A Robust AI Framework for Safety-Critical LIB Degradation Prognostics: SE-VMD and Dual-Branch GRU-Transformer

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Reviewer’s comments on electronics-3858728

This manuscript proposes a lithium-ion battery degradation prognostics framework integrating SE-VMD signal decomposition and a dual-branch GRU-Transformer network, presenting innovative research on battery health monitoring in safety-critical systems. The topic selection demonstrates theoretical importance and practical application value, particularly in safety-critical domains such as electric vehicles and grid-scale energy storage. The research methodology is systematic and comprehensive, with well-designed experiments and thorough result analysis, making it a relatively high-quality academic paper overall, while there are still some aspects need improvement,

1. Selection of SE-VMD Parameters: Algorithm 1 mentions that r = 0.15×σ, but it does not explain why the coefficient as 0.15 is chosen, so the authors should supplement the parameter sensitivity analysis and provide a theoretical basis.
2. Comparison of Computational Efficiency: Although it is mentioned that SE-VMD may incur computational overhead, specific runtime data is lacking, so the authors should supplement the comparison of computational time with traditional VMD and non-decomposition methods.
3. Overlapping in the Key Contributions:

In Introduction section, it is mentioned that “The following key contributions of this paper are as follows:

1) Multi-Scale Degradation Modeling via Dual-Branch Architecture

2) Adaptive Signal Decomposition via SE-VMD and K-means Clustering

3) Empirical Investigation of Temporal Window Sizes for Robust Degradation Prognostics

However, there are some overlap issues, such as,

(a) Excessively Strong Correlation Between Contribution 1) and Contribution 2)

The design of the dual-branch architecture (GRU + Transformer) directly relies on the signal decomposition results of SE-VMD. As shown in the model architecture in Figure 4, high-frequency signals are processed by GRU, while low-frequency signals are processed by Transformer. This clear division of tasks explicitly depends on the prior decomposition of SE-VMD.

Manifestation of Overlap: The implementation of the “frequency-aware fusion module” in Contribution 1) requires the decomposition results from Contribution 2).

b) Overlap Between Contribution 3) and Contributions 1) & 2)

The study on time window size essentially serves the dual-branch architecture (Contribution 1)) and signal decomposition (Contribution 2)), thus “Empirical Investigation of Temporal Window Sizes for Robust Degradation Prognostics” should not be listed as an independent contribution.

Optimization of the window size simultaneously affects: The short-term dynamic capture capability of GRU (Contribution 1)); The decomposition effect of SE-VMD (Contribution 2)).

Therefore, the authors should revise the key contributions of this work.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript proposes a novel framework but I have few queries and comments that should be addressed before the manuscript can be accepted, 

@ Parameters like  step size, Transformer layers, GRU units, and VMD parameters are not justified or tabulated.

@ Sample entropy is used to determine optimal 'k' in SE-VMD, the choice of embedding dimension 'm' is not mentioned. How was this set, and how sensitive is the result to 'm'. 

@ Can we visualize the clustered IMFs? 

@ The dual-branch model and VMD decomposition are computationally expensive, authors need to include computational cost, training time, or hardware requirements, which are important for practical applicability.

@ Why is the number of clusters in K-means fixed at 2? Like there can be multiple clusters as well belonging to once class. 

@ How does SE-VMD perform compared to CEEMDAN, EEMD, or standard VMD in terms of signal decomposition quality and final SOH prediction accuracy?

@ Why specifically pair GRU with high-frequency components and Transformer with low-frequency?

@ The feature fusion strategy (simple concatenation + FC layer) is very basic did authors tried using advanced fusion (like: attention-based fusion, gated fusion) for the enhance performance?

@ The authors should strengthen the methodology and introduction statements by backing them with stronger justification through integration of recent literature (I have observed some very old ref.), particularly in areas like adaptive signal decomposition, dual-branch neural architectures, and interpretable degradation modeling. The authors are encouraged to refer to recent works such as doi.org/10.3390/s24072156 and doi.org/10.1038/s41598-024-78784-7,  which demonstrate recent advances in fault diagnosis, battery modeling, and hybrid data-driven methods.

