Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript addresses an important topic and presents a technically well-structured machine learning framework for SOH estimation under elevated temperatures. The manuscript is generally well organized, and the validation across multiple datasets is appreciated. Nevertheless, several issues should be addressed to improve the scientific quality of the work.

Although the manuscript focuses on SOH estimation under elevated temperatures, the electrochemical basis of battery degradation is discussed only superficially. The authors should better explain which degradation mechanisms dominate at 40–50 °C (e.g., SEI growth, loss of lithium inventory, electrolyte decomposition, increased polarization, or active material degradation) and how the selected health features reflect these processes. At present, the selected features are introduced mainly from a data-driven perspective without sufficient physical interpretation. Such a discussion would considerably strengthen the scientific value of the manuscript.

The novelty of the proposed framework is not sufficiently justified. The manuscript would benefit from a clearer comparison with existing hybrid residual learning frameworks and transfer-learning-based SOH estimation methods, highlighting the specific methodological advances of the proposed approach.

The manuscript states that datasets from Tsinghua University, the University of Oxford, and Tongji University were used. However, the corresponding original dataset publications are not cited. In addition, the Data Availability Statement ("The datasets used in this study are available from the corresponding authors upon request.") appears inconsistent with the use of publicly available datasets. The authors should provide the appropriate dataset references and revise the Data Availability Statement accordingly.

The literature review relies heavily on Chinese dissertations and publications in local journals. Among the 28 references, at least six are dissertations ([1], [2], [5], [16], [18], [27]). The bibliography should be strengthened by including more internationally recognized and foundational publications in the field of lithium-ion battery SOH estimation. In addition, Reference [4] appears to be incorrectly formatted and should be carefully checked.

Table 1 mainly confirms the expected correlation between the selected health features and battery capacity but provides limited additional scientific insight. Since these results are not further discussed in the manuscript, the authors may consider moving this table to the Supplementary Information to improve the readability of the main text.

The manuscript does not discuss why the selected health features were preferred over widely used electrochemical health indicators such as incremental capacity analysis (ICA), differential voltage analysis (DVA), or impedance-based features. A brief discussion comparing the advantages and limitations of the selected features would improve the electrochemical rationale of the proposed methodology.

Author Response

#1 Comments and Suggestions for Authors

1.Although the manuscript focuses on SOH estimation under elevated temperatures, the electrochemical basis of battery degradation is discussed only superficially. The authors should better explain which degradation mechanisms dominate at 40–50 °C (e.g., SEI growth, loss of lithium inventory, electrolyte decomposition, increased polarization, or active material degradation) and how the selected health features reflect these processes. At present, the selected features are introduced mainly from a data-driven perspective without sufficient physical interpretation. Such a discussion would considerably strengthen the scientific value of the manuscript.

Response: Thank you for this important comment. We agree that the original manuscript introduced the selected health-related features mainly from the perspectives of statistical correlation and prediction performance, while the electrochemical degradation mechanisms at 40–50 °C and their relationships with the selected features were insufficiently discussed.

Accordingly, we have expanded the Introduction and Section 2.2 of the revised manuscript. We now explain that elevated temperature accelerates parasitic reactions at the electrode–electrolyte interfaces, including the growth and reconstruction of the solid electrolyte interphase and cathode electrolyte interphase, as well as electrolyte decomposition. These processes consume cyclable lithium and electrolyte components, thereby contributing to loss of lithium inventory and available-capacity fade. Meanwhile, interphase thickening, electrolyte depletion, and deterioration of electrode contact increase ionic and electronic transport resistance, resulting in enhanced polarization and power fade. Depending on the electrode chemistry and cycling protocol, transition-metal dissolution, particle cracking, structural degradation, and loss of active material may also contribute to long-term degradation.

We have also added a feature-by-feature physical interpretation of HF1–HF4. The charging time and partial charge capacity within fixed voltage intervals mainly reflect available-capacity loss and displacement of the voltage–capacity relationship; the pulse-derived internal resistance characterizes resistance growth caused by interfacial and transport degradation; and the characteristic voltage extracted during constant-current discharge reflects the combined influence of resistance growth, polarization, and capacity loss on the discharge-voltage response. We have further clarified that these features are measurable macroscopic indicators of coupled degradation processes rather than unique diagnostic signatures of individual electrochemical reactions. These revisions strengthen the electrochemical basis for the selection of the health-related features.

