition can be justified by providing references to real-world measurements.
7. With regards to the references, while fewer references are included, several are older (pre-2010), authors are requested to including more recent works (post-2020) in the area of dynamic load identification and regularization in structural dynamics.

 

 

Author Response

Comments 1:

Although the authors in the introduction section of the study established the importance of excitation force identification, however, the motivation for proposing specifically the Q-O and BL-curve methods could not be made clear and have to be highlighted and made clearer. This can be achieved if the authors can expand on why these two were chosen over other advanced approaches.

Response 1:

Thank you for your suggestion. I agree. I have provided additional explanations in lines 78-87 of the paper.

Comments 2:

Interestingly, the authors compare Q-O and BL-curve against TSVD, GCV, and L-curve. However, the study would be stronger if additional recent advanced techniques (e.g., hybrid adaptive regularization, machine learning–based methods) are not only benchmarked but discussed in this study.

Response 2:

Thank you for your valuable suggestions. The author fully agrees with your views and will make improvements in subsequent work.

Comments 3:

Looking at equations (1)–(7), it appears that some intermediate steps are missing, which may reduce reproducibility. The authors are encouraged to clarify these derivations with more explanation or an appendix.

Response 3:

Thank you for your valuable feedback. In the process of (1)-(7), the author omitted some steps, as they believed that an excessive number of steps would make the article quite lengthy.

Comments 4:

In the parameter sensitivity, the authors reported that the Q-O method expands the parameter search space by 7.3x, but did not specify how this was quantified or validated. The authors are recommended to provide more detail on the sensitivity analysis for the regularization parameters.

Response 4:

Thank you for your valuable feedback. The author has made the necessary revisions. For details, please refer to lines 88-90 of the paper.

Comments 5:

Considering the experimental reproducibility, the scaled 1:4 cabin model experiment is well described, but more detail on boundary conditions (e.g., how the mounting conditions replicate real ship environments) should be added to the manuscript to ensure reproducibility for other researchers.

Response 5:

Thank you for your valuable feedback. The scale model experiment was conducted on a certain lake. Meanwhile, experiments for other projects were also carried out there. Furthermore, the internal structure of the model is quite complex, which can be seen in Figure 10 of the paper. Therefore, the author believes that regarding replicability, it is not very feasible.

Comments 6:

The authors reported that the simulations and experiments use noise levels up to 20 dB. However, it is not clear if these values reflect actual ship operating conditions and the viability of the noise condition can be justified by providing references to real-world measurements.

Response 6:

Thank you very much for your valuable suggestions. The author introduced a 20dB noise interference to simulate a more demanding marine environment. In the actual ship experiment, the author found that the signal-to-noise ratio (SNR) of certain frequency bands in the measured data was extremely low (around 1dB). Therefore, the author introduced the 20dB noise interference. On the other hand, after introducing the 20dB noise interference, the actual SNR did not drop below 1dB. For this reason, the author considered this assumption reasonable at that time.

Comments 7:

With regards to the references, while fewer references are included, several are older (pre-2010), authors are requested to including more recent works (post-2020) in the area of dynamic load identification and regularization in structural dynamics.

Response 7:

Thank you very much for your valuable suggestions. Detailed information has been added in the reference section at the end of the article.

Reviewer 2 Report

Comments and Suggestions for Authors

The authors acknowledge that the methodology for dynamic load identification is already well established, and they claim that this technology has also been extended and applied to engineering fields such as transportation, building structures, wind resistance and disaster prevention, and health monitoring. However, its application in the marine field is relatively scarce. This statement can be misleading, as it may appear that the authors are simply applying the method to another type of structure. The authors should clearly state why the ship or marine field is unique, and what kinds of modifications or further methodological developments are required. Please note that this distinction is not evident from the abstract or the introduction.

Could the authors clearly identify why, in real-world shipboard scenarios characterized by multi-source interference, their case is different from other structures where multiple sources can also exist (aerospace, rotational machines, ...)?

By reading the introduction, it appears that the authors have simply applied some additional methods, such as Quasi-Optimal (Q-O) Refinement and Weighted B-spline Stabilization (BL-curve). Could the authors briefly explain in the introduction what modifications or developments were necessary for these methods, and highlight this more clearly?

Detailed comments:

In Equation (15), the residual confidence level wi ​ is defined as a function of the residual error. Could the authors clarify how the parameter a_run​ is determined in practice, and how sensitive the weighted B-spline interpolation results are to its chosen value?

