Mathematics-Driven Analysis of Offshore Green Hydrogen Stations

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1- The innovation is not well described in the abstract, the main research question is not clear in the abstract.

2- Identify the main difference between green hydrogen production at sea and on land from different aspects.

3- Some references in this study are very old, try to use newer references.

4- What optimization method did you use to optimize the mathematical model?

5- Why did you neglect to consider uncertainty in mathematical modeling?

6- What is the role of Python in your simulation? Did you use simulation or write code in your modeling?

7- How do offshore locations improve the atmospheric conditions for solar energy production compared to densely populated areas?

8- How do you clarify the effect of solar radiation reflection at sea on increasing electricity production?

9- The conclusion needs to be revised and could include important research findings.

Author Response

Dear reviewer:

We appreciate your feedback and suggestions. In response to your comments, we will provide a targeted answer, and the corresponding revision will be reflected in the manuscript (highlighted in yellow). Thank you for your careful and patient comments and your instructive recommendations.

Comment #1)

The innovation is not well described in the abstract, the main research question is not clear in the abstract.

Response to the reviewer:

The authors agree with this comment. In response, the abstract has been substantially revised to clearly emphasize the innovation and define the main research question of the study. Specifically, the updated abstract now highlights the development of a mathematical model as a generic framework applicable to any location worldwide and developed to analyze the integration of solar energy generation and green hydrogen production. Furthermore, it details the model's capabilities to evaluate the influence of various environmental and technical parameters on system performance, thereby addressing the central research objective: to provide a robust simulation-based tool to optimize offshore green hydrogen stations powered by solar energy.

Reference to the revised manuscript: See Abstract.

Comment #2)

Identify the main difference between green hydrogen production at sea and on land from different aspects.

Response to the reviewer:

The authors agree with this comment. In response, the revised manuscript now explicitly outlines the main differences between green hydrogen production at sea and on land, addressing key aspects such as energy efficiency, environmental conditions, infrastructure requirements, and system scalability. The updated text emphasizes that offshore production benefits from higher solar irradiance due to lower atmospheric attenuation and reflection from the sea surface, leading to increased hydrogen output or reduced photovoltaic surface area. It also highlights logistical and structural distinctions, including the challenges of marine corrosion and anchoring, as well as the advantages of proximity to consumption points.

Reference to the revised manuscript: i.e: see section 1. Introduction

Comment #3)

Some references in this study are very old, try to use newer references.

Response to the reviewer:

The authors agree with this comment. Accordingly, a new set of recent references has
been included in the new version of the manuscript: See bellow the list of these new references.
8. IRENA. Renewable Energy Statistics 2024. ISBN: 978-92-9260-614-5.
18. IRENA. Fostering a blue economy: Offshore renewable energy 2020. ISBN: 978-92-9260-288-8.
19. Liu, G.; Guo, J.; Peng, H.; Ping, H.; Ma, Q. Review of Recent Offshore Floating Photovoltaic Systems. J. Mar. Sci. Eng. 2024, 12, 1942, doi:10.3390/JMSE12111942.
20. Sahu, A.; Yadav, N.; Sudhakar, K. Floating Photovoltaic Power Plant: A Review. Renew. Sustain. Energy Rev. 2016, 66, 815–824, doi:10.1016/J.RSER.2016.08.051.
21. Djalab, A.; Djalab, Z.; El Hammoumi, A.; Marco TINA, G.; Motahhir, S.; Laouid, A.A. A Comprehensive Review of Floating Photovoltaic Systems: Tech Advances, Marine Environmental Influences on Offshore PV Systems, and Economic Feasibility Analysis. Solar Energy 2024, 277, 112711, doi:10.1016/J.SOLENER.2024.112711.
25. Costa, Á.M.; Orosa, J.A.; Vergara, D.; Fernández-Arias, P. New Tendencies in Wind Energy Operation and Maintenance. Appli. Sci. 2021, 11, 1386, doi:10.3390/APP11041386.
29. Alias, N.D.; Go, Y.I. Decommissioning Platforms to Offshore Solar System: Road to Green Hydrogen Production from Seawater. Renew. Energy Focus 2023, 46, 136–155, doi:10.1016/J.REF.2023.05.003.
47. Maurya Rajeev Gandhi Govt P G, M.K.; Kumar Kurre Assistant Professor, R.; Maurya, M.; Singh, H.; Pandey, S.; Kerketta, S.A.; Kumar Kurre, R. Study of Characteristic Properties of Electromagnetic Radiation in the Presence of Earth’s Atmosphere. Article in International Journal of Advanced Academic Studies 2024, 109, 109–116, doi:10.33545/27068919.2024.v6.i8b.1259.

