Excitation Pulse Influence on the Accuracy and Robustness of Equivalent Circuit Model Parameter Identification for Li-Ion Batteries

Round 1

Reviewer 1 Report (Previous Reviewer 1)

Comments and Suggestions for Authors

The authors have provided a revised and improved version of the manuscript fully addressing all reviewer comments. The manuscript is now suitable for publication.

Author Response

Thank you for your time!

Reviewer 2 Report (Previous Reviewer 2)

Comments and Suggestions for Authors

Good improvement.

Author Response

Thank you for your time!

Reviewer 3 Report (Previous Reviewer 3)

Comments and Suggestions for Authors

The authors have done what is required. Thanks.

Author Response

Thank you for your time!

Reviewer 4 Report (Previous Reviewer 4)

Comments and Suggestions for Authors

The Authors have now provided supporting files with the dataset (external: https://zenodo.org/records/17635366 "Excitation Pulse Influence on the Accuracy and Robustness of Equivalent Circuit Model Parameter Identification for Li-ion Batteries") and equivalent circuit model (ECM) parameter list (internal in DOC format).

The text has been thoroughly improved. The Abstract, for instance, now brings further information on methodology and main achievements. The Introduction has been almost rewritten. Multiple writing errors in the text were corrected. The Methodology has also been improved. It now provides detailed information on the dataset and the models used. After that, most of the rewriting was left for the Discussion and Conclusions. Many references were brought to the discussion, enriching the manuscript. The number of references is adequate, even excessive, and they are up-to-date. There are no issues of self-citations.

The only issue concerns the function/code used/developed for this particular work, as mentioned in the manuscript. It should be uploaded to either an external or internal source file. 

Author Response

Comment 1:
The only issue concerns the function/code used/developed for this particular work, as mentioned in the manuscript. It should be uploaded to either an external or internal source file. 

Response 1:

As was noted in data Availability Statement all the developed code and auxiliary scripts are provided externally at:
https://github.com/eealexey/TEVP-Thevenin-Equivalent-Model-Parameterization

(same as ref. 50)

New text was added to highlight this fact at line 187 if the Introduction section, where the TEVP code is first mentioned.

Thank you for your time!

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript employs first- and second-order Thevenin ECMs and identifies their parameters via nonlinear least squares. The authors conduct an extended series of tests considering the linear region across nine validation profiles, yielding relevant insights into how excitation-pulse characteristics affect ECM accuracy. Despite the relevant work, the manuscript requires several improvements.

The authors are encouraged to address the following points and provide a point-by-point response.

1. The problem formulation and the modeling framework are presented only implicitly. A dedicated subsection is needed to explicitly describe:
   a) the equations of the ECM,
   b) how the OCV is incorporated into the ECM model,
   c) the objective function minimized during parameter tuning,
   d) the rationale behind the chosen optimization algorithm,
   e) the performance index formulation (RMSE).

2. The training and validation datasets should also be described more clearly and precisely.

3. The manuscript should explicitly distinguish between what was performed on the real cell and what was simulated in Simscape. Including a photo of the experimental setup.

4. The introduction is well structured but too narrow. It overlooks significant developments in data-driven and machine-learning–based battery modeling methods. The authors are encouraged to discuss how the proposed methodology could be integrated into, or contrasted with, advanced ML-based or hybrid ECM–ML frameworks. The following works are suggested to refine both the introduction and the discussion of future research directions:
   – https://doi.org/10.1016/j.est.2025.118623
   – 10.23919/ECC54610.2021.9655051

Overall, the manuscript provides valuable insights and solid experimental work, but it requires minor revision to clarify the methodology, improve the state of the art, clarify the contributions, and better outline future work. With these improvements, the work can be considered for publication.

Comments on the Quality of English Language

english is ok

Author Response

A general note: we have extensively reworked the manuscript content to address all the reviewer’s comments. The major changes are:

1) The literature overview in the Introduction section is extended to provide a border context to the readers. The obtained results are compared to other relevant work in the Results and Discussion section. Total 24 new references are added, most of them are recent studies.

2) Theoretical background for ECM is added to the Methods section. It highlights the importance of the experimental data characteristic studied in this work.  

3) The Methods section is extended to provide a clearer description of the workflow. A new Figure 2 schematically illustrates all the phases of the study and the data processing pathways.

4) New results and analysis were added. ECM parameters sensitivity analysis was performed in response to the Reviewer 4 request (see the new Figure 9 and the associated discussion).

