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<p>This paper presents a novel algorithm based on the Enhanced Beluga Whale Optimization (EBWO), gated recurrent unit (GRU), and adaptive cubature Kalman filter (ACKF) for high-precision estimation of the state of charge (SOC) in lithium-ion batteries to ensure their safety and reliability. The experiments utilized a publicly available dataset from the University of Wisconsin-Madison, which includes battery performance test data under various temperatures (0&#xa0;°C, 10&#xa0;°C, − 10&#xa0;°C, − 20&#xa0;°C, and 25&#xa0;°C) and operating conditions (LA92, US06, UDDS, NN, and HWFET). The results show that the EBWO-GRU-ACKF model achieves significantly lower mean absolute error (MAE) and root mean square error (RMSE) compared to the standalone GRU model under multi-condition tests at 25&#xa0;°C. Specifically, under the US06 condition, the MAE is reduced to 0.078%, the RMSE to 1.58%, the maximum error to 2.92%, and the <i>R</i><sup>2</sup> value is increased to 0.98. The model also demonstrates strong robustness and adaptability under various temperature conditions, maintaining stable SOC estimation accuracy even under extreme low-temperature conditions (e.g., − 20&#xa0;°C), with an RMSE of 0.0048, an MAE of 0.0041, and a maximum error of 0.010. Furthermore, the study validates the model’s stability and significance across different operating conditions through uncertainty analysis, with all <i>p</i> values below the 0.05 significance threshold. Although the EBWO-GRU-ACKF model has slightly higher training time and energy consumption compared to the standalone GRU model, it achieves a good balance between real-time performance (inference time of 1.62&#xa0;s) and estimation accuracy, making it suitable for real-time deployment.</p>

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Enhanced Beluga Whale optimization meets GRU and adaptive cubature Kalman filter: a novel approach for state of charge estimation in lithium-ion batteries

  • 期刊论文

  • 发表日期：

    2025年8月12日

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  • Jingrui Liu,
  • Zhiwen Hou,
  • Yuhan Xu,
  • Yumeng He,
  • Boyu Wang

摘要

This paper presents a novel algorithm based on the Enhanced Beluga Whale Optimization (EBWO), gated recurrent unit (GRU), and adaptive cubature Kalman filter (ACKF) for high-precision estimation of the state of charge (SOC) in lithium-ion batteries to ensure their safety and reliability. The experiments utilized a publicly available dataset from the University of Wisconsin-Madison, which includes battery performance test data under various temperatures (0 °C, 10 °C, − 10 °C, − 20 °C, and 25 °C) and operating conditions (LA92, US06, UDDS, NN, and HWFET). The results show that the EBWO-GRU-ACKF model achieves significantly lower mean absolute error (MAE) and root mean square error (RMSE) compared to the standalone GRU model under multi-condition tests at 25 °C. Specifically, under the US06 condition, the MAE is reduced to 0.078%, the RMSE to 1.58%, the maximum error to 2.92%, and the R2 value is increased to 0.98. The model also demonstrates strong robustness and adaptability under various temperature conditions, maintaining stable SOC estimation accuracy even under extreme low-temperature conditions (e.g., − 20 °C), with an RMSE of 0.0048, an MAE of 0.0041, and a maximum error of 0.010. Furthermore, the study validates the model’s stability and significance across different operating conditions through uncertainty analysis, with all p values below the 0.05 significance threshold. Although the EBWO-GRU-ACKF model has slightly higher training time and energy consumption compared to the standalone GRU model, it achieves a good balance between real-time performance (inference time of 1.62 s) and estimation accuracy, making it suitable for real-time deployment.