Comment #4)

What optimization method did you use to optimize the mathematical model?

Response to the reviewer:
The authors agree with this comment. The mathematical model presented in the manuscript is structured as a configurable simulation framework rather than a fixed optimization algorithm. However, it has been designed to support optimization through multivariable parametric analyses, which allow the user to iteratively evaluate the influence of different design and environmental parameters (e.g., panel inclination, solar irradiance, electrolyzer efficiency) on green hydrogen production. This simulation-based approach enables the selection of optimal configurations based on specific performance
targets, such as maximizing green hydrogen output or minimizing photovoltaic surface area.
Reference to the revised manuscript: i.e: see Section 2.2. Generalization and particularization: Mathematical model configuration.

Comment #5)

Why did you neglect to consider uncertainty in mathematical modeling?

Response to the reviewer:
The authors agree with this comment and appreciate the opportunity to clarify this aspect. The present version of the mathematical model prioritizes the establishment of a deterministic framework that defines the fundamental relationships among system components and environmental parameters. While uncertainty analysis is indeed an important aspect of modeling, it was intentionally not incorporated in this initial development phase to maintain clarity and focus on the model’s structural foundation. Nonetheless, the model has been explicitly designed as a tool to be extensible and adaptable, allowing for the future integration of stochastic elements and uncertainty quantification.
Reference to the revised manuscript: i.e see Section 2.2. Generalization and particularization: Mathematical model configuration

Comment #6)

What is the role of Python in your simulation? Did you use simulation or write code in your modeling?

Response to the reviewer:
The authors agree with this comment and thank the reviewer for the opportunity to elaborate. Python plays a central role in the implementation of the mathematical model. Rather than relying on off-the-shelf simulation software, the authors developed custom code using Python to simulate the behavior of the green hydrogen production system. Python was chosen for its versatility, open-source nature, and extensive scientific libraries, which enable precise numerical modeling and easy visualization of simulation results. Python enables to code all relevant mathematical expressions describing the physical and operational relationships between solar energy input and green hydrogen production output, and supports a modular structure for conducting simulations under different parameter configurations.

Reference to the revised manuscript: i.e: see Section 2.1. Mathematical modeling and Simulation method

Comment #7)

How do offshore locations improve the atmospheric conditions for solar energy production compared to densely populated areas?

Response to the reviewer:
The authors agree with this comment and are grateful for the opportunity to clarify this point. Offshore locations generally offer improved atmospheric conditions for solar energy production compared to densely populated areas due to lower levels of air pollution and particulate matter, which result in reduced atmospheric attenuation of solar radiation. Furthermore, the sea surface enhances solar irradiance through reflection, which contributes to increased energy availability for photovoltaic systems. These conditions enhance the performance and efficiency of solar panels installed offshore, as acknowledged in the revised manuscript.

Reference to the revised manuscript: i.e see Section 1. Introduction,

Comment #8)

How do you clarify the effect of solar radiation reflection at sea on increasing electricity production?

Response to the reviewer:
The authors agree with this comment and appreciate the opportunity to elaborate. The effect of solar radiation reflection at sea is clarified in the manuscript by acknowledging that the reflective properties of the water surface can enhance the amount of solar irradiance reaching the photovoltaic panels, particularly under calm sea conditions. This phenomenon contributes to higher electricity generation compared to land-based systems.

Reference to the revised manuscript: i.e: see Section 1. Introduction

Comment #9)

The conclusion needs to be revised and could include important research findings.

Response to the reviewer:
The authors agree with this comment and have revised the conclusion to incorporate the key findings of the research. The updated conclusion now summarizes the main contributions of the mathematical model, including its configurability, applicability to diverse offshore locations, and ability to support multivariable simulations for optimizing green hydrogen production. Furthermore, it highlights the benefits of offshore implementation, such as enhanced solar irradiance and reduced surface area requirements for photovoltaic panels, which lead to more efficient and cost-effective system designs.

