Elsevier

Journal of Energy Storage
能源存储杂志

Volume 72, Part C, 25 November 2023, 108494
第 72 卷，第 C 部分，2023 年 11 月 25 日，第 108494 号
Journal of Energy Storage

Research papers 研究论文
Health status prediction of lithium ion batteries based on zero-shot learning
基于零样本学习的锂离子电池健康状况预测

https://doi.org/10.1016/j.est.2023.108494Get rights and content 获取权利和内容

Highlights 高光

  • •
    We proposed an adaptive transfer learning method based on Zero-Shot learning for battery health status prediction.
    我们提出了一种基于零样本学习的自适应迁移学习方法，用于预测电池健康状态。
  • •
    A framework for multi-task transfer learning is developed for predicting battery SOH across diverse usage scenarios.
    一个用于预测电池 SOH 的多任务迁移学习框架在多种使用场景下得到开发。
  • •
    An adaptive optimization method is proposed to assign the optimal weight of the multi-task objective function.
    一种自适应优化方法被提出，用于分配多任务目标函数的最佳权重。

Abstract 摘要

In this paper, we propose an adaptive transfer learning method for predicting battery health status. We construct a multi-task transfer learning framework to address the problem of transferring battery health status predictions across different usage scenarios. To overcome the challenge of determining the optimal weight for different task loss functions, we introduce an adaptive optimization method that automatically assigns the optimal weight to the multi-task objective function. Our experiments on lithium-ion battery data from Huazhong University of Science and Technology show that our proposed method outperforms other typical prediction methods.
在这篇论文中，我们提出了一种自适应迁移学习方法，用于预测电池健康状态。我们构建了一个多任务迁移学习框架，以解决在不同使用场景下转移电池健康状态预测的问题。为了克服确定不同任务损失函数最优权重的挑战，我们引入了一种自适应优化方法，该方法自动将最优权重分配给多任务目标函数。我们在华中科技大学锂离子电池数据上的实验表明，我们提出的方法优于其他典型预测方法。