Changes made: Section 1 and 2.2.

2.The novelty of the proposed framework is not sufficiently justified. The manuscript would benefit from a clearer comparison with existing hybrid residual learning frameworks and transfer-learning-based SOH estimation methods, highlighting the specific methodological advances of the proposed approach.

Response: Thank you for pointing out that the novelty of the proposed method and its comparison with existing approaches were not sufficiently demonstrated in the original manuscript. In response to your valuable comment, we have revised and expanded the manuscript from the perspectives of the related work, methodological distinctions, and experimental validation.

First, we added a detailed comparison with conventional residual-correction methods and single-stage neural-network transfer approaches in the Methods section. We further clarified the different sources of cross-battery errors addressed by the two transfer stages. Specifically, Ridge prior adaptation is employed to correct discrepancies in the global degradation trend, whereas residual-network fine-tuning is used to learn the target battery’s specific local and nonlinear degradation characteristics.

Second, we added a hierarchical ablation experiment, as presented in Figure 16. Under identical data partitions, network architectures, training hyperparameters, and 20 random seeds, four configurations were compared: no adaptation, Ridge prior adaptation only, residual-network fine-tuning only, and the complete two-stage transfer strategy. The complete two-stage transfer strategy achieved the lowest mean RMSE, MAE, and MAPE. Its RMSE was reduced by 9.39%, 4.14%, and 6.92% compared with A0, A1, and A2, respectively. Moreover, it achieved the lowest RMSE in 14 out of the 20 independent runs. These results demonstrate that the two transfer stages address different aspects of cross-battery distribution discrepancies and provide complementary improvements.

We also revised the figure caption, experimental settings, and discussion of the results accordingly. In addition, the descriptions of the methodological novelty in the Abstract and Conclusions were refined to ensure that the contributions of the proposed framework are stated more clearly and accurately.

We sincerely thank you again for this constructive comment. These revisions have substantially improved the clarity of the novelty claims and strengthened the experimental evidence supporting the proposed method.

Changes made: Section 3.3 and 4.4.

3.The manuscript states that datasets from Tsinghua University, the University of Oxford, and Tongji University were used. However, the corresponding original dataset publications are not cited. In addition, the Data Availability Statement ("The datasets used in this study are available from the corresponding authors upon request.") appears inconsistent with the use of publicly available datasets. The authors should provide the appropriate dataset references and revise the Data Availability Statement accordingly.

Response: We sincerely thank the reviewer for identifying the issues concerning the citation of the data sources and the Data Availability Statement. We agree that the original manuscript merely listed Tsinghua University, the University of Oxford, and Tongji University as the three data sources, without clearly distinguishing between data generated by the authors’ collaborating team and publicly available datasets. Moreover, the original Data Availability Statement described all data as being “available from the corresponding author upon request,” which was indeed insufficiently precise. In response to this comment, we systematically revised Section 2.1, the Supplementary Materials, the reference list, and the Data Availability Statement.

It should be clarified that the Tsinghua University data were not obtained from a public database. Instead, they were generated through battery cycling and aging experiments conducted by the collaborating research team at the Institute of Nuclear and New Energy Technology, Tsinghua University. Therefore, there is no previously published dataset article that can be cited for these data. The dataset has not been deposited in a public repository but may be made available by the corresponding author upon reasonable request.

In addition, we rewrote the Data Availability Statement to clearly distinguish among the different types of data used in this study. The revised statement now separately specifies how the publicly available Oxford and Tongji datasets can be accessed, as well as how the experimental data generated by the Tsinghua research team and the processed health-feature data produced in this study may be obtained.

Changes made: Section 2.1 and Data availability.

4.The literature review relies heavily on Chinese dissertations and publications in local journals. Among the 28 references, at least six are dissertations ([1], [2], [5], [16], [18], [27]). The bibliography should be strengthened by including more internationally recognized and foundational publications in the field of lithium-ion battery SOH estimation. In addition, Reference [4] appears to be incorrectly formatted and should be carefully checked.

Response: Thank you for this valuable comment regarding the quality, international coverage, and formatting of the references. We agree that several general statements in the original manuscript were mainly supported by Chinese dissertations, while internationally recognized peer-reviewed studies were insufficiently represented.

