Underwater DVL Optimization Network (UDON): A Learning-Based DVL Velocity Optimizing Method for Underwater Navigation

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Comments

Responses

Comments 1:

The DVL is modeled similarly as in other literature. When moving on to the navigation part, the lever arm impact when moving between sensors is not discussed. Authors should add a paragraph or sentence explaining why this is left out and whether it was compensated for in the collected data.

The issue you mentioned regarding the leverage arm effect between sensors during movement is indeed an important aspect that needs to be clearly explained in our research. Specifically, we recognize that the leverage arm effect between sensors is a non-negligible factor during the navigation process. However, in this study, due to the effective compensation for this effect by the experimental setup and data processing methods we employed, it was not elaborated upon in the main text discussion.

To clarify this point, we have added the following explanation on lines 328 of the manuscript: “In the design of the experimental setup and the data processing, we have thoroughly considered and compensated for the leverage arm effect between sensors, ensuring the consistency and accuracy of the data.”

Thank you again for your valuable suggestions and guidance.

Comments 2:

Looking at the network architecture, there is no deeper explanation why only the kernel length of 2 was used, as well as why there are 6 of them. Please explain in more detail what motivated exactly these choices?

Thank you very much for your thorough review of our research and the valuable feedback you provided. Your questions regarding the selection of kernel lengths and the number of kernels in the network architecture are indeed important aspects that we need to further clarify and explain. In response to your inquiries, we have provided a more detailed supplementary explanation in line 234 of the manuscript.

Specifically, regarding the use of only kernel lengths of 2, our choice is based on the following considerations: A kernel length of 2 can significantly reduce computational complexity while ensuring the ability to extract features, thereby improving the training and inference speed of the model.

As for why there are 6 such kernels, our design motivation is as follows: By using multiple kernels, we aim to capture features at different scales, thereby enhancing the model’s feature representation capabilities. While more kernels may slightly improve performance, they also bring unnecessary computational burden.

To more clearly explain these choices, we have added the following statement at line 203: “The selection of a kernel length of 2 is a comprehensive consideration of computational efficiency and feature capture capabilities, while the design of 6 kernels is to achieve multi-scale feature fusion.”

Thank you again for your valuable suggestions and guidance. We will continue to strive to improve our research work to ensure its rigor and transparency.

Comments 3:

In Fig 3., the last layer takes the DVL velocity from gyro/acc and the velocity from the sensor. What are the final weight in the last block? This combination is akin to a complementary filter combining high-rate and low-rate velocity data. Do the weights reflect this? If there is some conclusion from this please provide a comment in the paper.

Thank you very much for your detailed review of the paper and valuable feedback. You mentioned the last layer obtaining DVL velocity and sensor velocity from the gyroscope/accelerometer, and inquired about the weight setting in the final block. We find your insights extremely valuable and agree with your statement that “this combination is similar to a complementary filter that combines high-rate and low-rate velocity data.” The final weights are:

tensor([[ 1.1565, -0.7688,  0.3050,  0.0858], [-0.1418,  0.9440,  0.0114,  0.9930]])

We apologize for not knowing whether this weight reflects your opinion.

Comments 4:

Data collection included several shapes, but a paragraph discussing the choice of these shapes needs to be included. E.g., which parts of the dynamics does an M shape capture, etc.?

We greatly appreciate your valuable feedback on the data collection section. You pointed out the need to discuss the reasons for choosing different shapes and the dynamic aspects they capture, which is indeed an important aspect that we should elaborate on. In response to your suggestion, we will provide an explanation of the shape selection in line 310 of the paper.

Thank you again for your valuable suggestions and guidance. We will continue to strive to improve our research work to ensure its rigor and transparency.

Comments 5

Line 295/296 mention some self-compensation of 45 degrees between INS and DVL, which is just a consequence of PD6 format. The lever arm is not discussed here as well.

We deeply appreciate your meticulous review of the paper and the valuable insights you have provided. Your observation regarding the 45-degree self-compensation between the Inertial Navigation System (INS) and the Doppler Velocity Log (DVL) mentioned in lines 295/296, which only applies to the PD6 format, and the lack of discussion on the leverage arm effect, is indeed an important aspect that requires further clarification and supplementation.

In response to your suggestion, we have included a detailed discussion on the leverage arm effect in line 324 of the paper. Thank you once again for your valuable suggestions and guidance.