Keywords 关键词

Battery health status
Transfer learning
Multi-task
Domain adaptation

电池健康状态 转移学习 多任务 领域自适应

1. Introduction 1. 简介

Lithium-ion batteries have the advantages of low production cost, high energy density and long service life [1]. These batteries are widely used in automobiles, aerospace, daily electronic products, energy storage power stations, and other fields. However, lithium-ion batteries have a limited lifespan. As the number of charge and discharge cycles increases, the capacity and internal resistance of the batteries gradually decline. Eventually, the battery fails and can no longer meet usage requirements. In some cases, this may even cause safety accidents. Therefore, accurately predicting the health status of lithium-ion batteries is crucial for many applications.
锂离子电池具有生产成本低、能量密度高和寿命长的优点[1]。这些电池广泛应用于汽车、航空航天、日常电子产品、储能电站等领域。然而，锂离子电池的寿命有限。随着充放电循环次数的增加，电池的容量和内阻逐渐下降。最终，电池失效，无法满足使用要求。在某些情况下，甚至可能引发安全事故。因此，准确预测锂离子电池的健康状况对于许多应用至关重要。
Due to the complex nature of lithium-ion batteries, including their electrochemical systems, various failure modes, and manufacturing differences, degradation data can vary greatly even among batteries from the same batch [2]. This makes it difficult to accurately predict degradation trends using traditional mathematical models such as electrochemical models [3] or equivalent circuit models [4]. Data-driven models offer an alternative approach. These models do not require the establishment of a mathematical degradation model in advance. Instead, they extract relevant features directly from observation data (such as capacity and voltage) collected during the battery's charging and discharging process. The model then establishes an implicit regression relationship by correlating the battery's degradation process to predict its health status [5]. Common methods include support vector machines [6], Gaussian process regression [7], particle filters [[8], [9], [10], [11]], grey correlation analysis [12], backpropagation neural networks [13], gradient boosting regression trees [14], Bayesian networks [14], long short-term memory networks (LSTM) [15,16], and convolutional neural networks [17,18]. In addition to the methods mentioned earlier, other techniques such as wavelet decomposition [19], Wiener processes [20], empirical mode decomposition [15,21], and variational mode decomposition [22] can also be used to preprocess battery degradation data. This can improve the prediction accuracy of data-driven methods. While data-driven methods have strong learning and regression capabilities, their prediction accuracy can be affected by factors such as battery usage scenarios and manufacturing differences. These factors can cause large variations in degradation data, which can interfere with the ability of data-driven methods to learn the mapping rules of degraded data.
由于锂离子电池的复杂性质，包括其电化学系统、各种失效模式和制造差异，即使是同一批次的电池，退化数据也可能有很大差异[2]。这使得使用传统的数学模型，如电化学模型[3]或等效电路模型[4]来准确预测退化趋势变得困难。数据驱动模型提供了一种替代方法。这些模型不需要事先建立数学退化模型。相反，它们直接从电池充放电过程中的观测数据（如容量和电压）中提取相关特征。然后，模型通过将电池的退化过程与预测其健康状况相关联来建立隐式回归关系[5]。 常见方法包括支持向量机[6]、高斯过程回归[7]、粒子滤波[[8]，[9]，[10]，[11]]、灰色关联分析[12]、反向传播神经网络[13]、梯度提升回归树[14]、贝叶斯网络[14]、长短时记忆网络（LSTM）[15，16]和卷积神经网络[17，18]。除了上述方法外，还可以使用小波分解[19]、维纳过程[20]、经验模态分解[15，21]和变分模态分解[22]等技术对电池退化数据进行预处理。这可以提高数据驱动方法的预测精度。虽然数据驱动方法具有强大的学习和回归能力，但其预测精度可能会受到电池使用场景和制造差异等因素的影响。这些因素会导致退化数据出现较大波动，从而干扰数据驱动方法学习退化数据映射规则的能力。
To reduce the impact of variations in battery degradation data on the learning ability of data-driven methods, transfer learning techniques are increasingly being used in battery health status prediction research [[23], [24], [25]]. Deep networks [26] and recurrent neural networks [27] are commonly used. For example, long short-term memory networks (LSTM) [23,[28], [29], [30], [31], [32]], deep convolutional neural networks (DCNN) [24,33,34], and domain adaptive networks [35] are often used in combination with adaptive strategies for cross-domain prediction of battery health status. In cases where training samples are insufficient, techniques such as the square exponential covariance function and related penalty mechanisms can be introduced to control the cross-domain transfer of battery knowledge [36]. Transfer learning can improve the generalization ability of data-driven methods to variations in degradation data. However, due to differences in battery usage scenarios, the distribution of degradation data may vary significantly. The adaptive ability of typical transfer learning networks may be insufficient, leading to unstable prediction results. To apply transfer learning effectively, the source domain and the target domain need to have some commonality or connection. Otherwise, the transfer learning may have a negative impact. However, there is no definite and consistent way to evaluate the commonality or connection, or to select the suitable source domain and target domain.
为了减少电池退化数据变化对数据驱动方法学习能力的影响，电池健康状况预测研究中越来越多地使用迁移学习技术[[23]，[24]，[25]]。深度网络[26]和循环神经网络[27]被广泛使用。例如，长短期记忆网络（LSTM）[23]，[28]，[29]，[30]，[31]，[32]），深度卷积神经网络（DCNN）[24]，[33]，[34]和领域自适应网络[35]通常与自适应策略结合，用于跨域预测电池健康状况。在训练样本不足的情况下，可以引入平方指数协方差函数和相关惩罚机制来控制电池知识的跨域迁移[36]。迁移学习可以提高数据驱动方法对退化数据变化的泛化能力。然而，由于电池使用场景的不同，退化数据的分布可能差异很大。典型迁移学习网络的适应性可能不足，导致预测结果不稳定。 为了有效地应用迁移学习，源域和目标域需要有一些共同性或联系。否则，迁移学习可能会产生负面影响。然而，没有明确且一致的方法来评估共同性或联系，或者选择合适的源域和目标域。
Battery usage scenarios can vary greatly. For example, factors such as driving habits and load can cause significant variations in the degradation data of electric vehicle batteries, even among vehicles of the same model. This presents new challenges for predicting battery health status. To address this issue, we propose an adaptive multi-task and auto-optimization method for predicting the health of lithium-ion batteries based on the concept of transfer learning. Even when target domain data is not labeled, our method can maintain good prediction accuracy by using distributed source domain data. We tested our method using experimental data from lithium-ion batteries at Huazhong University of Science and Technology and found that it outperformed traditional data-driven methods. The term “zero-shot learning” refers to a situation where target domain samples are not labeled, while source domain samples are labeled. Additionally, the data distribution in the target domain is not consistent with that in the source domain.
电池使用场景可能差异很大。例如，驾驶习惯和负载等因素可能导致同型号电动汽车电池的退化数据出现显著差异。这为预测电池健康状况带来了新的挑战。为了解决这个问题，我们提出了一种基于迁移学习概念的适应性多任务和自动优化方法，用于预测锂离子电池的健康状况。即使目标域数据未标记，我们的方法也能通过使用分布式源域数据保持良好的预测精度。我们使用华中科技大学锂离子电池的实验数据测试了我们的方法，发现其优于传统的数据驱动方法。术语“零样本学习”指的是目标域样本未标记，而源域样本已标记的情况。此外，目标域中的数据分布与源域中的数据分布不一致。