In response, we retained the original reference-numbering structure and replaced the six dissertations previously listed as Refs. [1], [2], [5], [16], [18], and [27] with high-quality peer-reviewed journal articles that directly support the corresponding statements. Specifically, the importance and methodological development of battery SOH monitoring are now supported by the reviews of Xiong et al. in Journal of Power Sources and Berecibar et al. in Renewable and Sustainable Energy Reviews. The equivalent-circuit-model discussion now cites the comparative study of Hu et al. in Journal of Power Sources. The health-feature and partial-charging-segment discussion now cites the study of Feng et al. in IEEE Transactions on Vehicular Technology. The Pearson-correlation analysis is supported by the SOH-estimation study of Wang et al. in Journal of Energy Storage, while the transfer-learning discussion now cites the battery-SOH transfer-learning study of Tan and Zhao in IEEE Transactions on Industrial Electronics.

We also carefully checked the original Ref. [4]. The publication itself is valid, but the journal title, volume, and pagination were incorrectly reported in the original manuscript. The reference has now been corrected to the article by Pang published in Acta Physica Sinica, 2017, 66(23), Article 238801. In addition, the original publications associated with the Oxford and Tongji datasets have been added as Refs. [16] and [17], respectively.

These revisions preserve the original reference structure while substantially reducing the reliance on dissertations and improving the quality, international representativeness, traceability, and formatting accuracy of the bibliography.

5.Table 1 mainly confirms the expected correlation between the selected health features and battery capacity but provides limited additional scientific insight. Since these results are not further discussed in the manuscript, the authors may consider moving this table to the Supplementary Information to improve the readability of the main text.

Response: Thank you for this helpful suggestion. We agree that the original Table 1 mainly reported the Pearson correlation coefficients between the selected health-related features and battery capacity for each individual cell. The complete cell-level results occupied considerable space in the main text, while their scientific implications were not sufficiently discussed.

In response, the original Table 1 has been moved to the Supporting Information and renumbered as Table S2. The table retains the complete correlation coefficients for HF1–HF4 across the Tsinghua, Oxford, and Tongji cells, allowing readers to inspect and reproduce the feature-correlation analysis. The main manuscript now retains only the Pearson correlation method, the corresponding equation, and a concise summary of the principal findings.

We have also added a brief interpretation of the results. HF1 and HF4 show consistently positive correlations with capacity, with coefficients ranging from 0.9699 to 0.9988 and from 0.9742 to 0.9985, respectively, indicating that the charging time and partial charge capacity within the selected voltage windows generally decrease with available-capacity loss. In contrast, HF2 and HF3 are negatively correlated with capacity, with absolute correlation coefficients ranging from 0.7976 to 0.9986 and from 0.7699 to 0.9972, respectively. The wider cell-to-cell variation of HF2 and HF3 suggests that resistance- and discharge-voltage-related responses are more sensitive to differences in cell chemistry, cycling conditions, and degradation trajectories.

These revisions preserve the essential evidence supporting the selected features while improving the conciseness and readability of the main manuscript.

Changes made: Section 2.4,Table S2 in the Supporting Information; and the numbering of the subsequent tables in the main manuscript

6.The manuscript does not discuss why the selected health features were preferred over widely used electrochemical health indicators such as incremental capacity analysis (ICA), differential voltage analysis (DVA), or impedance-based features. A brief discussion comparing the advantages and limitations of the selected features would improve the electrochemical rationale of the proposed methodology.

Response: Thank you for this important suggestion. We agree that the original manuscript mainly described the extraction procedures and capacity correlations of HF1–HF4 but did not sufficiently explain why these features were selected instead of commonly used electrochemical indicators such as incremental capacity analysis (ICA), differential voltage analysis (DVA), and electrochemical impedance spectroscopy (EIS).

In response, we have added a comparative discussion at the end of Section 2.2. The revised manuscript explains that ICA and DVA can provide more mechanism-oriented diagnostic information through changes in the characteristic features of the dQ/dV and dV/dQ curves. However, numerical differentiation may amplify measurement fluctuations, and reliable feature extraction generally requires smooth and comparable constant-current voltage–capacity curves covering the relevant characteristic regions. The extracted peak locations and amplitudes may also be affected by current rate, temperature, resistance growth, and polarization. EIS provides frequency-dependent information related to ohmic, interfacial, and transport processes and therefore offers stronger electrochemical diagnostic capability; however, it requires dedicated excitation and measurement equipment and is sensitive to state of charge, temperature, rest condition, and the measurement protocol.

