Improved Electrochemical–Mechanical Parameter Estimation Technique for Lithium-Ion Battery Models
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe paper is nice and well written, having clearly formulated task and goals and great literature review. All the models are explained well. In addition, the paper has nice graphic illustrations. The were some parts not clear for me:
In the “No Battery Teardown” scenario, how does the inclusion of physical design parameters (tp, tn, N) affect the identifiability and uniqueness of the solution? Is there any indication of overfitting due to the increased parameter space?
The paper mentions that smaller ellipses could indicate convergence to a local minimum rather than true parameter stability. What measures were taken to ensure that the parameter estimation did not converge prematurely to a local minimum?
What steps were taken to ensure the experimental data (voltage profiles, DVA analysis) are clean and robust, especially given their influence on the optimization process? Were any data filtering or preprocessing methods applied?
Author Response
Comment 1: In the “No Battery Teardown” scenario, how does the inclusion of physical design parameters (tp, tn, N) affect the identifiability and uniqueness of the solution? Is there any indication of overfitting due to the increased parameter space?
Response 1: Thank you for the comment. We acknowledge that, as this is a non-convex optimization problem, multiple local optima may exist, and uniqueness of the solution cannot be guaranteed. The inclusion of additional physical design parameters (such as tp, tn, and N) introduces further degrees of freedom to the parameter estimation process. However, as demonstrated in the “No Battery Teardown” scenario, this does not affect the identifiability of the parameters while the physical design parameters converge strictly close to the values imposed in the “Teardown” scenario. As highlighted in the manuscript, it was also a way to prove that the model could work even without the need for teardown.
Regarding the risk of overfitting, we believe that adding physical design parameters to satisfy physically meaningful constraints helps the identification process making it harder for the model to adapt excessively to one target at the expense of physical plausibility.
Comment 2: The paper mentions that smaller ellipses could indicate convergence to a local minimum rather than true parameter stability. What measures were taken to ensure that the parameter estimation did not converge prematurely to a local minimum?
Response 2: Thank you for the note. While global convergence cannot be strictly guaranteed due to the non-convex nature of the parameter estimation problem — namely, the objective function may present multiple local minima — we address this limitation by adding mechanical measurements into the cost function, which is the scope of the whole work. This additional data provides further information and constraints that reduce the sensitivity to initial parameter guesses lowering the risk of the algorithm converging to a local minimum that is less representative of the actual cell response. In fact, as shown in the “teardown scenario”, with the same initial values, the electrochemical-only approach converged in few iterations but with significantly higher RMSEs with respect to the electrochemical-mechanical approach.
In addition, the manuscript has been revised to clarify this point more explicitly. In particular, a paragraph has been added explaining that parameter estimation was repeated using different initial values, specifically the lower and upper bounds of the parameter ranges. Despite the presence of multiple local minima in the objective function, the electrochemical‑mechanical approach resulted more stable, consistently converging to similar parameter values close to the set of parameters associated with the lowest RMSE. On the other hand, the electrochemical approach was more sensitive to the initial guesses.
Comment 3: What steps were taken to ensure the experimental data (voltage profiles, DVA analysis) are clean and robust, especially given their influence on the optimization process? Were any data filtering or preprocessing methods applied?
Response 3: Thank you for raising this important point. In response, we have added a dedicated paragraph in the “Experiment” section describing the steps taken to ensure the quality and robustness of the experimental data. In particular, differential voltage analysis was performed on low-rate charge/discharge profiles, with similar results observed for both. To mitigate noise amplification, the voltage signal was filtered before computing the derivation and the most effective filtering strategies were found to be the Gaussian-weighted moving average and the Savitzky–Golay filter.
We hope this addition in the manuscript clarifies our approach and explains our data handling procedures.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThe author builds a model to evaluate the reliability of batteries by considering both chemical and mechanical properties.
Take into consideration of mechanical properties should indeed enhance the reliability of the algorithm.
The author also made a comparison with experiments, that is also a good way to evaluate the model.
However, I would like to address a concern regarding the experimental methodology in this paper. During the experiments, “each charge/discharge test is conducted within a state of charge (SOC) range of 0%–100% and repeated five times on the same battery sample”.
As we know, a reliable battery should be able to endure thousands of cycles, and its performance will decay over time.
Moreover, capacity decay is not linear with the number of cycles. In this article, researchers only conducting 5 cycles may not provide a sufficient basis for the parameters, which were applied to test the module.
I suggest the author consider extending the testing to several hundred or even thousand cycles, then get the parameters for the module evaluation during the operation.
This will enhance the reliability and significance.
Line 198 and 218,241 are the first line in the paragraph, it should have the same structure as other paragraphs in the beginning.