Reference to the revised manuscript: see Section 4. Conclusions

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Review of materials Algorithms-3556289

Mathematical modelling of offshore green hydrogen stations

Álvaro García-Ruiz, Pablo Fernández-Arias, Diego Vergara

In the presented materials, the authors provide an analysis of the potential for producing "green" hydrogen by simulating a marine and/or land-based "green" hydrogen station. The model is focused on optimizing hydrogen production by integrating various prototype parameters, such as solar radiation received by solar panels, atmospheric conditions, and other key input parameters of solar panels, an electrolyzer, and a compressor. In the work, the authors provide the results of verification using Python-based simulations. The presented materials are a description of a certain process and it is difficult to understand the novelty of the author's research. When analyzing the work, a number of questions arise that require clarification:

1. The abstract should provide answers to the questions: what was done, using what methods, what is the novelty of the research and confirmation of the results obtained.
2. The introduction should present a constructive analysis of sources on the specified topic, indicating both positive results and shortcomings. The result of the analysis of publications should be the formulation of the purpose of the research, the methodology for conducting this research, and the author's novelty of the research. Involvement of these materials in the journal "Algorithms".
3. Section 3 Results - should contain the author's obtained results.
4. The text of the materials often mentions a mathematical model, but the content of the materials does not reveal such a model in its pure form. The text refers to a model containing technical, natural, physical and mathematical components.
5. In the text, all compared indicators should be reduced to a single metric, otherwise it is impossible to conduct a comparison. All comments "less", "more" should be replaced with numerical values ​​that are easier to perceive when comparing.
6. Discussion section. To understand the text, it is necessary to indicate the discussion scheme, the order of parameters by importance for discussion.
7. Conclusions section. The author's research results and their confirmation should be compactly formulated.

Conclusion. For publication, the materials must be edited taking into account the above comments.

Reviewer.

 

 

Comments for author File: Comments.pdf

Author Response

Dear reviewer:
We appreciate your feedback and suggestions. In response to your comments, we will provide a targeted answer, and the corresponding revision will be reflected in the manuscript (highlighted in yellow). Thank you for your careful and patient comments and your instructive recommendations.

In the presented materials, the authors provide an analysis of the potential for producing "green" hydrogen by simulating a marine and/or land-based "green" hydrogen station. The model is focused on optimizing hydrogen production by integrating various prototype parameters, such as solar radiation received by solar panels, atmospheric conditions, and other key input parameters of solar panels, an electrolyzer, and a compressor. In the work, the authors provide the results of verification using Python-based simulations. The presented materials are a description of a certain process and it is difficult to understand the novelty of the author's research. When analyzing the work, a number of questions arise that require clarification:

Comment #1)

The abstract should provide answers to the questions: what was done, using what methods, what is the novelty of the research and confirmation of the results obtained.

Response to the reviewer:
The authors agree with this comment and have revised the abstract accordingly. The updated version now explicitly addresses the essential components: what was done (development of a mathematical model for offshore green hydrogen production), using what methods (a simulation framework based on Python and parametric analysis), the novelty (a generic and configurable model applicable to any geographic location and capable of integrating environmental and technical parameters), and confirmation of results (demonstrating the benefits of offshore implementation in terms of efficiency and reduced surface area requirements). These modifications provide a concise and complete overview of the research contribution.

Reference to the revised manuscript: see Abstract.

Comment #2)
The introduction should present a constructive analysis of sources on the specified topic, indicating both positive results and shortcomings. The result of the analysis of publications should be the formulation of the purpose of the research, the methodology for conducting this research, and the author's novelty of the research. Involvement of these materials in the journal "Algorithms".

Response to the reviewer:
The authors agree with this comment and have revised the Introduction section to include a more constructive and critical analysis of relevant literature. The updated version now presents both the strengths and limitations of existing works related to offshore renewable energy systems and green hydrogen production. This literature review sets the context for the study and leads to a clearer formulation of the research objective, the methodological approach based on mathematical modeling and simulation, and the novelty of the work—namely, the development of mathematical model designed as a generic framework applicable to any location worldwide and developed to analyze the integration of solar energy generation and green hydrogen production. Furthermore, the content has been aligned with the scope and readership of the Algorithms journal by emphasizing the algorithmic formulation and simulation strategy underlying the model.

Reference to the revised manuscript: see section 1. Introduction

Comment #3)

Section 3 Results - should contain the author's obtained results.

