锂离子电池健康状态（state of health, SOH）估计对于保证锂离子电池管理系统的安全稳定运行至关重要。然而，由于锂离子电池在放电过程中存在容量再生现象，SOH的准确估计一直是一个挑战。为了提高估计精度，提出了一种基于变分模态分解（variational mode decomposition, VMD）和双向长短期记忆网络-注意力机制（bidirectional long short term memory-attention, BiLSTM-ATT）的混合模型估计方法。首先，采用VMD分解算法对锂电池容量进行分解，得到一组相对稳定的子序列。为了降低后续的计算规模，通过引入了排列熵的方法对各个子序列进行重构。然后，将重构后的序列输入到BiLSTM-ATT模型中，利用注意力机制来分配隐藏层的特征权重，并通过双向长短期记忆网络（bidirectional long short term memory, BiLSTM）模型对SOH值进行训练和估计。最后，将所有估计值进行相加得到完整的SOH估计结果。通过在CALCE锂电池数据集上的CS2_36、CS2_38和CX2_35进行验证，实验结果表明所提出算法的均方根误差始终保持在0.6%以内，平均绝对误差始终保持在0.4%以内，相比其他估计模型表现出更高的精度和性能。

The estimation of the state of health (SOH) for lithium-ion batteries is considered crucial for ensuring the safe and stable operation of battery management system. However, the accurate estimation of SOH has been a challenge due to the capacity regeneration phenomenon during the discharge process of lithium-ion batteries. To improve estimation accuracy, a hybrid model based on variational mode decomposition (VMD) and bidirectional long short-term memory network with attention mechanism (BiLSTM-ATT) was proposed. First, the battery capacity was decomposed using the VMD algorithm, producing a set of stable sub-sequences. Then, permutation entropy was introduced to reconstruct the sub-sequences to reduce computational complexity. The reconstructed sequences were input into the BiLSTM-ATT model, and feature weights were assigned by the attention mechanism. The SOH values were trained and estimated by the BiLSTM model. Finally, the complete SOH estimation result was obtained by summing all estimated values. Validation was performed using the CS2_36, CS2_38, and CX2_35 datasets from the CALCE lithium battery dataset. The results show that the proposed algorithm maintains a root mean square error within 0.6% and a mean absolute error within 0.4%, which demonstrates higher accuracy and performance compared to other estimation models.