2. Methodology 2. 研究方法

Variations in battery usage scenarios and manufacturing differences can easily lead to variations in battery degradation data. This presents a challenge for data-driven methods, which must deal with inconsistent data distributions in the target and source domains. This is known as a cross-domain training prediction problem. Traditional data-driven methods may have limited generalization ability when dealing with such problems, leading to significant fluctuations in prediction results. Our solution is to map the source and target domains to a common feature space and extract features from this space as input for prediction. This can help reduce variations in both domains.
电池使用场景和制造差异的变化可能导致电池退化数据的差异。这给数据驱动方法带来了挑战，这些方法必须处理目标域和源域中不一致的数据分布。这被称为跨域训练预测问题。在处理此类问题时，传统数据驱动方法可能具有有限的一般化能力，导致预测结果出现显著波动。我们的解决方案是将源域和目标域映射到公共特征空间，并从该空间提取特征作为预测的输入。这有助于减少两个域中的差异。

2.1. Predictive network framework
2.1. 预测网络框架

The proposed prediction network framework is shown in Fig. 1. It includes a convolutional module for feature extraction and two fully connected modules for predicting battery capacity and remaining useful life (RUL), respectively. The convolutional module uses three convolutional layers to extract features from each cycle. To make the distribution types of features extracted from the source and target domains as similar as possible, we use multiple kernel maximum mean discrepancy (MK-MMD) as the loss function during training. The first fully connected module consists of two fully connected layers and outputs the discharge capacity sequence of the battery in the source domain. The loss function for this module is the root mean square error. The second fully connected module consists of a single fully connected layer that outputs the RUL for the current training cycle. The loss function for this module is also the root mean square error.
图 1 展示了所提出的预测网络框架。它包括一个用于特征提取的卷积模块和两个分别用于预测电池容量和剩余使用寿命（RUL）的完全连接模块。卷积模块使用三个卷积层从每个周期中提取特征。为了使从源域和目标域提取的特征的分布类型尽可能相似，我们在训练过程中使用多个核最大均值差异（MK-MMD）作为损失函数。第一个完全连接模块由两个完全连接层组成，输出源域中电池的放电容量序列。该模块的损失函数是均方根误差。第二个完全连接模块由一个单独的完全连接层组成，输出当前训练周期的 RUL。该模块的损失函数也是均方根误差。
Fig. 1
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Fig. 1. The proposed predictive network framework.
图 1. 提出的预测网络框架。

