A New Orthogonal Least Squares Identification Method for a Class of Fractional Hammerstein Models

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Dear Authors, please find my comments, questions, and suggestions below.

The link to Reference [33] is missing in the text of the Article. Please add it.

You state that your proposed H-GOLS algorithm significantly reduces computational complexity. Has this been evaluated numerically? You might consider adding a table or performance graphs relative to the BPDN, LASSO, and H-GOLS-Integral methods you mention. This information could be useful to your colleagues in the field.

In my opinion, the conclusion section could be expanded to provide more details about the advantages of the proposed algorithm and to point out any disadvantages compared to previous studies. This will help to clarify the contribution of your research to the field. Also you could add future works if this is planned.

In general, I think your article deserves publication in Algorithms Journal after minor revision.

Author Response

Comments 1: The link to Reference [33] is missing in the text of the Article.

Response 1: Thank you for your carefully checking. We have added the citation for Reference [33]; please see Page 6 in Section 3.1 of the revised manuscript. Additionally, we have updated the references, and what was originally Reference [33] is now cited as [29] in the revised manuscript.

Comments 2: You state that your proposed H-GOLS algorithm significantly reduces computational complexity. Has this been evaluated numerically?

Response 2: Thank you for your valuable suggestion. We have added a table to present a comparison of the computational cost of the H-GOLS ,OMP, BPDN, and LASSO algorithms, please refer to table I on page 12 in Section 4.

Comments 3: The conclusion section could be expanded to provide more details about the advantages of the proposed algorithm and to point out any disadvantages compared to previous studies.

Response 3: Thank you for your good suggestion. We have added the advantages of the proposed H-GOLS algorithm and pointed out our future research of the study in the Conclusions section.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

Review on the article “A new orthogonal least squares identification method for a class of fractional Hammerstein models” by Xijian Yin, Yanjun Liu

The article develops and illustrates with examples a new algorithm for joint identification of orders and parameters of the fractional Hammerstein model. Based on the use of the Householder transformation algorithm for a triangular sub-information ill-conditioned matrix, the presented algorithm significantly reduces the complexity of calculations.

Numerical simulations, as the authors claim, confirm the effectiveness of the proposed method.

In my opinion, the paper is interesting, the results are new and practically significant.

Regarding the text, I have several questions and wishes.

1. I need an explanation of the notation in the left part of formula (17).
2. Without denying the importance of numerical experiments, I have the following questions regarding the examples given in the article:
3. a) is example 1 in a certain sense universal (illustrative)? For what reasons are such parameters given in the example? It is desirable to clarify this point in the article.
4. b) how relevant is the example about the CD player at the present time?
5. In the Conclusions, it is desirable to emphasize in more detail the computational efficiency of the method in comparison with analogues. Especially since there are such comparisons in the article. Why don't the authors focus the reader's attention on this in the Conclusions?

After the authors' responses and corresponding improvements to the text, the article can be accepted.

Author Response

Comments 1: I need an explanation of the notation in the left part of formula (17).

Response 1: Thank you for your comment. The left part of formula (17) (i.e., PΞk(:, 1:k)) represents the first k columns of the permutation matrix PΞk∈ℜn×k.

Comments 2: Is example 1 in a certain sense universal (illustrative)? For what reasons are such parameters given in the example? It is desirable to clarify this point in the article.

Response 2: Thank you for your comment. Example 1 is intended to serve as a standard numerical simulation case to demonstrate the effectiveness of the algorithm. The parameters are not fixed and can indeed be modified as needed. We have clarified this in the revised version of the manuscript.

Comments 3: How relevant is the example about the CD player at the present time?

Response 3: Thank you for your comment. The example of the CD player arm system demonstrates the effectiveness of the fractional model. In this case, the CD player arm system can be represented as a fractional order system with a commensurate order of 0.1 and only four parameters. Though CD players are no longer common in today's electronic consumer products, their robotic arm systems, as a type of flexible transmission system, are widely used in many fields such as robotics and smart logistics.

Comments 4: In the Conclusions, it is desirable to emphasize in more detail the computational efficiency of the method in comparison with analogues. Especially since there are such comparisons in the article. Why don't the authors focus the reader's attention on this in the Conclusions?

Response 4: Thank you for your valuable suggestions. We have revised the Conclusions section accordingly. The advantages of the proposed H-GOLS algorithm compared to other greedy algorithms have been summarized.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Dear Authors, thank you for improving the manuscript in accordance with my comments and suggestions. I have no further questions for you. I believe your article is now ready for publication in Algorithms Journal.

Reviewer 2 Report

Comments and Suggestions for Authors

I am satisfied with the authors' responses and the corresponding improvements to the text. I propose to accept the article as submitted now.