Kernel Regression Residual Decomposition-Based Polynomial Frequency Modulation Integral Algorithm to Identify Physical Parameters of Time-Varying Systems under Random Excitation

Round 1

Reviewer 1 Report

What specific problem do the physical parameters of time-varying systems under random excitation face?

How does the proposed multi-level kernel regression residual decomposition method overcome the issue of noise interference?

What are the advantages of using the derived polynomial frequency modulation integral algorithm and the correlation theory based on the fractional Fourier ambiguity function in the physical parameter identification method?

How does the proposed method provide a new idea in identifying the physical parameters of TV systems under random excitation?

How was the effectiveness of the method evaluated in the paper?

Were multiple sets of numerical simulations conducted to support the claims of the proposed method's effectiveness?

This review examines three significant papers from various fields that contribute to the advancement of knowledge in their respective domains. Xia, Ding, and Tang investigate the interaction effects of multiple input parameters on the integrity of safety instrumented systems under uncertainties, providing valuable insights for improving safety and risk management practices. Fan, Yang, and Bouguila propose a novel approach for modeling unsupervised grouped axial data using hierarchical Bayesian nonparametric models, offering a flexible framework with potential applications in computer vision and data analysis. Jin and Wang focus on the global stabilization of the attraction-repulsion Keller-Segel system, contributing to the understanding of pattern formation and dynamics in mathematical biology and chemical engineering. These papers showcase the diverse and impactful research being conducted across disciplines, providing valuable insights and advancements in their respective fields.

Interaction effects of multiple input parameters on the integrity of safety instrumented systems with the k-out-of-n redundancy arrangement under uncertainties. Quality and Reliability Engineering International. doi: https://doi.org/10.1002/qre.3359 Unsupervised Grouped Axial Data Modeling via Hierarchical Bayesian Nonparametric Models With Watson Distributions. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(12), 9654-9668. doi: 10.1109/TPAMI.2021.3128271 Global stabilization of the full attraction-repulsion Keller-Segel system. Discrete and Continuous Dynamical Systems- Series A, 40(6), 3509-3527. doi: 10.3934/dcds.2020027

How was the robustness of the method verified in the paper?

What were the varying levels of noise added to the input signal during the robustness verification process?

Did the paper present any limitations or potential areas for further improvement of the proposed method?

How does the novel multi-level kernel regression residual decomposition method contribute to the field of physical parameter identification in time-varying systems under random excitation?

 

In the realm of instrumentation and measurement, several recent papers have contributed to the advancement of signal estimation and analysis techniques. This introduction focuses on three notable papers from this domain. The first two papers, authored by Song, Mingotti, Zhang, Peretto, and Wen, were published in IEEE Transactions on Instrumentation and Measurement in 2022. The first paper introduces a fast iterative-interpolated Discrete Fourier Transform (DFT) phasor estimator that effectively considers out-of-band interference. This method offers a robust approach for accurately estimating the phase and magnitude of a signal in the presence of interference. The second paper by the same authors presents an accurate damping factor and frequency estimation technique specifically designed for damped real-valued sinusoidal signals. This method enhances the precision of estimating the damping factor and frequency, providing valuable insights into signal analysis and measurement. Moving on to the third paper, authored by Zhang, Xie, Shi, Huo, Ren, and He, it was published in Chaos: An Interdisciplinary Journal of Nonlinear Science in 2023. This study explores the resonance and bifurcation phenomena in a fractional quintic Mathieu-Duffing system. By investigating the system's dynamics, the authors uncover intriguing nonlinear behaviors and provide a deeper understanding of resonance and bifurcation phenomena

 

Fast iterative-interpolated DFT phasor estimator considering out-of-band interference. IEEE Transactions on Instrumentation and Measurement, 71. doi: 10.1109/TIM.2022.3203459 Accurate Damping Factor and Frequency Estimation for Damped Real-Valued Sinusoidal Signals. IEEE Transactions on Instrumentation and Measurement, 71. doi: 10.1109/TIM.2022.3220300 Resonance and bifurcation of fractional quintic Mathieu–Duffing system. Chaos: An Interdisciplinary Journal of Nonlinear Science, 33(2), 23131. doi: 10.1063/5.0138864

 

Moderate editing of English language required

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

This paper presents an approach for the identification of physical parameters in linear time-varying dynamical systems under random excitation. The topic of this paper is of interest and fits well the scope of Applied Science.