2.2. Loss function 2.2. 损失函数

Transfer learning is a machine learning technique where a model trained on one task is reused or adapted to another related task. This approach is particularly useful when there is limited data available for the target task, or when the target task is similar to the original task. Transfer learning usually includes the following modules:
迁移学习是一种机器学习技术，其中在一个任务上训练的模型被重用或调整以应用于另一个相关任务。这种方法在目标任务数据有限或目标任务与原始任务相似时特别有用。迁移学习通常包括以下模块：
Feature extraction: The pre-trained model is used to extract relevant features from the input data, and these features are then used as input to a new model that is trained for the target task.
特征提取：使用预训练模型从输入数据中提取相关特征，然后将这些特征用作训练针对目标任务的新的模型的输入。
Domain adaptation: Domain adaptation is a principle that aims to enhance the performance of a machine learning model on a target domain by utilizing the knowledge from a source domain. The rationale for domain adaptation is that the data distribution of the target domain may vary from that of the source domain due to various factors, such as noise, bias, or temporal or spatial variations. This variation can impair the model's performance on the target domain. To tackle this problem, domain adaptation methods try to either minimize the difference between the source and target domains, or find a common representation that is robust to the domain change. There are different types of domain adaptation methods, depending on whether there are labeled or unlabeled data from the target domain. Supervised domain adaptation assumes that there are some labeled data from the target domain, but not enough to train a model from scratch. In this situation, the methods can either merge the source and target data to train a single model, or fine-tune a model trained on the source data using the target data. Unsupervised domain adaptation assumes that there are no labeled data from the target domain, only unlabeled data. In this situation, the methods can either use some measures to match the source and target data distributions, or learn a feature extractor that can map both domains to a shared space. Semi-supervised domain adaptation assumes that there are some labeled data and some unlabeled data from the target domain. In this situation, the methods can either use self-training or co-training techniques to label the unlabeled data and update the model, or use adversarial learning techniques to learn a domain discriminator and a feature extractor that can trick it.
领域自适应：领域自适应是一种旨在通过利用源领域的知识来提高机器学习模型在目标领域性能的原则。领域自适应的原理是，由于各种因素，如噪声、偏差或时间或空间变化，目标域的数据分布可能与源域的数据分布不同。这种差异可能会损害模型在目标域的性能。为了解决这个问题，领域自适应方法试图最小化源域和目标域之间的差异，或者找到一个对领域变化具有鲁棒性的共同表示。根据目标域是否有标记或未标记的数据，存在不同类型的领域自适应方法。监督领域自适应假设目标域有一些标记数据，但不足以从头开始训练模型。在这种情况下，方法可以是合并源域和目标域的数据来训练单个模型，或者使用目标数据微调在源数据上训练的模型。 无监督领域自适应假设目标域没有标记数据，只有未标记数据。在这种情况下，方法可以使用一些措施来匹配源数据和目标数据分布，或者学习一个可以将两个领域映射到共享空间的特征提取器。半监督领域自适应假设目标域有一些标记数据和一些未标记数据。在这种情况下，方法可以使用自训练或协同训练技术来标记未标记数据并更新模型，或者使用对抗学习技术来学习一个领域判别器和可以欺骗它的特征提取器。
Multi-task learning: The principle of multi-task learning involves training a single model to simultaneously perform multiple related tasks. The key idea is to exploit the shared information and relationships among tasks to improve overall performance. In multi-task learning, the model architecture typically consists of two main components: a shared feature representation and task-specific layers. The shared feature representation captures the common patterns and features across all tasks. It aims to learn a set of high-level representations that are beneficial for all tasks. The task-specific layers are responsible for mapping the shared representations to the specific outputs required by each task. During training, the model optimizes a joint objective function that combines the losses from all the tasks. This objective function balances the contributions of each task and guides the model to learn a shared representation that benefits all tasks simultaneously. By jointly optimizing the model across tasks, the model can leverage the relationships and dependencies among tasks to improve performance. The benefits of multi-task learning arise from several factors. First, by learning from multiple tasks simultaneously, the model can access a larger and more diverse training dataset, which can improve generalization and robustness. Second, the shared representation allows the model to capture common knowledge and patterns, leading to more efficient learning. Third, multi-task learning enables the transfer of information between tasks, where knowledge gained from one task can aid in learning another task.
多任务学习：多任务学习的原理涉及训练一个单一模型同时执行多个相关任务。关键思想是利用任务之间的共享信息和关系来提高整体性能。在多任务学习中，模型架构通常由两个主要组件组成：共享特征表示和特定任务层。共享特征表示捕捉所有任务中的共同模式和特征。它旨在学习一组对所有任务都有益的高级表示。特定任务层负责将共享表示映射到每个任务所需的特定输出。在训练过程中，模型优化一个联合目标函数，该函数结合了所有任务的损失。此目标函数平衡每个任务的贡献，并指导模型学习一个对所有任务都有益的共享表示。通过跨任务联合优化模型，模型可以利用任务之间的关系和依赖来提高性能。多任务学习的优势源于几个因素。 首先，通过同时学习多个任务，模型可以访问更大、更多样化的训练数据集，从而提高泛化能力和鲁棒性。其次，共享表示允许模型捕捉共同知识和模式，导致更有效的学习。第三，多任务学习使得任务之间能够转移信息，其中一个任务中获得的知识可以帮助学习另一个任务。
Each module generally requires an objective function for optimization. The optimization function proposed in this paper is as follows:
每个模块通常需要一个目标函数进行优化。本文提出的优化函数如下：
  • (1)
    Domain adaptation 领域自适应
Due to differences in battery usage scenarios, the distribution of features in the source and target domains can often vary. To measure the difference between these distributions, we use multiple kernel maximum mean discrepancy (MK-MMD).
由于电池使用场景的不同，源域和目标域中功能的分布往往会有所差异。为了衡量这些分布之间的差异，我们使用多核最大均值差异（MK-MMD）。
Let PXS and PXT represent the marginal distributions of the features in the source and target domains, respectively. The maximum mean discrepancy (MMD) is defined as:
设 PXS 和 PXT 分别代表源域和目标域中特征的边缘分布。最大均值差异（MMD）定义为：(1)DPXSPXT=EPXS∅XS−EPXT∅XTH2where EPXS and EPXT are the expected operation of the edge distribution of XS and XT, respectively. ∙H2 denotes represents the 2-norm operation of the reproducing kernel Hilbert space (RKHS). ∅ is the mapping function for the source domain and target domain feature matrices to RKHS.
EPXS 和 EPXT 分别表示 XS 和 XT 的边缘分布的预期操作。 ∙H2 表示再生核希尔伯特空间（RKHS）的 2-范数操作。 ∅ 是将源域和目标域特征矩阵映射到 RKHS 的映射函数。
Due to the complexity of calculating the mean value of all features in the source and target domains, we approximate Eq. (1) using the mean values of samples in the source and target domains.
由于计算源域和目标域所有特征均值复杂，我们使用源域和目标域样本的均值来近似公式（1）。(2)DPXSPXT≈1nS∑i=1nS∅xSi−1nT∑i=1nT∅xTiH2
The inner product of mapping function ∅ is expressed by kernel function, and Eq. (2) can be expressed as.
映射函数 ∅ 的内积由核函数表示，式(2)可以表示为。(3)DPXSPXT≈1nS2∑i=1nS∑j=1nSkxSixSj−2nSnT∑i=1nS∑j=1nTkxSixTj+1nT2∑i=1nT∑j=1nTkxTixTj=trKS,SKS,TKT,SKT,TMwhere 哪里Mi,j=1nSnS,xi,xj∈DS1nTnT,xi,xj∈DT−1nSnT,otherwise
K is the kernel matrix computed by the Gaussian kernel. kxixi is the Gaussian kernel mapping of each sample.
K 是通过高斯核计算得到的核矩阵。 kxixi 是每个样本的高斯核映射。
  • (2)
    Prediction losses 预测损失
In this paper, we use the root mean square error (MSE) as the loss function for prediction results. This includes the loss for battery discharge capacity (as shown in Eq. (4)) and the loss for remaining useful life (as shown in Eq. (5)).
在这篇论文中，我们使用均方根误差（MSE）作为预测结果的损失函数。这包括电池放电容量损失（如图（4）所示）和剩余使用寿命损失（如图（5）所示）。(4)LC=1M∑i=1MyCi−ŷCi2(5)LRUL=1N∑i=1NyRULi−ŷRULi2

