State of Charge Estimation of Lithium-Ion Batteries Using LSTM and NARX Neural Networks

Wei, Meng; Ye, Min; Li, Jia Bo; Wang, Qiao; Xu, Xinxin

doi:10.1109/access.2020.3031340

Cited by 148Advanced Battery Technologies ResearchAdvancements in Battery MaterialsElectric and Hybrid Vehicle Technologies

State of Charge Estimation of Lithium-Ion Batteries Using LSTM and NARX Neural Networks

Open access

Wei, Meng, Ye, Min, Li, Jia Bo, Wang, Qiao, Xu, Xinxin·2020·IEEE Access

DOI 10.1109/access.2020.3031340

Open this paper in CoChat — free account Open PDF

Abstract

Highly accurate state of charge (SOC) estimation of lithium-ion batteries is one of the key technologies of battery management systems in electric vehicles. The performance of SOC estimation directly influences the driving range and safety of these vehicles. Due to external disturbances, temperature variation and electromagnetic interference, accurate SOC estimation becomes difficult. To accurately estimate the SOC of lithium-ion batteries, this article presents a novel machine-learning method to address the risk of gradient explosion and gradient decent using the dynamic nonlinear auto-regressive models with exogenous input neural network (NARX) with long short-term memories (LSTM).The proposed hybrid NARX model embeds LSTM memory, which provides jump-ahead connections in the time-unfolded model. These jump-ahead connections provide a shorter path for the propagation of gradient information, therefore reducing long-term dependence on the recurrent neural network. Experimental results show that the estimation performance root mean square error (RMSE) of the proposed model is less than 1%, and this model has better multitime prediction performance. Finally, the hybrid NARX and LSTM model is compared with the standard back propagation neural network based on particle swarm optimization (BPNN-PSO), the least-squares support vector machine (LS-SVM) and LSTM existing models under urban dynamometer driving schedule (UDDS) and dynamic stress test (DST) conditions. The proposed hybrid NARX-LSTM model yield relative to other methods and can estimate the battery SOC with high accuracy. The RMSE of proposed model is improved by approximately 60% compared with the standard LSTM.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

Integrity signals

Registry

Crossref · 10.1109/access.2020.3031340

Cites

37 of 37 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Wei et al. improved the error reduction to within 0.78%.
“Wei et al. improved the error reduction to within 0.78%[78].”
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 [78]