Comments 6:

The definition of which task is which and their connection for Figure 5 is missing. This needs to be specified. There are 4 tasks on Figure 8,9, 3 tasks on Figure 5, and five tasks mentioned in the intro of section 3.2. These should all be matched to make sense and what is Task1-4 should be defined (in spite of the fact that their shape can be seen on Fig 9).

We deeply appreciate your careful review of the paper, especially regarding the task definitions and the consistency between the figures and the text. Your observation of the inconsistencies in task numbers and definitions between Figure 5, Figure 8, Figure 9, and the introduction of Section 3.2 is indeed an issue that requires our clarification and correction.

In response to your valuable suggestions, we will take the following steps:

1.Supplement Figure 5: We will enhance Figure 5 to ensure it reflects the same number of tasks as mentioned in Figure 8, Figure 9, and the introduction of Section 3.2. We will also clarify the specific meaning of each task and its association with the corresponding figures.

2.Define Task1-4: At Table 2 and Table 3, we will provide detailed definitions of Task1-4, including their specific objectives, methodologies, and applications in our experiments. This will help readers better understand the role and significance of each task.

3.Revise the Introduction of Section 3.2: We will make appropriate changes to the introduction of Section 3.2 to ensure that the task numbers mentioned align with those in the figures and that the correspondence between each task and the figures is clear.

Thank you once again for your valuable suggestions and guidance.

Comments 7:

Figure 7 is not needed as there is not more info on it compared to description in line 308/309.

I appreciate your consideration of my suggestion regarding Figure 7. It’s commendable that you’ve decided to remove it to enhance the document’s readability and focus. Streamlining content to avoid redundancy and ensure each element contributes uniquely to the reader’s understanding is a key aspect of effective academic writing. Thank you again for your valuable suggestions and advice.

Comments 8:

The data analysis lacks discussion which is the biggest drawback of this paper. Many criteria for evaluation are provided, but the figures themselves are not discussed. Specifically, the Figure 8 is not discussed. There is no explanation of VL, VF,etc. Why is the DVL underperforming that much in lateral (VL?) measurement? And this seems to happen exactly during turns. This needs to be clarified why it is expected or why it is unexpected.

Thank you very much for your in-depth analysis and valuable suggestions regarding the data analysis section of the paper. You correctly pointed out that there is a lack of data analysis, especially the lack of discussion on the data in Figure 8, which is a crucial point. This has made me realize the importance of data analysis for this chapter. I fully agree with your view and realize that this part of the content needs to be strengthened and improved.

In response to your suggestion, I have planned to add explanations and descriptions of VL, VF, and other terms below the original Figure 8, and will begin a detailed discussion starting from line 356. I will also analyze the reasons for the poor performance of DVL in lateral (VL) measurements and explore whether this phenomenon is expected and the underlying reasons behind it. In the same manner, I have added explanations for East and North below the original Figure 9, and discussed the data in detail.

Thank you again for your valuable suggestions and advice. Your guidance is very important to me.

Comments 9:

There is also the open question of transferability, how can this be transferred between 1) different DVLs, 2) between different mounting setups, 3) between changes of INS, etc. Please add a few paragraphs on expected transferability and how this can be improved, ensured within your setup.

Thank you very much for raising the open question about transferability. The issues you pointed out regarding the transferability between different DVLs, various installation settings, and changes in the INS are indeed important aspects that need to be deeply explored and considered in our research. In response to your suggestion, I plan to specifically add a outlook on transferability in the Conclusion section of the paper.

In summary, we believe that INS and DVL should be fixed together, and it is not advisable to frequently replace the INS or DVL. Or through some other measures, these measures may include developing more universal algorithms, conducting more cross-platform tests, and establishing more comprehensive error compensation models. Through these supplements and discussions, we hope to provide readers with a more comprehensive and in-depth understanding, as well as valuable references and guidance for future research.

Thank you again for your valuable advice and guidance. Your opinions are of great importance for us to refine our research work.

Comments 10:

The paper also mentions sharing data and code on Github. However, these should have already been published and the URL added into the paper to give more weight and allow the reviewers to run and test the code.

Thank you very much for your valuable suggestions regarding the sharing of data and code in the paper. You correctly pointed out that adding URLs for the published data and code to the paper is crucial for emphasizing their importance and allowing reviewers to run and test the code. We will share key data and related code on Github, ensuring that reviewers and other researchers can access and verify our work. These shared resources will include the main datasets used in the experiments and the core code for implementing our methods.