Response to the reviewer:
The authors agree with this comment and have revised Section 3. Results to clearly present the outcomes obtained from the implementation of the mathematical model. This section now includes quantitative simulation results, such as the estimated hydrogen production rates, the required photovoltaic surface areas under varying environmental and operational conditions, and comparisons between different electrolyzer technologies (ALK and PEM). These results confirm the model’s ability to evaluate and optimize offshore green hydrogen production systems and demonstrate its applicability to real-world scenarios.

Reference to the revised manuscript: see section 3. Results.

Comment #4)
The text of the materials often mentions a mathematical model, but the content of the materials does not reveal such a model in its pure form. The text refers to a model containing technical, natural, physical and mathematical components.

Response to the reviewer:
The authors agree with this comment and have taken steps to clarify the scope and structure of the proposed model throughout the manuscript. Rather than presenting a single closed-form equation, the model is developed as a comprehensive simulation framework that integrates technical (engineering parameters), natural (solar irradiance, sea conditions), physical (energy conversion processes), and mathematical (trigonometric and thermodynamic equations) components. This multidisciplinary formulation reflects the complexity of modeling an offshore green hydrogen production system powered by solar energy. To address the reviewer’s concern, we have revised the relevant sections to make this integrative nature more explicit and to better define the boundaries and interrelations of the model's subcomponents.

Reference to the revised manuscript: i.e. see Section 2.1. Mathematical modeling and Simulation method, and also section 2.5. Modelling of solar electricity generation

Comment #5)

In the text, all compared indicators should be reduced to a single metric, otherwise it is impossible to conduct a comparison. All comments "less", "more" should be replaced with numerical values that are easier to perceive when comparing.

Response to the reviewer:

The authors agree with this comment and have revised the manuscript to include quantifiable metrics wherever comparisons are made, allowing for clearer interpretation and more objective evaluation of the results. At the same time, qualitative terms such as “more” or “less” have been retained in certain instances, as they effectively convey the underlying physical logic of the relationships between input parameters and resulting outputs. These terms are used to highlight trends and correlations derived from the model, which are further supported by the numerical data now provided in the results section.

Reference to the revised manuscript: i.e. see section 3. Results.

Comment #6)

Discussion section. To understand the text, it is necessary to indicate the discussion scheme, the order of parameters by importance for discussion.

Response to the reviewer:
The authors agree with this comment and have improved the Discussion section accordingly. To facilitate a clearer understanding of the results and their interpretation, the manuscript now includes a structured discussion scheme supported by a high-level flow diagram (Figure 2). This diagram outlines the sequential modeling process and provides a logical basis for the order in which parameters are analyzed and discussed. Furthermore, a description of the model’s workflow is provided, highlighting the relative importance of key parameters such as solar irradiance, panel inclination, electrolyzer efficiency, and compressor settings. This hierarchical approach guides the reader through the discussion based on the influence of each factor on hydrogen production and system performance.

Reference to the revised manuscript: see section 4. Discussion.

Comment #7)
Conclusions section. The author's research results and their confirmation should be compactly formulated.
Conclusion. For publication, the materials must be edited taking into account the above comments.

Response to the reviewer:
The authors agree with this comment and have revised the Conclusions section to provide a more compact and focused summary of the research findings and their validation. The updated text now clearly states the main outcomes of the study, including the successful implementation of a flexible mathematical model for offshore green hydrogen production powered by solar energy, its ability to simulate different configurations and environmental conditions, and the quantifiable benefits observed through simulation results.

Reference to the revised manuscript: see Section 4. Conclusions.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Mathematical modelling of offshore green hydrogen stations

Review

This article presents a mathematical model to simulate an onshore or offshore hydrogen station based on solar energy sources. The mathematical model integrates parameters such as the solar radiation received by the solar panels, atmospheric conditions and other input parameters of the solar panels, electrolyzer, and compressor. The results show that offshore locations enhance the electricity generation process due to improved atmospheric conditions and to the reflection of solar radiation on the sea surface. This is expected to lead to higher revenues, and reduced installation, production, and maintenance costs.

The topic is timely and important. The manuscript is interesting.

The state of the art is clearly presented. The selected references are relevant.

