Equivalent Identification of Distributed Random Dynamic Load by Using K–L Decomposition and Sparse Representation

Round 1

Reviewer 1 Report

The paper entitled “Equivalent identification of distributed random dynamic load by using K‐L decomposition and sparse representation” co-authored by Kun Li , Yue Zhao, Zhuo Fu, Chenghao Tan , Xianfeng Man , Chi Liu, aims to characterise and identification of the load random characteristics. The authors used K‐L series expansion, Interval process, Green’s and sparse representation Laplace transformation to derive Green’s kernel function method to model and identify different types of loads. The proposed method is relevant and applicable to engineering systems.  The subject is interesting, and there is its originality. However, this reviewer had a few issues provided below and some major comments.

 

General comments:

 

• The information on the interval and green’s methods should be included in the abstract. It will increase the visibility of the paper and the highlights of this application.

 

• The importance of the well-addressed literature review over the topic approaching past and present research linked to the paper subject is not just to summarise what is currently known about the subject but is also to provide a detailed justification for your research and support the lack of study present in the research paper. In the results section it is mentioned “At present, there are few reports on the time‐domain analysis method of the vibration problem under distributed random dynamic load”. It shows that the paper needs a literature review improvement; evermore, the author should carefully point out the contribution of the paper based on the lack of existing literature.

 

• Please provide a reference (s) of Green’s function and the interval method.

 

• Legends of figures are not well written. Please improve them in a way to provide a short description of the figures. Also, the authors must provide a physical explanation of the results.

 

• It page 16, it is stated “In addition, the high‐frequency eigenvectors are often disturbed by noise, which is difficult to be identified accurately.”. It is not clear when noise was assumed and mentioned. Why do only higher-mode suffer from noise? It is not precedent, noise-contaminated all signals not only in frequenciescyeis. Please give more detail and explanation.

 

• Please, explain figure 6(b).

 

• OMP algorithm is used in the optimization process. Is it possible to track the convergence on the estimated parameter? If so, the authors should present the convergence graphic to support the parameters estimation.

 

Summary

This reviewer feels a conceptual difficulty in a few points (see general comments) that needs to be properly addressed. The manuscript is a bit confusing. Therefore, in my opinion, the manuscript should suffer a major review before being considered for publication.

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

In this manuscript, the authors proposed an equivalent identification method based on K‐L decomposition and sparse representation to reconstruct distributed random dynamic loads. The dynamic distributed load is expressed as the product of the spatial and temporal parts. The interval process model is used to characterize the uncertainty in temporal part, while the spatial part is uncertainty-free. Then the random load is transformed into two parts through Karhunen–Loève theorem, i.e., median function and covariance matrix. Then these two parts are identified separately by the existing approaches for deterministic systems. The problem is interesting, the proposed method is appropriate and the results are convincing. The manuscript is also well-structured and well-written. I would suggest minor revisions for this manuscript.
My comments are:
1) I would suggest the authors to add a couple of paragraphs in the conclusions to summarize the drawbacks or limitations of the proposed method and some future work.
2) Since the authors only address the uncertainty in the temporal domain, how about the uncertainty in the spatial domain? Could the authors comment a little bit on this issue?
3) In the first paragraph of Page 6, the first F^{\Delta} should be F^m.
4) What is the mathematical formulation of \belta^{(i)} in Eq. (13)?
5) On Page 9, the authors states “Substituting this solution into Eq. (14), …”. I am not sure which solution or equation is substituted.
6) What are the boundary conditions in the numerical example?
7) What is the noise level that is used in the example? Is Figure 4 noisy or noise-free?
8) The labels in Figure 9 are not shown completely.
9) What is Eq. (41)?

Author Response

Please see the attachment.

Author Response File: Author Response.pdf