Thank you again for your valuable advice and guidance; your opinions are of great importance for us to refine our research work.

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Comments

Responses

Comments 1:

However, although the study employs a navigation system for performance evaluation, it lacks fundamental explanations regarding navigation principles. Additionally, while deep learning methods are utilized, the provided descriptions are insufficient to ensure   reproducibility or verification by readers.

Thank you very much for your careful review of the paper and your valuable suggestions. The issues you pointed out regarding the insufficient explanation of the navigation principle and the replicability of the deep learning method description are of great guiding significance to our research. In response to your suggestions, we plan to make the following modifications and supplements:

1.We will add a basic explanation of the navigation principle at line 336 of the paper, including the fundamental working principle of the navigation system, key components, and their role in performance evaluation. We will add the reasons for using the navigation system to perform the performance evaluation at line 368.

2.We attach great importance to the replicability of our research. To ensure that readers can verify our results, we have submitted the relevant code and data on GitHub. Specifically, this includes: complete test set code, test set data.       

Comments 2:

The evaluation dataset appears to overlap with the training dataset, which inherently biases the results toward favorable outcomes. Alternative evaluation methodology has to be made. The manuscript proposes an algorithm comparable to RTK velocity performance, yet fails to include RTK performance benchmarks and inconsistently refers to GPS instead of RTK in Chapters 1 and 2, which introduces confusion.

We are very grateful for your careful review of our paper and your valuable suggestions. Your identification of the issue regarding the overlap between the evaluation dataset and the training dataset, as well as the confusion in the representation of GPS and RTK, is of significant guidance for our research. In response to your suggestions, we plan to make the following modifications and supplements:

1.Dataset Division: We apologize for not making it clear that the training dataset and the test dataset are divided, which led you to believe that the test dataset seems to overlap with the training dataset. We will improve our explanations at the beginning and end of Section 3.2, so that readers can clearly distinguish between the training dataset and the test dataset. Specifically, we will clearly explain the method of dividing the dataset, ensuring the independence and fairness of the evaluation dataset, thereby avoiding biased results.

2.Confusion between GPS and RTK: Regarding the issue of confusion between GPS and RTK that you mentioned, we apologize for not making it clear. The GPS we use adopts RTK for differential positioning to improve positioning accuracy. To facilitate clear reading by readers, we will provide a detailed explanation of this in line 111 of the text, and ensure consistent use of GPS to describe our positioning method in Chapter 1 and Chapter 2, avoiding confusion.

Comments 3:

The manuscript fails to include any discussion of the study's limitations, which is essential for enabling other researchers to build upon and expand related work. Identifying and clearly articulating the limitations would provide valuable context for interpreting the findings and guide future studies in addressing unresolved challenges. Without this critical component, the study risks being perceived as incomplete and lacking transparency.

We are very grateful for your in-depth review of our paper and your valuable suggestions. The issue you raised about the lack of discussion on research limitations is of great guiding significance for our study. We also deeply recognize the importance of this aspect for other researchers to build upon our work. In response to your suggestions, we have taken the following measures:

1.Adding a discussion on research limitations: We have added a new section in the fifth part of the article, specifically discussing the main limitations of our study. In this section, we elaborate on the limitations related to the scope of data collection, the restrictions of method application, and other aspects, and analyze the potential impact of these limitations on the research results.

2.Providing guidance for future research: While discussing limitations, we have also proposed possible solutions to these limitations and directions for future research. This aims to provide valuable background information and guidance for subsequent studies to address the challenges that are not resolved in the current research.

Comments 4:

The manuscript appears to be written in a shallow manner overall, diminishing its academic value and leaving the contributions unclear. The proposed study lacks credible and robust analysis, making it difficult to validate the findings.

Firstly, we sincerely thank you for your in-depth review of our paper and the valuable suggestions you have provided. The issues you pointed out regarding writing quality, research contribution, analytical robustness, and result verification are of crucial guiding significance for enhancing the academic value and readability of our research.

1.Regarding writing quality: We deeply recognize the importance of clear and profound writing in conveying research content and academic value. In response to your comments, we have meticulously revised and polished the entire text to strive for greater accuracy and depth in our expression, making the paper more academic and readable.

