State of Charge Estimation for Lithium-Ion Battery Based on NARX Recurrent Neural Network and Moving Window Method
Open accessAbstract
An accurate state of charge (SOC) estimation depends on an accurate battery model. The influence of nonlinear and unstable interference factors makes the accurate SOC estimation difficult. To obtain an accurate battery model, a method based on the NARX (nonlinear autoregressive network with exogenous inputs) recurrent neural network and moving window method is proposed. This paper improves the accuracy, modelling speed and robustness of SOC estimation from the following three aspects. First, to overcome the excessive reliance on the amount of data in the model training process, the NARX recurrent neural network is used to establish the battery model. NARX (nonlinear autoregressive with external input) recurrent neural network with the delay and feedback functions can keep the input and output of a previous moment and add it to the calculation of the next moment. Therefore, better estimation results are achieved using a small amount of data; second, the moving window method is used against the gradient explosion and the gradient vanishing that may occur in the NARX model training process. Third, by comparing it with other methods under different working conditions and different temperatures, the validity of the proposed model is verified. The results indicate that the proposed model has a higher accuracy and speed of the SOC estimation. The RMSE performance of the proposed model is reduced by approximately 65%, and the execution time is shortened by approximately 50%.
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Ma et al. significantly reduced the window length to 50 seconds, resulting in a slight decrease in estimation accuracy but still within an acceptable range.
“Ma et al. significantly reduced the window length, with the optimal length set to just 50 seconds, resulting in a slight decrease in estimation accuracy but still within an acceptable range[76,82].”
From Advancements in the estimation of the state of charge of lithium-ion battery: a comprehensive review of traditional and deep learning approaches (2025) · cites this paper as [76]
In IV. Results and Discussion (page unavailable), the paper compares variable window sizing with fixed sizes of 225 and 450, then adopts the variable-window model because it has higher accuracy. It does not identify 50 seconds as an optimal length or report a slight accuracy decrease; V. Conclusion (page unavailable) says the method improves estimation accuracy. (LLM, conf=0.86)
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Experimental — accuracy not yet measuredWang et al. improved SRNN with a dynamic window size that adapts to data fluctuations, reducing the maximum RMSE to 0.34%, outperforming the fixed window approach.
“They improved this method with a dynamic window size that adapts to data fluctuations, reducing the maximum RMSE to 0.34%, outperforming the fixed window approach.”
From Advancements in the estimation of the state of charge of lithium-ion battery: a comprehensive review of traditional and deep learning approaches (2025) · cites this paper as [76]
The Results and Discussion section reports that the adaptive-window model achieved an RMSE of 0.34% under CCCV conditions, lower than the two fixed-window models. But 0.34% is not the model’s maximum RMSE across conditions: the same section reports higher RMSEs under DST and UDDS. The paper describes its model as a NARX recurrent neural network, not an SRNN. (LLM, conf=0.89)
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- QIAO WANG (Graduate Student Member, IEEE) received the B.E. degree in process equipment and control engineering from the Shaanxi Uni- versity of Science and Technology, Xi'an, China, in 2019. He is currently pursuing the Ph.D. degree in mechanical engineering with the National Engi- neering Laboratory for Highway Maintenance Equipment, Chang'an University, Xi'an. His research interest includes battery manage- ment systems.
- MIN YE (Member, IEEE) received the B.Sc. and M.Sc. degrees in mechatronics engineering from Chang'an University, in 2000 and 2004, respectively, and the Ph.D. degree in mechatron- ics engineering from Xi'an Jiaotong University, in 2008. From 2008 to 2010, he was a Postdoc- toral Researcher with Sany Heavy Industry Com- pany. In 2013, he was a Visiting Scholar with the University of Michigan-Dearborn. Since 2015, he has been a Full Professor and the Vice Dean of the School of Construction Machinery, Chang'an University. His research interests include energy saving technology, hybrid power technology, and computational fluid mechanic.
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- Authors
- Wang, Q., Gu, H., Ye, M., Wei, M., & Xu, X.
- Affiliations
- Chang'an University (CN)
- Venue
- IEEE Access
- Published
- 2021
- Volume
- 9
- Pages
- 83364-83375
- ISSN
- 2169-3536 (ISSN-L)
- OpenAlex
- W3172458106
- Cited by
- 52
- References
- 38
- Citations by year
- 2026: 13 · 2025: 5 · 2024: 9 · 2023: 18 · 2022: 6 · 2021: 1
- FWCI
- 2.76
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- IEEE Access (publishedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Funders
- National Natural Science Foundation of China (51805041)
- Science and Technology Innovation Team of Shaanxi Province (2020TD0012)
- National Key Research and Development Program of China (2018YFC0808204)
- Topics
- Physical Sciences › Engineering › Automotive Engineering › Advanced Battery Technologies Research
- Physical Sciences › Engineering › Control and Systems Engineering › Control Systems and Identification
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Advancements in Battery Materials
- Keywords
- state of charge estimation, lithium-ion batteries, moving window technique, battery modeling, small datasets, gradient explosion, gradient vanishing, temperature effects
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