I think that the paper might be considered for publication after careful revision by the author. However, while the approach is surely interesting, I am not able to recommend it at this stage. My main concerns are related to the results:

- While in Figures 6-7 the estimated stiffness and damping seem to mimic their actual values, the discrepancy is still quite large. This is particularly true for the damping, where additional patterns also appear. Can the authors further comment on this?

- In Figure 5, the reconstructed displacements and velocities are shown for all the masses of the system. I would require the authors to compare them to those obtained from the numerical simulation and comment on this.

Other comments and questions are listed below:

- In the example, the mass is assumed as time-invariant. Can the approach also deal with case of a time-variant mass? And also in this example, are the time-invariant masses known or estimated by the proposed approach.

- I suggest placing Figure 2 earlier in the text and refer to it to better explain the flow of the proposed procedure.

- In Section 1, at line 37, the authors mention that "Short-time Fourier transform (STFT) [15, 16] and empirical mode decomposition (EMD) [17, 18] still have flaws such as theoretical deficiencies and endpoint effects.". Could you please more specific about the limitations of these approaches? Also I suggest including some basic, quick explanation about Kernel regression in what follows.

- Section 3 appears to miss some statements at the end on how parameters are finally recovered from Eq.(46).

- At line 149, "cm" should "c_m".

- It is not specified to which level of noise the figures 5-6-7 are referred. Please include this information.

- In the same figures, I would encourage the authors to replace the labels "amplitude" on the y-axis with the name of the variable.

 

I consider acceptable the quality of English language in this paper. However, I would encourage the authors to carefully re-read the manuscript, particularly the introduction, checking for mistakes. Moreover:

- [98] I suggest rephrasing the opening sentence as "The raw acceleration signal s(t) can be expressed by..."

- [137] I suggest replacing "consistent" with "equal" to improve clarity.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Accept

Author Response

Thank you for your comments.

Reviewer 2 Report

I appreciate the authors' efforts in quickly reviewing their manuscript, whose quality and clarity is indeed improved. While many of my comments have been exhaustively addressed, I feel that further revisions are needed before the manuscript can be considered for publication. My comments are reported in what follows - many of them being small annotations - but further attention is needed on the main comments.

 

Main comments:

 

1) I surely agree that the damping coefficient, due to its nature and usually small values in structural contexts, is more prone to error than the stiffness. However, the authors' response suggest that the errors produced by the identification approach can also depend by the very different values of the parameters in Eq.(46). If this is the case, I would encourage the authors to explore the use of a normalisation or scaling factors in the process - is there any improvements in the identification performance if the normalised stiffness and viscous damping have the same order of magnitude? In addition, I would also like to ask if there is any specific explanation for the "wavy" patterns displayed in Figure 8, or if they can somehow depend on settings used in the identification approach.

 

2) I appreciate the addition of comments regarding figures 5 and 6. While a visual comparison of these figures suggest that the simulated and reconstructed mass motions are indeed similar, I would again encourage to overlap them, so that the comparison and the differences between them can be better captured by the reader.

 

Minor comments:

 

3) I agree that assuming the mass as time-invariant is a reasonable assumption for this problem. I do not have further suggestions on this, but I would like to add that while the mass and the stiffness identification is indeed easier than for damping, a problem is often related to distinguish between effects related to a change in the mass or of the stiffness parameters.

 

4) With respect to comment 9 of the previous review, I cannot see modifications carried out on y-axis labels. In all Figures from 4 to 8, I would encourage the authors to specify the quantities plotted, with their unit (if any), in the y-axis and to check that units are also consistently reported on the other axes (i.e., (s) is sometimes reported for time and sometimes not).

 

5) I suggest replacing "caused" with "causes" at line 32

 

6) At line 88, I suggest rephrasing "which contains a lot of TV parameter information" with a more clear technical statement.

 

7) In Section 2.1, I appreciate the addition of an introductory paragraph, but I suggest checking and rephrasing the first paragraph of the section, as some sentences appear to be unclear or grammatically incorrect.

 

8) At line 334, I don't understand the meaning of "more representative" in this statement.

 

9) At line 336, please rephrase as "three different cases of variation in time".

 

10) At line 419, a capital letter is missing at the beginning of the sentence.

I have already included any grammar comments above. 

Author Response

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Author Response File: Author Response.pdf

Round 3

Reviewer 2 Report

No further comments from my side.

My only remaining suggestion for the authors, for future work, is to consider normalising the coefficients m, c and k in the estimation procedure, so that they can maintain the same order of magnitude in the process. 

I recommend the acceptance of the manuscript in the present form.