2.About research contribution: We appreciate your pointing out the ambiguity in our research contribution. After re-evaluating the research content, we have revised the relevant parts of the paper to ensure a more factual and straightforward explanation of the innovation and contribution of our research, allowing readers to clearly understand the value of our work in both academic and practical contexts.

3.Concerning analytical robustness: In response to your concern about the lack of robust analysis, we have added detailed discussions and analyses to key sections such as speed graphs and trajectory graphs, aiming to provide a more comprehensive and in-depth explanation, enhancing the credibility and persuasiveness of our research.

4.Regarding result verification: We understand your concerns about the difficulty in verifying the results. To improve the transparency and replicability of our research, we have submitted the relevant code and data to GitHub for readers to verify and replicate. We believe that this initiative will help to strengthen readers’ trust and recognition of our research findings.

Comments 5

To improve, the authors should focus on providing comprehensive and detailed explanations of the methodologies used, ensuring clarity and reproducibility for readers. The evaluation data must not be used for training, as this compromises the validity of the study's results. To ensure a fair and unbiased assessment, the study should be reevaluated using separate datasets for training and testing. This will provide a more accurate representation of the algorithm's true performance. Also, the limitations of the study should be clearly outlined to provide transparency and guide other researchers in building upon the work. Highlighting areas where the methodology or results may fall short allows for constructive development and prevents potential misinterpretation of the findings.

We sincerely appreciate your thorough review of our paper and the valuable suggestions you have provided. Each of your recommendations has pointed us in the direction of improvement, which is of great significance for enhancing the quality and transparency of our research.

1.Regarding the comprehensiveness and replicability of the method explanation: We have provided a comprehensive and detailed re-explanation of the methods used, ensuring that every step is clear and replicable for the readers. To further support this, we have published the relevant code and data on a public platform, allowing readers to easily replicate the experiments and verify our results.

2.Concerning the division of the dataset: We attach great importance to the criterion you raised that evaluation data should not be used for training. To address this, we have more clearly articulated the process of dividing the training and testing datasets, and have detailed in the paper that our evaluation data was not used for training, thus ensuring the reliability and fairness of our research results.

3.Discussion of research limitations: In response to your suggestion, we have added a separate section in the fifth part of the paper, specifically discussing the limitations of our research. In this section, we not only highlight the potential shortcomings of the methods or results but also provide in-depth analysis of these limitations, aiming to provide other researchers with a transparent research background and guidance for future work.

Once again, we thank you for your valuable advice and guidance, and we will continue to strive to improve our research work in order to make more valuable contributions to the academic community.

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Comments

Responses

Comments 1:

It is recommended that the abstract be more concise, and include specific numerical results in both abstract and conclusion as well to highlight the experimental analysis outcomes of the study.

Thank you very much for your valuable suggestions on the abstract and conclusion of the paper. You pointed out that the abstract should be more concise and include specific numerical results in both the abstract and conclusion to highlight the experimental analysis results of the research, which is indeed important guidance for improving the quality and readability of the paper. In response to your suggestions, we plan to make the following modifications:

We will streamline the abstract by removing redundant information to ensure that every sentence closely aligns with the core of the research, making the abstract more concise and clear. In this way, readers can quickly grasp the focus and main findings of the research. In the revised abstract and conclusion, we will explicitly include specific numerical results of the experiments. These specific numbers will help highlight the experimental analysis results of our research, giving readers a more intuitive understanding of the actual effects of the study.

Comments 2:

Although the paper cites some studies related to deep learning, it lacks an in-depth discussion of the theoretical basis for using components such as LSTM in the research. It is recommended to provide additional explanations on the rationale behind selecting this neural network architecture and method, as well as its advantages compared to other architectures or approaches.

Thank you very much for your in-depth comments on the selection of neural network architecture and its theoretical basis in the paper. You pointed out that we lack a thorough discussion of the theoretical basis for using components such as LSTM, and that we need to provide more explanation and reasoning for the choice and advantages of the CNN-LSTM architecture, which is indeed a part that we need to strengthen in the paper. We simply explained the advantages of LSTM over RNN in the paper. In response to your suggestions, we plan to make the following improvements in the revised version:

We will elaborate on the theoretical basis for choosing the CNN-LSTM neural network architecture at line 254. Specifically, we will discuss the advantages of LSTM in processing sequential data, such as its ability to effectively capture long-term dependencies and mitigate the vanishing gradient problem, as well as the powerful capability of CNN in extracting local features. We will also further explain why the CNN-LSTM architecture is suitable for our research problem. For example, this architecture combines the spatial feature extraction capabilities of CNN with the temporal dynamic modeling capabilities of LSTM, thus better adapting to our data and analytical objectives.