However, some recommendations for improving the content, accuracy and reliability are below:

1. The novelty of this paper, as resulting from studying other publications and the state of the art, is not clearly described: this novelty must be demonstrated.
2. The optimization method mentioned in Abstract “optimizing hydrogen production” (line 13) is unclear. It is well-known that an optimal solution cannot be deducted from various parameters only. A real optimization procedure should be developed, then be validated, and demonstrated that indeed the obtained results are optimal solutions of the problem.
3. It is unclear too how to use the 48 equations in an integrated computer program. The flow diagram from Figure 2 must be accompanied by a logic flow chart with all relevant equations of the model.
4. Most of the 44 equations are retrieved and cited from sources from bibliography. It is important to clarify which equations were deduced by the authors, showing the authors’ contribution to the novelty of the article.
5. How the proposed model “leads to lower costs in terms of supply, installation, and maintenance of the station”? (in line 522). The economics of hydrogen produced and the real economic benefits versus other reported procedures must be demonstrated. The economic analysis for a true comparison between procedures is missing.
6. If I correctly understood, the location Santoña (Cantabria, Spain) is giving to the paper the geographical and solar data only. No technical description of equipment used in hydrogen production is provided. More, no experiments applying the described methodology are described. Further clarification of this method for a real application in a real case study or a prototype must be added with details and data.

Author Response

Dear reviewer:
We appreciate your feedback and suggestions. In response to your comments, we will provide a targeted answer, and the corresponding revision will be reflected in the manuscript (highlighted in yellow). Thank you for your careful and patient comments and your instructive recommendations.

This article presents a mathematical model to simulate an onshore or offshore hydrogen station based on solar energy sources. The mathematical model integrates parameters such as the solar radiation received by the solar panels, atmospheric conditions and other input parameters of the solar panels, electrolyzer, and compressor. The results show that offshore locations enhance the electricity generation process due to improved atmospheric conditions and to the reflection of solar radiation on the sea surface. This is expected to lead to higher revenues, and reduced installation, production, and maintenance costs.

The topic is timely and important. The manuscript is interesting.

The state of the art is clearly presented. The selected references are relevant.

However, some recommendations for improving the content, accuracy and reliability are below:

Comment #1)

The novelty of this paper, as resulting from studying other publications and the state of the art, is not clearly described: this novelty must be demonstrated.

Response to the reviewer:
The authors agree with this comment and have revised the manuscript to more clearly articulate the novelty of the proposed research in light of existing literature and current state-of-the-art developments. The novelty lies in the development of a generic, modular, and location-independent mathematical model that integrates technical, physical, and environmental variables to simulate and optimize offshore green hydrogen production powered by solar energy. This study presents a comprehensive simulation framework capable of multivariable analysis, allowing for the parametric evaluation of design alternatives and customization to diverse marine contexts.

Reference to the revised manuscript: see Section 1. Introduction, and section 2.1. Mathematical modeling and Simulation method,

Comment #2)

The optimization method mentioned in Abstract “optimizing hydrogen production” (line 13) is unclear. It is well-known that an optimal solution cannot be deducted from various parameters only. A real optimization procedure should be developed, then be validated, and demonstrated that indeed the obtained results are optimal solutions of the problem.

Response to the reviewer:

The authors agree with this comment and acknowledge the need to clarify the terminology used in the Abstract. In the revised version, the term “optimizing hydrogen production” has been reworded to reflect the actual scope of the study, which is based on simulation-driven parametric analysis rather than formal optimization algorithms. The model allows users to explore the influence of key parameters on system performance and to identify favorable configurations. We have also clarified in the main text that the model’s output is intended to support decision-making.

Reference to the revised manuscript: see abstract and section 2.2. Generalization and particularization: Mathematical model

Comment #3)

It is unclear too how to use the 48 equations in an integrated computer program. The flow diagram from Figure 2 must be accompanied by a logic flow chart with all relevant equations of the model.

Response to the reviewer:

The authors agree with this comment and appreciate the opportunity to clarify this important aspect. In response, we have complemented the high-level flow diagram presented in Figure 2 with a detailed explanation of the model’s internal logic, describing how it is organized and sequentially applied within the simulation process. Although a full equation-by-equation flow chart would be too complex for inclusion in a single figure, the revised text now clearly outlines how the model is structured into five logical phases, each corresponding to a specific subsystem: time definition, solar energy, photovoltaic conversion, electrolysis, and compression. Within each phase, the order and dependencies among the equations are described to facilitate understanding of the integrated computation process.

Reference to the revised manuscript: see section 2.1. Mathematical modeling and Simulation method, and also sections from 2.2 to 2.8.

Comment #4)

Most of the 44 equations are retrieved and cited from sources from bibliography. It is important to clarify which equations were deduced by the authors, showing the authors’ contribution to the novelty of the article.