Author Response
Comment 1:
However, I would like to address a concern regarding the experimental methodology in this paper. During the experiments, “each charge/discharge test is conducted within a state of charge (SOC) range of 0%–100% and repeated five times on the same battery sample”.
As we know, a reliable battery should be able to endure thousands of cycles, and its performance will decay over time.
Moreover, capacity decay is not linear with the number of cycles. In this article, researchers only conducting 5 cycles may not provide a sufficient basis for the parameters, which were applied to test the module.
I suggest the author consider extending the testing to several hundred or even thousand cycles, then get the parameters for the module evaluation during the operation.
This will enhance the reliability and significance.
Response 1: Thank you for the comment. We agree that long-term cycling is important for assessing battery degradation, but that is not the focus of the present work: the aim is not to describe capacity fade over time, but rather to parameterize physics-based battery model at a specific state of health, in this case the beginning of life. The five repeated cycles were conducted to assess the repeatability error of the measurements used for parameter estimation at the beginning of life. Nevertheless, we would like to note that such long-term testing and capacity fade modeling are currently part of our ongoing research, the preprint is accessible here: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5273872.
Comment 2: Line 198 and 218,241 are the first line in the paragraph, it should have the same structure as other paragraphs in the beginning.
Response 2: Thank you for the note. The structure of the paragraphs starting at lines 198, 218, and 241 has been revised to ensure consistency with the rest of the manuscript.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsThis manuscript provides a way to predict the models of lithium-ion batteries. This method integrates mechanical measurements with the electrical data, and the effect of the mechanical measurements of the battery deformation on parameter estimation is deeply investigated through an optimization model developed in COMSOL Multiphysics with a specific application to lithium iron phosphate (LFP) cells. Nevertheless, some issues should be solved as the following comments.
- In the experiment section, the author used three batteries for electrical, thermal and mechanical characterization. Although the charge and discharge were repeated five times, the reviewer believes that the amount of data was still too small and the number of batteries needed to be increased.
- Why use the experimental data under 3C discharge current to evaluate RC, and whether the experimental data under higher current have an impact on the results?
- The reviewer believes that it is necessary to provide relevant images to increase the reliability of the electrode thickness data in teardown scenario.
- The initial values of diffusion coefficient and reaction rate mentioned in line 314 are commonly used values reported in the literature, but the source is not indicated. Therefore, the reviewer believes that the data was not authentic enough.
- This relevant work regarding energy storage applications of batteries could be added to enrich the text: https://doi.org/10.1002/adfm.202312664
Author Response
Comment 1: In the experiment section, the author used three batteries for electrical, thermal and mechanical characterization. Although the charge and discharge were repeated five times, the reviewer believes that the amount of data was still too small and the number of batteries needed to be increased.
Response 1: Thank you for the comment. Each battery sample has its own parameter set, because cell to cell differences exist even among the same commercial battery model. Increasing the number of tested batteries does not necessarily increase the statistical robustness of a single parameter set, but rather provides multiple distinct parameter sets, each corresponding to an individual cell. We used three battery samples to exclude possible outliers and verify that the experimental values are reasonably close to each other. Further statistical discussion on this dataset can be found in an authors’ previous work https://doi.org/10.1016/j.trpro.2023.11.030.
Comment 2: Why use the experimental data under 3C discharge current to evaluate RC, and whether the experimental data under higher current have an impact on the results?
Response 2: Thank you for the comment. We think that this point is already described in lines 297-300 of the original manuscript, citing literally the manuscript “…and the contact resistance R_c — which is another challenging parameter to assess — is voltage-insensitive at low current rates, namely its value does not influence the voltage when the current is low. Therefore, the experimental data at 3C discharge current rate are then used to assess R_c and…”. Briefly, contact resistance obviously influences the results at high current because it causes greater voltage drop, while at low current any value would give the same results.
Comment 3: The reviewer believes that it is necessary to provide relevant images to increase the reliability of the electrode thickness data in teardown scenario.
Response 3: Thank you for the advice. A relevant SEM image has been added in Figure 3 to support the electrode thickness data in the teardown scenario.
Comment 4: The initial values of diffusion coefficient and reaction rate mentioned in line 314 are commonly used values reported in the literature, but the source is not indicated. Therefore, the reviewer believes that the data was not authentic enough.
Response 4: Thank you for the note. The appropriate references to support the values of the diffusion coefficients and reaction rates have been inserted in the manuscript.
Comment 5: This relevant work regarding energy storage applications of batteries could be added to enrich the text: https://doi.org/10.1002/adfm.202312664
Response 5: Thank you for the suggestion. I reviewed the proposed reference and appreciate its relevance to the field of energy storage. However, we believe that the reference proposed does not align with the specific scope of this work, which focuses on parameter estimation in lithium-ion battery models.
Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
Comments and Suggestions for AuthorsThe manuscript has been well revised and could be accepted in the present form.
