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<p>The state of charge (SOC) and state of energy (SOE) of lithium-ion batteries are of vital importance to battery management systems (BMS). However, the strong nonlinearity, temperature dependence, and time-varying characteristics still pose challenges to precise state estimation. This paper proposes an eagle-fish optimization algorithm (HFOA) combined with a deep temporal network, namely the HFOA–TCN–BiGRU–SelfAttention model. The temporal convolutional network (TCN) extracts multi-scale dynamic features, the bidirectional gated recurrent unit (BiGRU) captures bidirectional temporal dependencies, and the self-attention mechanism highlights key operational condition information. Meanwhile, a Kalman filter is applied at the output stage to suppress estimation noise and enhance the temporal consistency of the jointly estimated SOC and SOE. The HFOA adaptively optimizes the learning rate, regularization, and network structure, enhancing robustness. Experiments conducted under multiple temperatures (15&#xa0;°C, 25&#xa0;°C, 35&#xa0;°C) and various operating conditions, including the hybrid pulse power characteristic (HPPC), dynamic stress test (DST), and Beijing bus dynamic stress test (BBDST), demonstrate that the proposed method achieves an average absolute error (MAE) of less than 0.467%, a root mean square error (RMSE) of less than 0.668%, and a coefficient of determination (R²) greater than 0.999 in the joint estimation of SOC and SOE. These results indicate that the method has high accuracy, stability, and universality in complex environments.</p>

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A hybrid deep learning framework for joint state-of-charge and state-of-energy estimation of lithium-ion batteries under multiple operating conditions

  • 期刊论文

  • 发表日期：

    2026年3月24日

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  • Miao Yu,
  • Kaiming Shi,
  • Shunli Wang,
  • Qin Zhang,
  • Lei Zhou,
  • Quan Dang,
  • Carlos Fernandez,
  • Shaoqing Chen

摘要

The state of charge (SOC) and state of energy (SOE) of lithium-ion batteries are of vital importance to battery management systems (BMS). However, the strong nonlinearity, temperature dependence, and time-varying characteristics still pose challenges to precise state estimation. This paper proposes an eagle-fish optimization algorithm (HFOA) combined with a deep temporal network, namely the HFOA–TCN–BiGRU–SelfAttention model. The temporal convolutional network (TCN) extracts multi-scale dynamic features, the bidirectional gated recurrent unit (BiGRU) captures bidirectional temporal dependencies, and the self-attention mechanism highlights key operational condition information. Meanwhile, a Kalman filter is applied at the output stage to suppress estimation noise and enhance the temporal consistency of the jointly estimated SOC and SOE. The HFOA adaptively optimizes the learning rate, regularization, and network structure, enhancing robustness. Experiments conducted under multiple temperatures (15 °C, 25 °C, 35 °C) and various operating conditions, including the hybrid pulse power characteristic (HPPC), dynamic stress test (DST), and Beijing bus dynamic stress test (BBDST), demonstrate that the proposed method achieves an average absolute error (MAE) of less than 0.467%, a root mean square error (RMSE) of less than 0.668%, and a coefficient of determination (R²) greater than 0.999 in the joint estimation of SOC and SOE. These results indicate that the method has high accuracy, stability, and universality in complex environments.