Response to the reviewer:
The authors agree with this comment. All external equations used in the manuscript have been properly referenced. The integration of well-established and validated formulas from the literature was a deliberate choice to improve the reliability and accuracy of the model’s results. The authors’ main contribution lies in the combination and implementation of these equations into a unified computational framework. Particular attention has been given to ensuring that the model outputs are presented in formats that are easily interpretable and comparable across different case studies.

Reference to the revised manuscript: See Section 2 materials and methods.

Comment #5)

How the proposed model “leads to lower costs in terms of supply, installation, and maintenance of the station”? (in line 522). The economics of hydrogen produced and the real economic benefits versus other reported procedures must be demonstrated. The economic analysis for a true comparison between procedures is missing.

Response to the reviewer:
The authors agree with this comment and acknowledge that the original manuscript did not include a detailed economic analysis. The reference to “lower costs in terms of supply, installation, and maintenance” was based on logical implications derived from the reduction in photovoltaic surface area requirements, as demonstrated through the simulation results. This reduction potentially simplifies structural and anchoring systems in offshore environments, which are significant cost drivers.

Reference to the revised manuscript: See Abstract, Section 1 introduction, 4. Discussion, 5. Conclusions.

Comment #6)

If I correctly understood, the location Santoña (Cantabria, Spain) is giving to the paper the geographical and solar data only. No technical description of equipment used in hydrogen production is provided. More, no experiments applying the described methodology are described. Further clarification of this method for a real application in a real case study or a prototype must be added with details and data.

Response to the reviewer:
The authors agree with this comment and appreciate the opportunity to clarify. The location of Santoña (Cantabria, Spain) has been used as a theoretical case study where a green hydrogen production station powered by solar energy is intended to be installed. No physical prototype or experimental setup has been developed at this stage. The current contribution focuses on the development and validation of a simulation-based mathematical framework, which is adaptable to different locations and configurations.

Reference to the revised manuscript: see section 3. Results, Abstract, section 1. Introduction, 2.1. Mathematical modeling and simulation method, section 2.2. Generalization and particularization: Mathematical model configuration, section 5. Conclusions.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I have no other comment.

Author Response

Thank you very much for your constructive comments, which have helped us to improve our article.

Reviewer 2 Report

Comments and Suggestions for Authors

Second stage of review of materials Algorithms-3556289

Mathematical modelling of offshore green hydrogen stations

Álvaro García-Ruiz, Pablo Fernández-Arias, Diego Vergara

The authors' responses to the comments of the first stage were analyzed. The authors revised the text taking into account the comments. But they did not take into account the fact that the concept of "mathematical model" and mathematical calculations of the parameters of the technical model are completely different concepts. Therefore, in the text of the materials, "mathematical model" should be replaced with the phrase "mathematical calculations of the parameters ...". And also the title of the materials should be replaced with a new version. For example: "Mathematical calculations of the parameters of the technical model of development ...".

Conclusion. The text should be edited, since in fact there is no mathematical model in the materials.

Reviewer.

 

Author Response

Dear reviewer:

We appreciate your feedback and suggestions. In response to your comments, we will provide a targeted answer, and the corresponding revision will be reflected in the manuscript (highlighted in green). Thank you for your careful and patient comments and your instructive recommendations.

 Comment #1). The author’s response to the comments of the first stage were analysed. The authors revised the text taking into account the comments. But they didn’t take into account the fact that the concept "mathematical model" and mathematical calculation of parameters of the technical model are completely different concepts. Therefore, in the text of materials "mathematical model" should be replaced with the phrase "mathematical calculation of the parameters" and also the title of the materials should be replaced with a new version. for example: "mathematical calculation of the parameters of the technical model of development". Conclusion: the text should be edited, since in fact, there is no mathematical model in the materials.

Response to the reviewer:

The authors thank the reviewer for the valuable comment. We acknowledge the distinction between a mathematical model and the mathematical calculation of parameters within a technical model. Accordingly, we have revised the manuscript to replace the term “mathematical model” with more accurate expressions such as “mathematics-driven formulation of a technical model”, “mathematics-based framework”, and “mathematics-based technical model”. Additionally, we have replaced the title “mathematical modelling” with “mathematics-driven analysis” to better reflect the scope and nature of the work.

Reviewer 3 Report

Comments and Suggestions for Authors

The revised manuscript can advance for publication.

Author Response

Thank you very much for your constructive comments, which have helped us to improve our article.