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Data-driven prediction of battery cycle life before capacity degradation
Severson, K. A., Attia, P. M., Jin, N., Perkins, N., Jiang, B., Yang, Z., Chen, M. H., Aykol, M., Herring, P. K., Fraggedakis, D., et al. (2019) · Nature Energy · doi:10.1038/s41560-019-0356-8 · Cited by 3,228 · see citing works
Long Short-Term Memory Recurrent Neural Network for Remaining Useful Life Prediction of Lithium-Ion Batteries
Zhang, Y., Xiong, R., He, H., & Pecht, M. G. (2018) · IEEE Transactions on Vehicular Technology · doi:10.1109/tvt.2018.2805189 · Cited by 1,326 · see citing works
State of Charge Estimation for Lithium-Ion Batteries Using Model-Based and Data-Driven Methods: A Review
How, D. N. T., Hannan, M. A., Lipu, M. S. H., & Ker, P. J. (2019) · IEEE Access · doi:10.1109/access.2019.2942213 · Cited by 823 · see citing works
Overview of model-based online state-of-charge estimation using Kalman filter family for lithium-ion batteries
Shrivastava, P., Soon, T. K., Idris, M. Y. I. B., & Mekhilef, S. (2019) · Renewable and Sustainable Energy Reviews · doi:10.1016/j.rser.2019.06.040 · Cited by 704 · see citing works
State-of-charge estimation of lithium-ion batteries based on gated recurrent neural network
Yang, F., Li, W., Li, C., & Miao, Q. (2019) · Energy · doi:10.1016/j.energy.2019.03.059 · Cited by 543 · see citing works
Machine Learning Applied to Electrified Vehicle Battery State of Charge and State of Health Estimation: State-of-the-Art
Vidal, C., Malysz, P., Kollmeyer, P., & Emadi, A. (2020) · IEEE Access · doi:10.1109/access.2020.2980961 · Cited by 512 · see citing works
State-of-charge estimation of lithium-ion batteries using LSTM and UKF
Yang, F., Zhang, S., Li, W., & Miao, Q. (2020) · Energy · doi:10.1016/j.energy.2020.117664 · Cited by 452 · see citing works
Online estimation of internal resistance and open-circuit voltage of lithium-ion batteries in electric vehicles
Chiang, Y., Sean, W., & Ke, J.-C. (2011) · Journal of Power Sources · doi:10.1016/j.jpowsour.2011.01.005 · Cited by 396 · see citing works
A combined method for state-of-charge estimation for lithium-ion batteries using a long short-term memory network and an adaptive cubature Kalman filter
Tian, Y., Lai, R., Li, X., Xiang, L., & Tian, J. (2020) · Applied Energy · doi:10.1016/j.apenergy.2020.114789 · Cited by 357 · see citing works
Lithium Polymer Battery State-of-Charge Estimation Based on Adaptive Unscented Kalman Filter and Support Vector Machine
Meng, J., Luo, G., & Gao, F. (2015) · IEEE Transactions on Power Electronics · doi:10.1109/tpel.2015.2439578 · Cited by 353 · see citing works
A Lithium-Ion Battery-in-the-Loop Approach to Test and Validate Multiscale Dual H Infinity Filters for State-of-Charge and Capacity Estimation
Chen, C., Xiong, R., & Shen, W. (2018) · IEEE Transactions on Power Electronics · doi:10.1109/tpel.2017.2670081 · Cited by 295 · see citing works
Neural Network Approach for Estimating State of Charge of Lithium-Ion Battery Using Backtracking Search Algorithm
Hannan, M. A., Lipu, M. S. H., Hussain, A., Saad, M. H. M., & Ayob, A. (2018) · IEEE Access · doi:10.1109/access.2018.2797976 · Cited by 289 · see citing works
Stacked bidirectional long short-term memory networks for state-of-charge estimation of lithium-ion batteries
Bian, C., He, H., & Yang, S. (2020) · Energy · doi:10.1016/j.energy.2019.116538 · Cited by 284 · see citing works
Online joint-prediction of multi-forward-step battery SOC using LSTM neural networks and multiple linear regression for real-world electric vehicles
Hong, J., Wang, Z., Chen, W., Wang, L. Y., & Qu, C. (2020) · Journal of Energy Storage · doi:10.1016/j.est.2020.101459 · Cited by 217 · see citing works
Condition monitoring in advanced battery management systems: moving horizon estimation using a reduced electrochemical model
Hu, X., Cao, D., & Egardt, B. (2018) · IEEE/ASME Transactions on Mechatronics · doi:10.1109/tmech.2017.2675920 · Cited by 205 · see citing works
A Battery Management System With a Lebesgue-Sampling-Based Extended Kalman Filter
Yan, W., Zhang, B., Zhao, G., Tang, S., Niu, G., & Wang, X. (2018) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2018.2842782 · Cited by 203 · see citing works
Data-driven heating and cooling load predictions for non-residential buildings based on support vector machine regression and NARX Recurrent Neural Network: A comparative study on district scale
Koschwitz, D., Frisch, J., & van Treeck, C. (2018) · Energy · doi:10.1016/j.energy.2018.09.068 · Cited by 193 · see citing works
Battery Management Systems—Challenges and Some Solutions
Balasingam, B., Ahmed, M. S., & Pattipati, K. R. (2020) · Energies · doi:10.3390/en13112825 · Cited by 172 · see citing works
State of Charge Estimation for Lithium-Ion Battery Using Recurrent NARX Neural Network Model Based Lighting Search Algorithm