5) All the obtained ECM parameter set are provided as Supporting Information document. A set of MATLAB scripts (‘TEVP’) developed and used for mass processing of parameterization and validation data was made available for the readers.

Comment 1:

The problem formulation and the modeling framework are presented only implicitly. A dedicated subsection is needed to explicitly describe:

a) the equations of the ECM,

b) how the OCV is incorporated into the ECM model,

c) the objective function minimized during parameter tuning,

d) the rationale behind the chosen optimization algorithm,

e) the performance index formulation (RMSE).

Response 1:

All the points were addressed in the revised manuscript:

a) a new subsection 2.1 ‘Theoretical background’ was added (line 197)

b) a clarification was added (subsection 2.4, line 290)

c) and e) equation 7 and a clarification was added (subsection 2.4, line 289)

d) a clarification was added to subsection 2.4 (line 294), a relevant discussion was also added to Introduction section (line 122).

 

Comments 2 and 3:

The training and validation datasets should also be described more clearly and precisely.

The manuscript should explicitly distinguish between what was performed on the real cell and what was simulated in Simscape. Including a photo of the experimental setup.

Response 2,3:

We thank the Reviewer for pointing out this ambiguity. All parameterization and validation were performed using only experimental data obtained by cell discharge tests. A new detailed workflow scheme (Figure 2, including a photo of the experimental setup) and a new subsection 2.2 ‘General concept of the study’ were added to clarify how the data were obtained and processed.

 

Comment 4:

The introduction is well structured but too narrow. It overlooks significant developments in data-driven and machine-learning–based battery modeling methods. The authors are encouraged to discuss how the proposed methodology could be integrated into, or contrasted with, advanced ML-based or hybrid ECM–ML frameworks. The following works are suggested to refine both the introduction and the discussion of future research directions:
– https://doi.org/10.1016/j.est.2025.118623
– 10.23919/ECC54610.2021.9655051

Response 4:

The literature review in the Introduction section was significantly broadened and extended. Particularly ML-based methods are discussed in the 7-th paragraph (line 94), including the mentioned references.  

Reviewer 2 Report

Comments and Suggestions for Authors

The paper is a simpification of the paper Jinghua Sun, Josef Kainz, "Optimization of hybrid pulse power characterization profile for equivalent circuit model parameter identification of Li-ion battery based on Taguchi method",Journal of Energy Storage,Volume 70,2023,108034,ISSN 2352-152X, https://doi.org/10.1016/j.est.2023.108034 https://www.sciencedirect.com/science/article/pii/S2352152X23014317 
In this study, the Taguchi method was employed to investigate the effect of four HPPC parameters (positive and negative pulse height, length of pulse and length of relaxation) on ECM's performance under various application conditions (dynamic test, non-dynamic test and quasi-static test). The results show that all four parameters have an effect on ECM performance. For batteries operated only with the predictable charge and discharge patterns, the optimal combination of HPPC parameters values was determined based on Taguchi experiments. If batteries face unpredictable application scenarios, lower positive pulse heights, higher negative pulse heights, shorter pulse lengths and longer relaxation lengths within a certain range should be considered. Compared to established standard parameter values, this makes it possible to build a more accurate general model.

Author Response

Comment 1:

The paper is a simpification of the paper Jinghua Sun, Josef Kainz, "Optimization of hybrid pulse power characterization profile for equivalent circuit model parameter identification of Li-ion battery based on Taguchi method"

Response 1:

The mentioned paper is indeed a very closely related and high-quality work devoted to optimization of the HPPC test characteristics. A respectful discussion of the new ref. [37] is added to the revised manuscript: in the Introduction section (line 155) and in the subsection 3.4 ‘Achievable accuracy’ (line 485). The authors study the impact of the test pulse duration and relaxation time on the accuracy of the parameterized ECM. However, the test pulse duration range was restricted to 5-20 s, the relaxation time range to 20-80 s. Our study encompasses much wider ranges: pulse duration up to 144 s, relaxation time up to 2300 s. The extended variation ranges enabled us to achieve excellent ECM accuracy - RMSE 1.1 mV in contrast to the best RMSE = 5.3 mV in ref. [37]. We hope such an improvement is worthy of publication.    

A general note: we have extensively reworked the manuscript content to address all the reviewer’s comments. The major changes are:

1) The literature overview in the Introduction section is extended to provide a border context to the readers. The obtained results are compared to other relevant work in the Results and Discussion section. Total 24 new references are added, most of them are recent studies.