By contrast, HF1–HF4 can be extracted directly from the voltage, current, and time signals that are consistently available across the three datasets. They do not require numerical differentiation or additional impedance-measurement hardware and can be obtained from partial charge–discharge segments and current-step responses. These characteristics make them more suitable for the online-oriented, cross-dataset, and cross-battery SOH-estimation setting considered in this study.

We have also clarified the limitations of the selected features. HF1–HF4 describe the coupled macroscopic consequences of capacity loss and resistance/polarization growth and therefore have lower mechanism specificity than ICA, DVA, and EIS. They cannot uniquely distinguish loss of lithium inventory, loss of active material, interphase-film growth, or electrolyte degradation. In particular, HF2 is a lumped pulse-derived resistance indicator and does not provide the frequency-resolved process separation available from EIS. Accordingly, the selected features are positioned as practical and complementary SOH indicators rather than substitutes for dedicated electrochemical diagnostic techniques.

Representative publications concerning ICA/DVA-based capacity estimation, direct comparison between IC-DV and EIS diagnostics, and impedance variation under different operating and aging conditions have also been added.

Changes made: Section 2.2, Page 8-9.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript is generally well organized, but a few minor revisions would improve clarity and reproducibility. In particular, the authors should standardize notation, provide brief justification for the selected preprocessing and hyperparameter settings, and strengthen the physical interpretation of the extracted features. In addition, the transfer-learning analysis would be more informative if the effect of calibration sample size were reported explicitly.

The manuscript would benefit from a more consistent notation and terminology throughout the text, particularly for the health-related features, temperature conditions, and performance metrics.
Several methodological choices, such as the LOESS smoothing settings and key hyperparameters, appear empirical; a brief justification or sensitivity analysis would improve reproducibility.
The physical interpretation of the selected features could be strengthened by linking each feature more explicitly to the underlying degradation mechanisms under high-temperature aging.
The paper makes strong claims regarding accuracy and robustness, but these statements would be more convincing if each claim were paired more directly with the corresponding quantitative result.

Author Response

# 2 Comments and Suggestions for Authors

1.The manuscript would benefit from a more consistent notation and terminology throughout the text, particularly for the health-related features, temperature conditions, and performance metrics.

Response: Thank you for pointing out the inconsistencies in notation and terminology. We agree that the original manuscript used several inconsistent expressions for the health-related features, temperature conditions, performance metrics, and model components, which could reduce the clarity of the methodological description.

In response, we conducted a systematic terminology and notation audit throughout the manuscript. First, the term “health-related feature” has been standardized. It is now introduced as “health-related features (HFs)” at its first occurrence, with “HF” and “HFs” used consistently for the singular and plural forms, respectively. The four features are now uniformly named “Charge Time within a Fixed Voltage Window,” “Pulse-Derived Internal Resistance,” “Voltage Drop during Constant-Current Discharge,” and “Partial Charge Capacity within a Fixed Voltage Window.” Inconsistent or potentially ambiguous expressions, including “equalization charge time,” “ohmic resistance value,” “termination voltage,” and “incremental capacity at constant voltage,” have been removed or replaced.

Second, the temperature terminology and unit format have been standardized. “High-temperature” is consistently used as a compound adjective, as in “high-temperature aging” and “high-temperature conditions,” whereas “at high temperatures” is used as a noun phrase. All temperature values are now written with a space between the value and the unit, for example, 40 °C, 45 °C, and 50 °C, and the symbol “°C” is used consistently. Because the high-temperature range investigated in this study is defined as 40–50 °C, the 35 °C condition is no longer described as “moderate-high” or “medium-high temperature.”

Third, the performance metrics have been standardized as root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and coefficient of determination (R²). Because R² is not an error metric, figure captions previously labeled “Error metrics” have been revised to “Performance metrics.” Percentage changes calculated from RMSE are now consistently described as “RMSE reductions” rather than general “accuracy improvements.” Repeated-run results are reported uniformly as mean ± standard deviation, and scientific notation has been standardized using the ×10ⁿformat.