Lipu, M. S. H., Hannan, M. A., Hussain, A., Saad, M. H. M., Ayob, A., & Blaabjerg, F. (2018) · IEEE Access · doi:10.1109/access.2018.2837156 · Cited by 162 · see citing works
A double-scale and adaptive particle filter-based online parameter and state of charge estimation method for lithium-ion batteries
Ye, M., Guo, H., Xiong, R., & Yu, Q. (2017) · Energy · doi:10.1016/j.energy.2017.12.061 · Cited by 152 · see citing works
Self-citation
Recursive State of Charge and State of Health Estimation Method for Lithium-Ion Batteries Based on Coulomb Counting and Open Circuit Voltage
Gismero, A., Schaltz, E., & Stroe, D. (2020) · Energies · doi:10.3390/en13071811 · Cited by 113 · see citing works
An SOC estimation approach based on adaptive sliding mode observer and fractional order equivalent circuit model for lithium-ion batteries
Zhong, F., Li, H., Zhong, S., et al. (2015) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2014.12.015 · Cited by 108 · see citing works
Estimating the State-of-Charge of Lithium-Ion Battery Using an H-Infinity Observer Based on Electrochemical Impedance Model
Chen, N., Zhang, P., Dai, J., & Gui, W. (2020) · IEEE Access · doi:10.1109/access.2020.2971002 · Cited by 98 · see citing works
Using Dynamic Neural Networks for Battery State of Charge Estimation in Electric Vehicles
Jiménez, D., Fraile-Ardanuy, J., Castaño-Solis, S., Merino, J., & Álvaro-Hermana, R. (2018) · Procedia Computer Science · doi:10.1016/j.procs.2018.04.077 · Cited by 75 · see citing works
Hybrid VARMA and LSTM Method for Lithium-ion Battery State-of-Charge and Output Voltage Forecasting in Electric Motorcycle Applications
Caliwag, A. C., & Lim, W. (2019) · IEEE Access · doi:10.1109/access.2019.2914188 · Cited by 69 · see citing works
Second-Order Discrete-Time Sliding Mode Observer for State of Charge Determination Based on a Dynamic Resistance Li-Ion Battery Model
Kim, D., Koo, K., Jeong, J. H., Goh, T., & Kim, S. (2013) · Energies · doi:10.3390/en6105538 · Cited by 50 · see citing works
State of Charge Estimation of Power Battery Using Improved Back Propagation Neural Network
Zhang, C., Chen, S.-R., Gao, H., Xu, K.-J., & Yang, M.-Y. (2018) · Batteries · doi:10.3390/batteries4040069 · Cited by 43 · see citing works
Dynamic data-driven and model-based recursive analysis for estimation of battery state-of-charge
Li, Y., Chattopadhyay, P., Xiong, S., Ray, A., & Rahn, C. D. (2016) · Applied Energy · doi:10.1016/j.apenergy.2016.10.025 · Cited by 38 · see citing works
A novel piezoelectric hysteresis modeling method combining LSTM and NARX neural networks
Wang, G., Yao, X., Cui, J., et al. (2020) · Modern Physics Letters B · doi:10.1142/s0217984920503066 · Cited by 33 · see citing works
Combined estimation of the state of charge of a lithium battery based on a back-propagation– adaptive Kalman filter algorithm
Zhao, W., Kong, X., & Wang, C. (2017) · Proceedings of the Institution of Mechanical Engineers Part D Journal of Automobile Engineering · doi:10.1177/0954407017701533 · Cited by 28 · see citing works
A parameter adaptive method with dead zone for state of charge and parameter estimation of lithium-ion batteries
Guo, F., Hu, G., & Hong, R. (2018) · Journal of Power Sources · doi:10.1016/j.jpowsour.2018.09.015 · Cited by 27 · see citing works
Hybrid method based on particle filter and NARX for real-time flow rate estimation in multi-product pipelines
He, L., Wen, K., Wu, C., Gong, J., & Ping, X. (2020) · Journal of Process Control · doi:10.1016/j.jprocont.2020.02.004 · Cited by 25 · see citing works
State of Charge Estimation for Lithium-Ion Batteries Based on NARX Neural Network and UKF
Qin, X., Gao, M., He, Z., & Liu, Y. (2019) · IEEE International Conference on Industrial Informatics (INDIN) · doi:10.1109/indin41052.2019.8972319 · Cited by 15 · see citing works
A Novel Approach Based Deep RNN Using Hybrid NARX-LSTM Model For Solar Power ForecastingPreprint
Massaoudi, M., Chihi, I., Sidhom, L., et al. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1910.10064 · Cited by 14 · see citing works
State-Of-Charge Estimation for Lithium-Ion Battery Using Improved DUKF Based on State-Parameter Separation
Yu, C., Xie, Y., Sang, Z.-Y., et al. (2019) · Energies · doi:10.3390/en12214036 · Cited by 14 · see citing works
Online State Estimation Using Particles Filters of Lithium-Ion Polymer Battery Packs for Electric Vehicle
Hao, X., & Wu, J. (2015) · Conference proceedings/Conference proceedings - IEEE International Conference on Systems, Man, and Cybernetics · doi:10.1109/smc.2015.146 · Cited by 8 · see citing works
An Improved Prediction Method of SOC Based on the GA-RBF Neural Network
Liang, M. D., & Wu, T. Z. (2014) · Advanced materials research · doi:10.4028/www.scientific.net/amr.953-954.800 · Cited by 7 · see citing works