@ I also encourage the authors to explore and cite additional relevant studies available on platforms like Google Scholar to strengthen the scientific grounding of the manuscript.

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

1. In Fig. 1, Flowchart of the Proposed Methodology, the authors should also include the influence of the intermediate frequency signal in the battery capacity estimation
2. Raw data are missing. Authors should clearly specify them (cell current (I), cell voltage (V), temperature (T), etc.
3. The authors need to justify the use of the construction of the variational model to estimate the capacity signal of the LIB (equation 1). They stated that '' This formulation aims to minimize the sum of the bandwidths of all modal compo- 237
   nents 𝑢𝑘 = {𝑢1, 𝑢2, . . . , 𝑢𝑘 } centered at their respective frequencies 𝜔𝑘 = {𝜔1, 𝜔2, . . . , 𝜔𝑘 }." Why did you not use a continuous distribution instead? Why only a discontinuous distribution, and what benefit does this present? Authors should clarify it.
4.  What would justify the similarity in B0005 capacity sequence decomposition for in-signal IMF 5, 6, and 7 based on VMD in Figure 2.
5. Please add discussion on the transformer-based intermediate-Frequency Feature Extraction Branch as well in section 3.3
6. In Figure 5, the legends for true and predicted data are missing. The authors should add an explanation of the method used for prediction. Did the authors use the least-squares regression line?  RMSE?
7. The authors stated 'The design further improves system robustness by isolating high-frequency noise from critical degradation trends, reducing vulnerability to adversarial perturbations. While the SE-VMD-based decomposition is validated in ablation studies, the dual-branch framework itself demonstrates strong generalization across heterogeneous datasets and resilience to input variability. Please indicates how the the OURS model which provides the lowest Performance Metrics can validate the VMD-based signal
   composition on NASA and CALCE Battery Datasets
8. Please check all the typos and grammatical mistakes

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

All of my comments are addressed!

Author Response

Dear Reviewer,

Thank you very much for your time and constructive feedback on our manuscript (ID: electronics-3858728).

We are grateful that you have confirmed all your comments have been addressed. 
We sincerely appreciate your insightful comments, which have helped improve the clarity, rigor, and overall quality of the paper.

Thank you again for your thoughtful review and support.

Reviewer 3 Report

Comments and Suggestions for Authors

Dear authors,

Your revised manuscript reads well, and all comments have been incorporated as required. However, there are repeated instances where acronyms are redefined after they have already been introduced. For example: lithium-ion batteries (LIBs), high frequency (HF), low frequency (LF), etc. Once an acronym has been defined the first time, it should not be redefined again in later sections. The authors are advised to carefully check the manuscript and correct these repetitions.

Minor revisions

Author Response

Comments:
Dear authors,

Your revised manuscript reads well, and all comments have been incorporated as required. However, there are repeated instances where acronyms are redefined after they have already been introduced. For example: lithium-ion batteries (LIBs), high frequency (HF), low frequency (LF), etc. Once an acronym has been defined the first time, it should not be redefined again in later sections. The authors are advised to carefully check the manuscript and correct these repetitions.

Minor revisions

Response:
Dear reviewers,

Thank you for your valuable feedback on our revised manuscript (ID: electronics-3858728).

We appreciate the comment regarding the repeated definition of acronyms. We have carefully reviewed the entire manuscript and ensured that all acronyms are defined **only once at their first appearance**, and not redefined in subsequent sections.

Specifically:
- The acronym "LIBs" (lithium-ion batteries) was defined at its first occurrence (Line 40), and used consistently without redefinition at Lines 77,207 and 593.
- The acronyms “HF” (high frequency) and “LF” (low frequency) were defined at Line 230, and subsequently used without parentheses or redefinition at Lines 238,332, 334, 356, 364, 369, 377, 380, 503, 506, 532, 669, 670, and 692.

All instances of redundant acronym definitions have been removed. We confirm that the revised manuscript now adheres to standard academic writing practices regarding acronym usage.

Thank you again for your constructive comments. We hope the manuscript is now suitable for publication.