Comments 3:

The paper does not sufficiently discuss the tuning of hyperparameters, overfitting mitigation, and analysis of model stability during the model training process. It is recommended to include relevant details to enhance the credibility of the research.

Thank you very much for your deep attention and valuable suggestions regarding the model training details in the paper. You pointed out that we did not sufficiently discuss hyperparameter tuning, overfitting mitigation, and model stability analysis, which are indeed areas that needed strengthening in our writing process. In response to your suggestion, we plan to add the following content in the revised version at line 281:

1.We used the Adam optimizer to achieve adaptive adjustment of the learning rate, aiming to improve the efficiency and stability of model training. Specifically, we set an initial learning rate of 0.001 and allowed the Adam optimizer to adjust it automatically. Additionally, we selected Mean Squared Error (MSE) as the loss function and found in our experiments that the model typically converges after 500 iterations. Regarding the batch size, we chose 4 as a compromise to balance memory usage and model performance. The selection of these hyperparameters was based on the results of multiple experiments.

2.To mitigate overfitting, we employed regularization techniques during model training. Specifically, we added an L2 regularization term to the loss function to constrain the model weights and prevent the model from becoming too complex.

3.Model Stability Analysis: In multiple experiments, the model’s performance fluctuated little at the same number of training epochs, indicating high stability, and the loss value eventually stabilized.

Comments 4:

The paper employs various metrics to describe the prediction accuracy and navigation precision of the model but does not evaluate the computational cost of the method on specific hardware platforms. Further assessment results are needed to demonstrate whether the proposed method can meet the real-time requirements of underwater navigation.

Thank you very much for your valuable opinions on the computational cost and real-time requirements of the model. You pointed out that we did not assess the computational cost of our method on specific hardware platforms, and that we need to further demonstrate whether the proposed method can meet the real-time requirements of underwater navigation. The comments you raised are exactly the direction of our follow-up research.

We recognize the importance of real-time performance for underwater navigation and will further verify the real-time capabilities of our proposed method in practical applications. This will be achieved through real-time testing on underwater navigation hardware platforms to ensure that the model can meet real-time requirements. Although our current experimental conditions are limited, we have made the following plans: We currently adopt a method of training with GPU after data collection and plan to import the trained model into the mainboard of the underwater navigation system. To verify the feasibility of this scheme, we will conduct field experiments with an AUV in the follow-up to test the performance and real-time capabilities of the model in real-world environments. We will note the current limitations of this study in the outlook section for the readers' reference.

Comments 5

Figures 8 and 9 provide a significant amount of visualized experimental results, but the accompanying textual descriptions are insufficient. Adding such discussions will enhance the understanding of the model's performance under different conditions. It is recommended to include corresponding explanations to clarify the results or interpret specific situations shown in the figures. (e.g. In Figure 8(d) around the 4300-second mark, why does the predicted result align closely with the original value while showing a significant deviation from the GPS data, rather than maintaining a good alignment with the GPS data as observed in most other cases?)

Thank you very much for your valuable suggestions on the visualization of experimental results in Figures 8 and 9. You pointed out that the corresponding text descriptions are insufficient, which indeed highlights an important aspect of our work that needs improvement. Your advice has made us deeply aware that detailed explanations and discussions are crucial for helping readers understand the performance of the model under different conditions. In response to your suggestions, we have taken the following measures:

We have added detailed data result descriptions below Figures 8 and 9, providing in-depth explanations of the specific situations displayed in the figures. In the added descriptions, we not only describe the phenomena but also analyze the underlying reasons, which may include factors such as sensor noise, dynamic environmental changes, and model characteristics that affect the prediction results.

Through these improvements, we believe readers will be able to understand our experimental results and model performance more comprehensively and deeply. Thank you again for your valuable suggestions and guidance, your opinions are of great significance to us in improving the quality and readability of the paper.