Flagged first, then by citations

Research works printed but not linked: 2

Q. Wei et al., ''Study on the state of health detection of power batteries based on adaptive unscented Kalman filters and the battery echelon utiliza- tion,'' Trans. China Electrotechnical Soc., vol. 34, no. 18, pp. 3937-3948, 2019.
MIN YE (Member, IEEE) received the B.Sc. and M.Sc. degrees in mechatronics engineering from Chang'an University, in 2000 and 2004, respec- tively, and the Ph.D. degree in mechatronics engi- neering from Xi'an Jiaotong University, in 2008.

Sorted by citations

Deep learning approach towards accurate state of charge estimation for lithium-ion batteries using self-supervised transformer model
Hannan, M. A., How, D. N. T., Lipu, M. S. H., Mansor, M., Ker, P. J., Dong, Z. Y., Sahari, K. S. M., Tiong, S. K., Muttaqi, K. M., Mahlia, T. M. I., et al. (2021) · Scientific Reports · doi:10.1038/s41598-021-98915-8 · Cited by 196 · see citing works
A machine learning-based battery management system for state-of-charge prediction and state-of-health estimation for unmanned aerial vehicles
Shibl, M. M., Ismail, L. S., & Massoud, A. M. (2023) · Journal of Energy Storage · doi:10.1016/j.est.2023.107380 · Cited by 92 · see citing works
A comprehensive review of hybrid battery state of charge estimation: Exploring physics-aware AI-based approaches
Sorouri, H., Oshnoei, A., Che, Y., & Teodorescu, R. (2024) · Journal of Energy Storage · doi:10.1016/j.est.2024.113604 · Cited by 62 · see citing works
State of Charge Estimation for Lithium-Ion Battery Based on NARX Recurrent Neural Network and Moving Window Method
Wang, Q., Gu, H., Ye, M., Wei, M., & Xu, X. (2021) · IEEE Access · doi:10.1109/access.2021.3086507 · Cited by 52 · see citing works
Self-citation
Uncorrelated Sparse Autoencoder With Long Short-Term Memory for State-of-Charge Estimations in Lithium-Ion Battery Cells
Savargaonkar, M., Oyewole, I., Chehade, A., & Hussein, A. A. (2024) · IEEE Transactions on Automation Science and Engineering · doi:10.1109/tase.2022.3222759 · Cited by 45 · see citing works
Exploiting Artificial Neural Networks for the State of Charge Estimation in EV/HV Battery Systems: A Review
Dini, P., & Paolini, D. (2025) · Batteries · doi:10.3390/batteries11030107 · Cited by 40 · see citing works
Accurate state of charge prediction for lithium-ion batteries in electric vehicles using deep learning and dimensionality reduction
Jayaraman, R., & Thottungal, R. (2024) · Electrical Engineering · doi:10.1007/s00202-023-02227-1 · Cited by 21 · see citing works
Advancements in the estimation of the state of charge of lithium-ion battery: a comprehensive review of traditional and deep learning approaches
Wu, Y., Bai, D., Zhang, K., Li, Y., & Yang, F. (2025) · Journal of Materials Informatics · doi:10.20517/jmi.2024.84 · Cited by 20 · see citing works