2) Theoretical background for ECM is added to the Methods section. It highlights the importance of the experimental data characteristic studied in this work.  

3) The Methods section is extended to provide a clearer description of the workflow. A new Figure 2 schematically illustrates all the phases of the study and the data processing pathways.

4) New results and analysis were added. ECM parameters sensitivity analysis was performed in response to the Reviewer 4 request (see the new Figure 9 and the associated discussion).

5) All the obtained ECM parameter set are provided as Supporting Information document. A set of MATLAB scripts (‘TEVP’) developed and used for mass processing of parameterization and validation data was made available for the readers.

Reviewer 3 Report

Comments and Suggestions for Authors

The paper name is " excitation pulse influence on the accuracy and robustness of equivalent circuit model parameter identification for Li-ion batteries". There are some comments on how to improve the paper's quality. The comments are:

1. The novelty of the work is not clear. It must be presented in the abstract and the introduction.
2. Also, the state of the art and the research gap must be elaborated.
3. The methods of validation or simulation are not clear. This issue must be discussed in detail.
4. In line 114, Fig. 1a must be Figure 1a. Do this for Figures 1b and 1c.
5. Figure 2 is missing in the text. Only Fig. 2c is present in the text that is not present as a figure. Fix this.
6. Figure 2 must be subdivided into 2a and 2b. The caption must be modified. Do this for Figures 4, 5, 6, and 7.
7. In line 237, Figure 3a, only Figure 3 is present. Fix this.
8. In general, throughout the manuscript, it is recommended to say "the authors" instead of saying " we". Please correct this throughout the manuscript.
9. To validate the results, compare them with recent research on the same topic.
10. One third of the references are beyond 2020. Hence, the references and literature survey must be updated with recent references.

Comments on the Quality of English Language

Must be Improved

Author Response

A general note: we have extensively reworked the manuscript content to address all the reviewer’s comments. The major changes are:

1) The literature overview in the Introduction section is extended to provide a border context to the readers. The obtained results are compared to other relevant work in the Results and Discussion section. Total 24 new references are added, most of them are recent studies.

2) Theoretical background for ECM is added to the Methods section. It highlights the importance of the experimental data characteristic studied in this work.  

3) The Methods section is extended to provide a clearer description of the workflow. A new Figure 2 schematically illustrates all the phases of the study and the data processing pathways.

4) New results and analysis were added. ECM parameters sensitivity analysis was performed in response to the Reviewer 4 request (see the new Figure 9 and the associated discussion).

5) All the obtained ECM parameter set are provided as Supporting Information document. A set of MATLAB scripts (‘TEVP’) developed and used for mass processing of parameterization and validation data was made available for the readers.

Comments 1 and 2:

The novelty of the work is not clear. It must be presented in the abstract and the introduction.

Also, the state of the art and the research gap must be elaborated.

Responses 1 and 2:

We thank the Reviewer for pointing out this flaw of the original manuscript. The discussion of the research gap in the Introduction section was broadened and emphasized – see the paragraphs 11, 12 and 13 (line 152-169). We also edited the abstract to highlight the advantages of this work.  

 

Comment 3:

The methods of validation or simulation are not clear. This issue must be discussed in detail.

Response 3:

We thank the Reviewer for pointing out this ambiguity. A new detailed workflow scheme (Figure 2) and a new subsection 2.2 ‘General concept of the study’ were added to clarify how the parameterization and validation procedures were performed.

 

Comment 4, 5, 6, 7, 8:

In line 114, Fig. 1a must be Figure 1a. Do this for Figures 1b and 1c.

Figure 2 is missing in the text. Only Fig. 2c is present in the text that is not present as a figure. Fix this.

Figure 2 must be subdivided into 2a and 2b. The caption must be modified. Do this for Figures 4, 5, 6, and 7.

In line 237, Figure 3a, only Figure 3 is present. Fix this.

In general, throughout the manuscript, it is recommended to say "the authors" instead of saying " we". Please correct this throughout the manuscript.

Responses 4, 5, 6, 7, 8:

All the listed problems were fixed. We tried our best to improve the technical quality of the revised text.

 

Comment 9:

To validate the results, compare them with recent research on the same topic.

