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  • Huawei Wang1,
  • Xinyue Wang2 and
  • Youxing Guo3
  • et al.

Reviewer 1: Anonymous Reviewer 2: Mohammad Ali Sahraei Reviewer 3: Anonymous

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The article presents a study of modeling the movement of high-speed trains using the distributed adaptive fault-tolerant control (DAFTC) approach. The research topic is relevant. The article fills a gap in existing research and proposes an improved method for modeling tasks using a multi-component dynamic model at the level of a high-speed train car. In the study, the authors presented a comparison of the centralized adaptive fault-tolerant control (CAFTC) and DAFTC methods. To explain the proposed model, the article presents the mathematical basis of the proposed method. The results presented using Figures and Tables demonstrate the effectiveness of the proposed method. The Figures, Tables, and list of references used in the article have the appropriate references. The authors analyzed the presented research results and identified future research.

If the presented study has limitations, they should be noted in the Discussion section, and attention should be paid to the following comments:

At the end of the Introduction section, it is advisable to give a brief description of the content of the following sections of the article.

Lines 83-90: ‘…c1, c2 and c3.’ – but c1, c2 and c3 are missing in formulas (2)-(4). There is no description in formulas (2)-(4) for a0, a1 and a2 .

Line 118: Further in the text, the symbol ‘T’ is used in the formulas, which is not explained. In formula (8), ϕx is used, so it is better to use this same designation in the explanation of this formula, rather than ϕp

Line 182: It is necessary to indicate the environment in which the simulation was performed and describe the technical characteristics of the computer and the software used. For a better explanation of the logic of the proposed model, it is recommended to present the corresponding algorithm.

Line 240: In the Discussion section, it is recommended to analyze the results in more detail by comparing numerical data, which confirms the effectiveness of the proposed method.

Line 535: In the Conclusions section, it is recommended to indicate the most important results in percentages, demonstrating the effectiveness of the proposed method.

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper is entitled “Adaptive Distributed Fault-Tolerant Control for High-Speed Trains Based on a Multi-Body Dynamics Model” In this case, the idea and results of the paper are interesting but the following comments can be utilized to improve this paper in future.

 

Abstract

  • The abstract immediately begins with a problem statement but lacks a short contextual background (e.g., why actuator faults or input saturation are significant in distributed train control systems).
  • The abstract mentions several control challenges but does not explicitly define what gap in the literature this work addresses (e.g., lack of distributed fault-tolerant strategies under saturation).
  • The abstract effectively mentions the multi-agent model, adaptive law, and auxiliary system. It uses technical terms (“dual-closed-loop tracking,” “second-order auxiliary system”) without brief interpretation.
  • The abstract states that simulations “demonstrate effectiveness,” but no quantitative or comparative results are provided.
  • The conclusion restates the result without indicating potential applications or future work.

 

General comment: There is a lack of the suitable literature review.

                                    There is a lack of the sutable methodology.

                                    There is a ack of the appropriate discussion.

                                    The procedure of the formula is not very clear.

                                    There is a lack of appropriate conclusion.

 

Results:

  • The controller design section is mathematically dense and difficult to follow. Many equations appear consecutively without sufficient explanation of why each step is taken or how it contributes to the controller structure.
  • The design parameters k_1,k_2,k_3,p,qare introduced, but the manuscript does not justify:
    1. acceptable ranges,
    2. tuning guidelines, or
    3. stability conditions related to their selection.

This makes reproduction difficult and weakens the methodological transparency.

  • The tracking errors and (Eq. 10) are defined using λ₁ and λ₂, but the authors do not clearly explain how these auxiliary states reshape the error dynamics or how they avoid error blow-up under actuator faults.
  • The controller shown in Eq. (12) is presented suddenly, combining several estimated parameters and nonlinear compensation terms.

The adaptive laws (Eq. 13–18) are presented without clear motivation for each term.
Reviewers familiar with adaptive control will understand the format, but the manuscript needs:

  1. justification of diagonal structures,
  2. rationale for using trace operators,
  3. explanation of how the laws avoid parameter drift.

Simulation Verification

  • The section provides basic information about the train configuration (4 motor cars + 4 trailer cars), but does not clearly describe the simulation platform, numerical solver, integration step size, or computing environment.
  • CAFTC is mentioned briefly, but:
    1. No controller structure for CAFTC is described.
    2. No mathematical formulation is given for how centralized forces are computed and distributed.
    3. It is unclear whether CAFTC is optimally tuned or merely a baseline.
  • Table 1 lists high-speed train parameters (e.g., mk, lh, lr), but:
    1. Several parameters (a(t), b(t), c(t)) appear time-varying but lack physical interpretation.
    2. No references are provided to justify these values.
    3. No explanation is given for the sinusoidal disturbances—are they modeling aerodynamic drag or uncertain resistance?
  •  

Final decision: This manuscript has interesting objectives; however, it is not suitable for publication and must be rejected.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The study is relevant and timely, especially as distributed control architectures are becoming central in next-generation high-speed rail systems, including virtual coupling and intelligent train control systems. Overall, it represents a solid contribution to the field of railway control engineering. The following issues should be addressed.

  • Abstract: Clarify the practical significance of the results. Mention quantitative findings to strengthen impact.
  • Introduction section: The distinction between single-train internal vs multi-train coordination is correct, but consider adding a sentence connecting this dichotomy directly to the motivation for distributed control.
  • A short reference to safety and HSR literature could enhance the introduction’s context (e.g., https://doi.org/10.1016/j.hspr.2024.08.004)
  • Simulation verification: The simulation scenario is informative, but it would benefit from a brief explanation of why the chosen actuator efficiency degradation values are representative of real faults (e.g., traction converter thermal derating).
  • Discussion: Consider expanding the limitations paragraph with assumptions.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have addressed the comments.

Author Response

Dear Editors,
        Thank you once again for your positive feedback on the manuscript revisions and for pointing out the remaining  issues. We have carefully addressed each of your suggestions as detailed below:
        1. Regarding introductory text under section headings: We have added brief transitional paragraphs between Section 2 and Section 2.1, as well as between Section 3 and Section 3.1.
        2.Regarding the bracket hierarchy in mathematical formulations: We have thoroughly reviewed and corrected the use of brackets throughout the manuscript according to your specification. The format 
is now standardized as follows: first-level parentheses use round brackets ”( )“, and second-level parentheses use square brackets ”[ ]“.
        3.Regarding grid lines in graphical outputs:We have added grid lines to the graphical outputs in Figures 6 and 7, making their format consistent with earlier figures such as Figures 2 and 3.