State of charge estimation at battery level from multiple cells management
Pichon, X., Collet, A., Riu, D. M., & Crébier, J.-C. (2015) · International Conference on Ecological Vehicles and Renewable Energies (EVER) · doi:10.1109/ever.2015.7112977 · Cited by 2 · see citing works
Enhanced NARX Neural Network Model for Specific Time-Series Prediction. Case Study: Battery State of Charge in Electric Vehicles
Saïd-Romdhane, M. B., Boussaada, Z., Curea, O., et al. (2023) · International Renewable Energy Congress · doi:10.1109/irec59750.2023.10389508 · Cited by 8 · see citing works
Battery State of Charge Estimation Considering the Battery Aging
Lee, S., & Park, M.-K. (2014) · Journal of IKEEE · doi:10.7471/ikeee.2014.18.3.298 · Cited by 2 · see citing works
Daily solar radiation prediction using NARX and MLP-NNs networks: A Case study of Kenitra City, Morocco
Elmousaid, R., Adnani, Y., Hamdaouy, A. E., et al. (2022) · IEEE International Conference on Electronics, Control, Optimization and Computer Science (ICECOCS) · doi:10.1109/icecocs55148.2022.9983450 · Cited by 4 · see citing works
NARX Model Based Estimation of State of Charge of Lithium-Ion Batteries in Electric Vehicles under Varying Temperature Ranges
Tiwari, S., Kumar, B., & Tyagi, A. (2023) · International Conference on Computing, Communication and Networking Technologies (ICCCNT) · doi:10.1109/icccnt56998.2023.10306403

Authors: Wei, M., Ye, M., Li, J. B., Wang, Q., & Xu, X.
Affiliations: Chang'an University (CN)
ORCID: Wei, Meng
Ye, Min
Wang, Qiao
Xu, Xinxin
Venue: IEEE Access
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Published: 2020
Volume: 8
Pages: 189236-189245
ISSN: 2169-3536 (ISSN-L)
DOI: 10.1109/access.2020.3031340
OpenAlex: W3093838722
Cited by: 148
References: 37
Citations by year: 2026: 27 · 2025: 31 · 2024: 26 · 2023: 31 · 2022: 21 · 2021: 11 · 2020: 1
FWCI: 5.92
Type: journal article
Language: en
Open access: gold
doi.org
Licence: cc-by
creativecommons.org/licenses/by/4.0/legalcode (vor)
Locations: IEEE Access (publishedVersion, cc-by)
DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
Funders: National Key Research and Development Program of China (2018YFE0120200)
National Natural Science Foundation of China (51805041)
Major Scientific and Technological Projects in Henan Province (191110211500)
National Engineering Laboratory for Highway Maintenance Equipment, Chang’an University, Xi’an, Shaanxi, for experimental equipment
Topics: Physical Sciences › Engineering › Automotive Engineering › Advanced Battery Technologies Research
Physical Sciences › Engineering › Electrical and Electronic Engineering › Advancements in Battery Materials
Physical Sciences › Engineering › Automotive Engineering › Electric and Hybrid Vehicle Technologies
Keywords: state of charge estimation, lithium-ion batteries, battery management systems, electric vehicles, NARX neural network, long short-term memory, gradient explosion, multi-step forecasting, UDDS, dynamic stress test

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

State of Charge Estimation of Lithium-Ion Batteries Using LSTM and NARX Neural Networks

Abstract

Integrity signals

Claims the paper makes

Claims other papers make about this one

Self-check

Cites

Cited by

Related

Record

About these checks