Response 9: We absolutely agree with the suggestion. In the subsection ‘3.4 Achievable accuracy’ two new paragraphs are devoted to the comparison of the obtained results to the ones published in recent literature (line 485).

 

Comment 10: One third of the references are beyond 2020. Hence, the references and literature survey must be updated with recent references.

Response 10: The literature overview in the Introductions section was substantially extended. Total 24 new references are added (marked in green), most of them are recent studies.

 

Reviewer 4 Report

Comments and Suggestions for Authors

The manuscript, entitled "Excitation Pulse Influence on the Accuracy and Robustness of Equivalent Circuit Model Parameter Identification for Li-ion Batteries," presents a systematic study of the influence of experimental test pulse characteristics on the accuracy of the parameterized equivalent circuit model (ECM). The paper is well-written; however, a few more improvements are necessary before publication. More details are provided below.

The abstract is too shallow. More numbers from the Results Section should be included in this section to better highlight the main achievements and make the manuscript more engaging to readers.

In "Li-ion", use capital "L", since Li is the chemical element. It appears in many sentences of the text. Correct the writing in "Data Availability Statement: The obtained excremental data are available at zenodo.org: https://zenodo.org/records/17635365 (DOI 10.5281/zenodo.17635365). ". In “regardless on the number” (page 9, line 2), the correct is “regardless of...”.

There is an error in "The equivalent circuit models (ECM) and data-driven models are both rely on the empirical approach" (page 2, line 46). Please correct it.

According to the Authors, "There is a wide scatter of the test pulse duration values: 10 s [17–19], 18 s [20], 20 s [21], 30 s [22], 45 s [12], 60 s [22], 90 s [23] [12], 180 s [12,23,24], 360 s [12,23,25], 720 s [26] and 900 s [27]. The length of the post-pulse relaxation segment processed by the parameter identification algorithm is also scattered widely or is not even stated clearly in many sources. Few studies have taken effort to compare different test pulses." This background research was important in establishing the innovation; therefore, this work has the potential to be published. However, the Authors should deepen this research as well as the discussion section since the innovation appears to be too shallow.

The artwork quality is fine. No issues were detected. The only presented table is fine too. However, a summary of the main achievements should be brought up in a new table in the Results and Discussion Section.

Electrical circuit modeling is used, so no equations are provided. According to the Authors, "Two models were parametrized for each data set: 1RC and 2RC (see Fig. 1b)".

Methods and Results Section should include uncertainty and repeatability analysis, focusing on parameter variance (e.g., resistances, capacitances) and RMSE variance across repetitions. The Authors should provide confidence intervals for fitted parameters. For instance, the Authors could enhance the discussion with parameter covariance matrices, confidence intervals, and the condition number of the Jacobian. The proposed fitting method must be used against at least one alternative. More in-depth results should bring an evaluation of robustness across multiple temperatures. Since nonlinearity increases with current amplitude, it must be explicitly quantified by providing a sensitivity analysis of pulse amplitude versus model linearity. The Authors should add or at least discuss implications for online BMS. Please provide open scripts or pseudo-code in a supplementary file.

The number of references brought to the text is adequate, and there are no self-citations. Unfortunately, more up-to-date references are necessary. There is just one reference from the 2023-2025 period. These references should be discussed to make this work more acceptable for publication and more relevant to the readers. For instance, just 4 references are cited in the Results and Discussion Section.

Author Response

A general note: we have extensively reworked the manuscript content to address all the reviewer’s comments. The major changes are:

1) The literature overview in the Introduction section is extended to provide a border context to the readers. The obtained results are compared to other relevant work in the Results and Discussion section. Total 24 new references are added, most of them are recent studies.

2) Theoretical background for ECM is added to the Methods section. It highlights the importance of the experimental data characteristic studied in this work.  

3) The Methods section is extended to provide a clearer description of the workflow. A new Figure 2 schematically illustrates all the phases of the study and the data processing pathways.

4) New results and analysis were added. ECM parameters sensitivity analysis was performed in response to the Reviewer 4 request (see the new Figure 9 and the associated discussion).

5) All the obtained ECM parameter set are provided as Supporting Information document. A set of MATLAB scripts (‘TEVP’) developed and used for mass processing of parameterization and validation data was made available for the readers.

 

Comment 1:

The abstract is too shallow. More numbers from the Results Section should be included in this section to better highlight the main achievements and make the manuscript more engaging to readers.

Response 1: We tried our best to highlight the main advantages of the work while keeping the abstract concise.  

