The state of charge (SOC) estimation of lithium-ion battery is an important function in the battery management system (BMS) of electric vehicles. The long short term memory (LSTM) model can be employed for SOC estimation, which is capable of estimating the future changing states of a nonlinear system. Since the BMS usually works under complicated operating conditions, i.e the real measurement data used for model training may be corrupted by non-Gaussian noise, and thus the performance of the original LSTM with the mean square error (MSE) loss may deteriorate. Therefore, a novel LSTM with mixture kernel mean p-power error (MKMPE) loss, called MKMPE-LSTM, is developed by using the MKMPE loss to replace the MSE as the learning criterion in LSTM framework, which can achieve robust SOC estimation under the measurement data contaminated with non-Gaussian noises (or outliers) because of the MKMPE containing the p-order moments of the error distribution. In addition, a meta-heuristic algorithm, called heap-based-optimizer (HBO), is employed to optimize the hyper-parameters (mainly including learning rate, number of hidden layer neuron and value of p in MKMPE) of the proposed MKMPE-LSTM model to further improve its flexibility and generalization performance, and a novel hybrid model (HBO-MKMPE-LSTM) is established for SOC estimation under non-Gaussian noise cases. Finally, several tests are performed under various cases through a benchmark to evaluate the performance of the proposed HBO-MKMPE-LSTM model, and the results demonstrate that the proposed hybrid method can provide a good robustness and accuracy under different non-Gaussian measurement noises, and the SOC estimation results in terms of mean square error (MSE), root MSE(RMSE), mean absolute relative error (MARE), and determination coefficient R² are less than 0.05%, 3%, 3%,and above 99.8% at 25℃, respectively.

锂离子电池的荷电状态（SOC）估计是电动汽车电池管理系统（BMS）中的一项重要功能。长短期记忆（LSTM）模型可用于SOC估计，能够估计非线性系统未来的变化状态。由于BMS通常在复杂的操作条件下工作，即用于模型训练的真实测量数据可能会被非高斯噪声破坏，因此具有均方误差（MSE）损失的原始LSTM的性能可能会恶化。因此，通过使用 MKMPE 损失代替 MSE 作为 LSTM 框架中的学习准则，开发了一种具有混合核平均 p 幂误差 (MKMPE) 损失的新型 LSTM，称为 MKMPE-LSTM，由于 MKMPE 包含误差分布的 p 阶矩，因此可以在被非高斯噪声（或异常值）污染的测量数据下实现稳健的 SOC 估计。此外，使用一种称为基于堆的优化器（HBO）的元启发式算法来优化所提出的 MKMPE 的超参数（主要包括学习率、隐藏层神经元的数量和 MKMPE 中的 p 值）- LSTM模型进一步提高其灵活性和泛化性能，并建立了一种新型混合模型（HBO-MKMPE-LSTM）用于非高斯噪声情况下的SOC估计。最后，通过基准测试在各种情况下进行了多项测试，以评估所提出的 HBO-MKMPE-LSTM 模型的性能，25℃时R ² 分别小于0.05%、3%、3%和99.8%以上。