准确预测锂电池的剩余使用寿命(remaining useful life，RUL)可以及时了解电池内部的性能退化情况，降低电池的使用风险并为日常维护提供可靠的理论依据。为了提高预测结果的准确性和稳定性，提出了一种基于集合经验模态分解(ensemble empirical mode decomposition，EEMD)、门控循环单元网络(gated recurrent unit，GRU)和多元线性回归(multiple linear regression，MLR)相结合的锂电池RUL预测模型。该模型首先采用EEMD算法将锂电池容量数据分解为若干个高频分量和低频分量，以此减少容量数据中的噪声干扰，然后针对各个分量的特点，分别利用GRU和MLR网络基于获得的高频和低频序列建立预测子模型，最后叠加融合各个子模型的预测值得到锂电池的RUL结果，通过使用NASA和Oxford提供的锂电池公开数据，并采用不同的预测起点与其他单一模型和组合模型进行对比。实验结果表明，EEMD-GRU-MLR预测模型能够提供准确的RUL结果，相比于LSTM、GRU和EEMD-GRU预测模型，最大平均绝对误差分别降低了0.0311、0.0234、0.0182，最大均方根误差分别降低了0.0235、0.0153、0.0098，证明了本模型具有较好的锂电池RUL预测能力。
关键词：锂电池
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剩余使用寿命
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集合经验模态分解
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门控循环单元网络
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多元线性回归
Abstract
Accurately predicting the remaining useful life (RUL) of lithium batteries can ensure timely understanding of the internal performance degradation of the battery, reduce the risks associated with battery use, and provide a reliable theoretical basis for routine maintenance. To improve the accuracy and stability of prediction results, a lithium-battery RUL prediction model based on the combination of ensemble empirical mode decomposition (EEMD) and gated recurrent unit (GRU) with multiple linear regression (MLR) is proposed. First, the model decomposes the lithium-battery capacity data into several high-frequency and low-frequency components using the EEMD algorithm to reduce noise interference in the capacity data. Then, based on the characteristics of each component, the model builds prediction submodels based on the obtained high-frequency and low-frequency sequences using the GRU and MLR networks, respectively. Finally, the predicted values of each submodel are superimposed and fused to obtain the RUL of the battery based on the public data on lithium batteries provided by NASA and Oxford; furthermore, using different prediction starting points, the obtained results are compared with those of other single and combined models. The experimental results show that the EEMD-GRU-MLR prediction model can provide accurate RUL results, compared with LSTM, GRU, and EEMD-GRU prediction models, with the maximum mean absolute error decreased by 0.0311, 0.0234, and 0.0182, respectively, and the maximum root mean square error decreased by 0.0235, 0.0153, and 0.0098, respectively, This proves the satisfactory ability of the proposed EEMD-GRU-MLR model to predict the RUL of lithium batteries.
Keywords：lithium battery
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remaining useful life
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ensemble empirical mode decomposition
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gated recurrent unit network
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multiple linear regression
WU Minghu. Combined GRU-MLR method for predicting the remaining useful life of lithium batteries via multiscale decomposition[J]. Energy Storage Science and Technology, 2023, 12(7): 2220-2228
锂电池因其能量密度高、自放电率低、循环寿命长等优点被大量应用在电子产品、新能源汽车以及储能系统等众多领域，然而随着充放电循环周期的增加，锂电池会出现可用容量下降、内阻增大等性能退化现象，最终将会失效。在电池剩余使用寿命(remaining useful life，RUL)预测研究中通常将电池容量作为健康特征，用来定量描述电池健康状况的退化程度，使用电池容量作为表征电池性能的健康特征能够直观反映电池的退化情况[1]。通常认为当电池容量衰减至70%～80%时表示锂电池的使用寿命结束(end of life，EOL)[2]，如果在失效前无法及时更换电池，将会给设备运行带来巨大的安全风险，严重影响系统运行稳定性和可靠性[3]。因此，对锂电池的剩余使用寿命进行准确预测，提前获取电池状态的相关信息，在衰退到安全阈值之前及时更换，可以有效减少电池事故的发生。
与之相比，基于数据驱动的方法步骤较少、操作方便，具有较强的实用性[9]。基于数据驱动的方法无需了解电池内部复杂的反应机理，只需从外部特性的历史数据中挖掘性能退化的规律，就能精确地构建出RUL预测模型[10]。文献[11]提出一种基于差分电压和Elman神经网络的方法，通过分析电池差分电压曲线和充放电曲线，提取电池容量的退化特征作为健康特征，构建电池容量为输出的Elman神经网络，提高了锂电池RUL预测精度。文献[12]通过使用随机森林算法对电池容量数据分解出来的每个分量进行重要性排序，避免了波动分量里的噪音对模型预测能力的影响，且又保留了波动分量里的特征信息。对于锂电池性能退化过程中存在的容量再生问题，文献[13]提出了一种多尺度逻辑回归(logistic regression，LR)和高斯过程回归(gaussian process regression，GPR)相结合的预测方法，使用经验模态分解(empirical mode decomposition，EMD)将容量数据分解为整体退化、部分回升以及各种波动，从而削弱了容量再生现象对状态评估的影响。文献[14]采用EMD算法将容量数据分解为高频和低频两种分量，分别通过Elman和长短期记忆(long short term memory，LSTM)网络建模，并叠加预测结果得出RUL。但这种方法忽视了EMD本身的局限性，EMD在分解过程中会产生模态混叠现象，无法根据前期的容量退化趋势完成精确的性能评估，而集合经验模态分解(ensemble empirical mode decomposition，EEMD)算法克服了模态混叠现象，分解结果更为彻底、重构误差更小，在提升预测模型的精度方面具有突出的优势。文献[15-16]使用LSTM神经网络较好地预测出RUL结果，并且降低了预测误差，但是网络结构较复杂，参数量过多。文献[17]构建了基于变分模态分解(variational modal decomposition，VMD)与门控循环单元(gated recurrent unit，GRU)相结合的RUL预测模型，因为GRU所需参数更少，可在确保模型精度的同时，加快模型的收敛速度。
基于以上分析，本工作选择以锂电池容量数据作为健康特征，提出了一种基于EEMD多尺度分解下GRU与多元线性回归(multiple linear regression，MLR)组合的锂电池RUL预测方法。该方法首先采用EEMD算法将容量数据分解为高频分量和低频分量，然后分别使用GRU和MLR网络对所分解的退化数据进行趋势预测，再对各个预测结果进行叠加重构，这样既可以准确反映出电池退化的整体趋势，又能够捕捉到高频分量中隐藏的退化信息，提高了预测精度。最后选取NASA和Oxford提供的锂电池数据集作为研究对象来评估模型的性能，验证本模型的准确性和稳定性。实验结果表明，该预测模型能够克服锂电池在寿命预测过程中存在的剧烈波动，准确挖掘到锂电池容量变化过程的潜藏特征，具有性能稳定且精度更高等优点。
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