 

Comment 2:

In "Li-ion", use capital "L", since Li is the chemical element. It appears in many sentences of the text. Correct the writing in "Data Availability Statement: The obtained excremental data are available at zenodo.org: https://zenodo.org/records/17635365 (DOI 10.5281/zenodo.17635365). ". In “regardless on the number” (page 9, line 2), the correct is “regardless of...”.

Response 2:

We thank the Reviewer for finding these typos. Everything was fixed.

 

Comment 3: There is an error in "The equivalent circuit models (ECM) and data-driven models are both rely on the empirical approach" (page 2, line 46). Please correct it.

Response 3: This sentence was edited.

 

Comment 4:

According to the Authors, "There is a wide scatter of the test pulse duration values: 10 s [17–19], 18 s [20], 20 s [21], 30 s [22], 45 s [12], 60 s [22], 90 s [23] [12], 180 s [12,23,24], 360 s [12,23,25], 720 s [26] and 900 s [27]. The length of the post-pulse relaxation segment processed by the parameter identification algorithm is also scattered widely or is not even stated clearly in many sources. Few studies have taken effort to compare different test pulses." This background research was important in establishing the innovation; therefore, this work has the potential to be published. However, the Authors should deepen this research as well as the discussion section since the innovation appears to be too shallow.

Response 4: The Results and Discussion section was substantially extended. Particularly, new data presented in Figure 9 and relevant analysis were added.  

 

Comment 5:

The artwork quality is fine. No issues were detected. The only presented table is fine too. However, a summary of the main achievements should be brought up in a new table in the Results and Discussion Section.

Response 5:

A new Table 2 summarizing the best parameterization results was added to the Results and Discussion section. Also, a list of the main results was added to the Conclusions section.

 

Comment 6:

Electrical circuit modeling is used, so no equations are provided. According to the Authors, "Two models were parametrized for each data set: 1RC and 2RC (see Fig. 1b)".

Response 6:

A new subsection 2.1 ‘Theoretical background’ is specifically devoted to the mathematical equation describing the ECM behavior. It was added to the Methods section (line 197).

 

 

Comment 7:

Methods and Results Section should include uncertainty and repeatability analysis, focusing on parameter variance (e.g., resistances, capacitances) and RMSE variance across repetitions. The Authors should provide confidence intervals for fitted parameters. For instance, the Authors could enhance the discussion with parameter covariance matrices, confidence intervals, and the condition number of the Jacobian. The proposed fitting method must be used against at least one alternative. More in-depth results should bring an evaluation of robustness across multiple temperatures. Since nonlinearity increases with current amplitude, it must be explicitly quantified by providing a sensitivity analysis of pulse amplitude versus model linearity. The Authors should add or at least discuss implications for online BMS. Please provide open scripts or pseudo-code in a supplementary file.

Response 7:

The parameters variation in response to training data characteristics is presented in the new Figure 9 and discussed in the subsection 3.5 ECM parameters variation. Also, a sensitivity analysis was performed to estimate the uncertainty of the identified parameter values. The associated discussion was added (line 534).

In the subsection ‘3.4 Achievable accuracy’ two new paragraphs are devoted to the comparison of the obtained results to the results of other methods presented in recent literature (line 477).

A paragraph discussing the benefits for the online BMS is presented in the subsection 3.4 ‘Achievable accuracy’ of the revised manuscript (line 477).

A detailed workflow scheme (Figure 2) were added to clarify data processing procedures. The Matlab class “TEVP” developed by the authors and used to automate ECM parameterization, validation and results analysis was made available at: https://github.com/eealexey/TEVP-Thevenin-Equivalent-Model-Parameterization.

A thorough investigation of the temperature effect on the ECM parameters and optimal parameterization conditions is an ongoing work. It is planned as a separate publication due to the large amount of data to describe and analyze. Thus, we would prefer not disclose the preliminary results within this manuscript.  

 

Comment 8:

The number of references brought to the text is adequate, and there are no self-citations. Unfortunately, more up-to-date references are necessary. There is just one reference from the 2023-2025 period. These references should be discussed to make this work more acceptable for publication and more relevant to the readers. For instance, just 4 references are cited in the Results and Discussion Section.

Response 8:

The literature overview in the Introductions section was substantially extended. Total 24 new references are added (marked in green), most of them are recent studies. More literature discussion and comparisons were introduced in the Results and Discussion section (e.g. see lines 477-512).