Comments 6:

The experiments presented in the manuscript were conducted in a lake environment, which differs significantly from the primary application scenario of ocean environments. This leaves the method's performance in complex oceanic conditions unverified. It is recommended to include additional experiments in ocean environments or simulate oceanic conditions through data augmentation and modeling to further demonstrate the method's robustness and anti-interference capabilities under real-world ocean scenarios.

Thank you for your suggestion. Regarding the issue of data augmentation and modeling to simulate marine conditions, we acknowledge that the persuasiveness of this approach may be lacking, as it is difficult to prove the accuracy of the modeling. Validating in the marine environment would further demonstrate the robustness and anti-interference ability of the method in real marine scenarios, but such validation comes with significant costs and risks. We will consider conducting validations in the marine environment in our subsequent work.

We fully agree with the issue you raised about the difference between the experimental environment and the main application scenario. Indeed, due to the limitations of experimental conditions, the current research has been mainly conducted in lake environments and has not yet been validated under complex marine conditions.Our research has proven to be effective in lake environments, and we will also state in the conclusion that our study is based on the lake environment and provide prospects for future researchers to distinguish.

Your suggestion for additional experiments in the marine environment is very pertinent, but unfortunately, we currently do not have the conditions to conduct experiments in the marine environment. We will seriously consider your suggestions regarding data augmentation and modeling. At the same time, we will also actively seek opportunities to collaborate with other research institutions or teams, with the hope of being able to conduct experiments in the real marine environment in the future. Thank you again for your valuable suggestions and guidance, and we will continue to work hard to improve our research.

Comments 7:

The experimental analysis results presented in this article only prove the effectiveness of this method, but do not clarify whether it has advantages over other similar methods. Furthermore, it does not provide evidence that machine learning methods incur relatively high computational costs over more traditional numerical processing methods, such as filtering. Recommendations include comparative experiments or analyzes to demonstrate the accuracy, robustness, or other metrics of the proposed approach and to justify the computational cost trade-offs.

Thank you very much for your in-depth analysis and valuable suggestions regarding our manuscript. The issues you raised about validating the advantages of our method and comparing computational costs are deeply appreciated. Indeed, our focus in the experimental analysis was primarily on the effectiveness of the proposed method, with relatively less emphasis on direct comparison with other similar methods. Your point is well-taken, and we recognize that this is indeed a shortcoming of our research. Due to our limited understanding of other methods, conducting comprehensive comparative experiments does pose certain difficulties.

Your suggestions have pointed us in the direction for future research. We plan to strengthen our study of other similar methods in our future work, strive to overcome technical challenges, and carry out more comprehensive comparative experiments. We will raise this limitation in the outlook section of the manuscript for the reference of subsequent researchers.

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Comments

Responses

Comments 1:

There are grammatical issues in some parts of the article.

We greatly appreciate your valuable feedback, which has made us realize the importance of grammatical correctness for the readability of the article. We have made the relevant modifications according to your suggestions and highlighted them in the article.

Comments 2:

Why is the training set 80%?

We apologize for the confusion in our explanation. We extracted 20% of the dataset as the test set, as shown in the four figures in the article. Then we took out 10% as the validation set, leaving the remaining 70% as the training set. The test set has distinct dynamic characteristics and reliable representativeness. The modified sections have been highlighted.

Comments 3:

It is recommended to discuss the figures and tables.

We greatly appreciate your suggestion and realize that it is necessary to discuss the data. We have already added relevant discussions below each figure and table. The modified sections have been highlighted.

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Comments

Responses

Comments 1:

The authors have sufficiently addressed the comments from the reviewer, the presentation of the paper has been improved in general. Please review the entire manuscript once again for any grammatical, expression, or spelling errors. Additionally, it is recommended to adjust the size and font of the figures in the manuscript to ensure clarity and visual appeal. For example, consider enlarging the smaller text in Figures 2 and 3 and slightly reducing the size of the two photographs in Figure 4.

Thank you for your valuable feedback on the manuscript. We recognize the importance of font size in charts and appropriate image proportions for smooth reading by the audience. We have made corresponding adjustments in the manuscript, and we have also reviewed the grammar, expression, and spelling errors. Specifically, the changes made in this revised draft are as follows:

1.      Adjusted the font size in Figure 2 and Figure 3. Adjusted the size of Figure 4.

2.      The expressions on lines 140, 197, and 268 have been modified, and the title of Figure 5 has been revised.