The curvature L′(λ) in Equation (19) is used to determine the optimal regularization parameter when it reaches its maximum value. Here the numerical stability of this approach should be presented/8elaborated, especially in cases where noise causes multiple local maxima in the curvature function?

In the description of the test acquisition and analysis system, the excitation force is calculated using the transfer function matrix H. Is this sensitive to sensor placement errors and whether the choice of RM5 as the verification point might bias the accuracy assessment of the reconstructed acceleration field?

By reading the whole paper, the novelty becomes clearer than it does in the introduction, and the results produced are of good quality. Therefore, I strongly recommend revising and improving the weaker parts of the paper to make the paper suitable for publication

Author Response

Comments 1:

The authors acknowledge that the methods for dynamic load identification are already well-established and claim that this technology has also been extended and applied to engineering fields such as transportation, building structures, wind resistance and disaster prevention, and health monitoring. However, its application in the marine field is relatively scarce. This statement may be misleading, as the authors seem to merely apply this method to another type of structure. The authors should clearly explain why the ship or marine field is unique and what modifications or further method development are required. It should be noted that this is not evident from the abstract or introduction. Can the authors clearly indicate why their case differs from other structures (e.g., aerospace, rotating machinery) that may also have multiple sources in real-world on-board scenarios characterized by multi-source interference?

Response 1:

Thank you very much for your valuable suggestions. The authors have added supplementary explanations in Lines 56-62 of the paper.

Comments 2:

After reading the introduction, it appears that the authors have simply applied some additional methods, such as quasi-optimal (Q-O) refinement and weighted B-spline stabilization (BL curve). Can the authors briefly explain in the introduction what modifications or developments these methods require and emphasize this point more clearly?

Response 2:

Thank you very much for your valuable suggestions. The authors have added supplementary explanations in Lines 78-87 of the paper.

Comments 3:

In Equation (15), the residual confidence level wi is defined as a function of the residual. Can the authors clarify how the parameter a_run is determined in practice and the sensitivity of the weighted B-spline interpolation results to the selected value of a_run?

Response 3:

Thank you for your valuable feedback. The value of a_run is determined through actual measurements using sensors after the equipment is in operation. This value is substituted into the calculation to counteract the influence of noise and improve the stability of the solution.

Comments 4:

In the description of the test acquisition and analysis system, the excitation force is calculated using the transfer function matrix H. Is this sensitive to sensor placement errors, and will the selection of RM5 as the verification point bias the accuracy evaluation of the reconstructed acceleration field?

Response 4:

Thank you for your valuable comments. The arrangement of sensors will definitely affect the transfer function matrix H, thereby influencing the calculation of the excitation force. The authors are currently conducting relevant research on this aspect. The arrangement of sensors affects the correlation of the matrix columns, which in turn impacts the degree of ill-conditioning of the matrix. This is due to the influence of factors such as structure and mode. The purpose of this paper is to test the regularization algorithm. Therefore, under the same sensor arrangement, when comparing the effects of regularization algorithms, the errors caused by sensor arrangement can be considered to offset each other, which refers to the issue of relative accuracy.

Reviewer 3 Report

Comments and Suggestions for Authors

Good afternoon, colleagues! I have reviewed the work and would like to make a number of comments. First, drawings from 3rd to 8th are difficult to perceive and understand in the context of research. In my opinion, the presentation of this material should be reviewed. Perhaps it should be reduced to a text statement for some of the figures and a more detailed description. Secondly, Figures 13 to 16 illustrate spectrograms in octave bands. Why is such a rough sampling of accelerograms presented? In my opinion, the results of the analysis should also be presented in the generally accepted form of Fourier spectra. As a suggestion, you can consider building Wavelet images for analysis. This would be very interesting in the light of the experiment. Third, why is a full-scale experiment chosen for validation rather than a numerical experiment to begin with? Overall, the work is interesting.

Author Response

 

Comments 1:

 

First, it is difficult to perceive and understand Figures 3 to 8 in the context of the research background. In my view, the presentation of these materials should be reviewed. Perhaps they should be simplified into textual statements with some numerical data and supplemented with more detailed descriptions.

 

Response 1:

Thank you for your valuable comments. The authors have added supplementary explanations in Lines 353-360 of the article.

Comments 2:

Why was a full-scale experiment chosen for verification at the very beginning instead of a numerical experiment? Overall, this work is quite interesting.

Response 2:

Thank you for your valuable comments. In fact, this paper first conducted numerical simulation experiments on simply supported plates, and then used full-scale experiments for verification.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have provided satisfactory response and the paper can now be accepted.

Reviewer 2 Report

Comments and Suggestions for Authors

Accept