We also standardized the model-related terms, including “Ridge–Conv–Bi-LSTM,” “Conv–Bi-LSTM,” “dual-level transfer learning,” “source-domain,” and “target-domain.” The variable definitions in the HF2, Ridge-regression, and evaluation-metric equations were rechecked and revised, and the Abbreviations section was updated accordingly.

Changes made: Abstract and Keywords; Sections 1, 2.2–2.4, 3.1–3.4, and 4.1–4.4; figure and table captions; Conclusion; and the Abbreviations section.

2.Several methodological choices, such as the LOESS smoothing settings and key hyperparameters, appear empirical; a brief justification or sensitivity analysis would improve reproducibility.

Response: Thank you for this constructive comment. We agree that the rationale and implementation details of the LOESS settings and model hyperparameters should be stated more clearly to improve reproducibility. Accordingly, we have revised Section 2.3 to report the LOESS polynomial order, smoothing span/window, weighting scheme, boundary treatment, and robust reweighting setting. We have also clarified that the same LOESS configuration was applied consistently to all health features and battery datasets and was not adjusted using the test data.

In addition, a new explanatory paragraph has been added after Tables 1 and 2 in Section 4.1. It describes the hyperparameter-selection protocol and explains the choices of network size, learning rates, regularization strengths, sliding-window lengths, mini-batch sizes, and maximum epoch numbers. We further clarify that parameter selection was conducted using only the training and calibration data and that the selected parameters were subsequently fixed for all batteries within each evaluation scenario. These revisions provide the requested methodological justification and improve reproducibility without changing the experimental results.

We have also revised the term “adaptive LOESS” to “LOESS-based denoising” throughout the manuscript to ensure that the terminology is consistent with the actual implementation.

Changes made: Section 2.3 and 4.1.

3.The physical interpretation of the selected features could be strengthened by linking each feature more explicitly to the underlying degradation mechanisms under high-temperature aging.

Changes made: Section 1 and 2.2.

4.The paper makes strong claims regarding accuracy and robustness, but these statements would be more convincing if each claim were paired more directly with the corresponding quantitative result.

Response: Thank you for this valuable comment. We agree that several statements regarding estimation accuracy, stability, and cross-battery generalization were previously qualitative and were not directly linked to the corresponding quantitative evidence. Accordingly, we have revised the Abstract, the main contributions in the Introduction, the single-battery and cross-battery result discussions, the ablation analysis, and the Conclusion. In the revised manuscript, each accuracy-related statement is directly supported by RMSE, MAE, MAPE, and R²results. For example, the proposed method achieves an RMSE of 0.0009 on cell B6 at 50 °C, representing reductions of 82.0%–91.1% relative to the four benchmark models. It also achieves an RMSE of 0.0023 on cell D6 at 45 °C, corresponding to reductions of 50.0%–81.3%. Moreover, the ablation results show that the dual-level transfer strategy reduces the cross-battery RMSE from approximately to , corresponding to a reduction of approximately 68.9%. We have also reported the mean ± standard deviation over 20 independent runs to quantify run-to-run stability. Statements such as “strong robustness” and “consistently outperforms” have been revised or moderated where direct quantitative support was insufficient.

Changes made: Section 4.2-4.4.

In addition, the transfer-learning analysis would be more informative if the effect of calibration sample size were reported explicitly.

Response: We sincerely thank the reviewer for the insightful correction. In the original manuscript, directly adopting “15%” to describe the target-domain calibration proportion indeed lacked sufficient rigor. We have thoroughly addressed this issue in the revised manuscript. In fact, the adaptive target-domain calibration strategy employed in this work takes 15% as the nominal benchmark: the number of calibration samples is initially set to 15% of the total target-domain samples, and is then subjected to three constraints—no fewer than 80 samples, no more than 180 samples, and no more than 35% of the total target-domain sample size. As a result, the effective calibration proportion varies adaptively with the size of the target-domain dataset across different transfer tasks. In addition, following the ablation study, we have added a target-domain sample proportion calibration experiment. This experiment involves eight cross-battery transfer tasks selected from the Tsinghua, Oxford, and Tongji datasets, with five calibration proportions of 5%, 10%, 15%, 20%, and 30%, in order to systematically evaluate the influence of this parameter on transfer performance.

Changes made: We add the new Section of 4.5.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The author adequately answered all the questions. Therefore, I recommend to accept the manuscript

Review Reports

#1 Comments and Suggestions for Authors

# 2 Comments and Suggestions for Authors