2.3. Multi-task objective function weight adaptive optimization
2.3. 多任务目标函数权重自适应优化

In multi-task learning, model training typically involves weighting multiple loss functions to obtain an overall loss. However, accurately quantifying the magnitude of the loss function used by different tasks and the importance of each task can be difficult. Many existing studies choose an optimal value through trial and error, which can be time-consuming. Others use industry-wide parameters, but whether these are optimal remains to be proven. One potential solution is to automatically adjust the weight of each loss function to improve training efficiency and potentially optimize model performance.
在多任务学习中，模型训练通常涉及对多个损失函数进行加权以获得总体损失。然而，准确量化不同任务所使用的损失函数的幅度以及每个任务的重要性可能很困难。许多现有研究通过试错选择最优值，这可能很耗时。其他人使用行业参数，但这些是否最优尚待证明。一个潜在的解决方案是自动调整每个损失函数的权重，以提高训练效率并可能优化模型性能。
Assuming that the multi-task loss function is represented by Li and the corresponding weight is represented by ωi, the overall loss function can be expressed as:
假设多任务损失函数由 Li 表示，相应的权重由 ωi 表示，整体损失函数可以表示为：(6)LMTL=∑iωi∙Li
Battery health status prediction belongs to regression task. Any task can be defined as
电池健康状态预测属于回归任务。任何任务都可以定义为(7)pyfWx=NfWxσ2where fWx is the network prediction value. The above equation represents a multivariate Gaussian distribution with y as the mean vector and σ2 as the variance.
fWx 是网络预测值。上述方程表示一个以 y 为均值向量、 σ2 为方差的多元高斯分布。
The logarithmic likelihood of the above equation is
对上述方程的对数似然为(8)logpyfWx=logNfWxσ2=log12πσe−y−fWx22σ2∝12σ2y−fWx2+logσ
Define the regression loss as LW=y−fWx2. According to the above equation, the loss function of the overall training task can be expressed as.
定义回归损失为 LW=y−fWx2 。根据上述方程，整体训练任务的损失函数可以表示为。(9)LWσ1⋯σK=∑k=1K12σk2LkW+logσk
The goal of the training is to minimize this maximum likelihood estimate. As σ increases, the corresponding weight will decrease. Conversely, as σ decreases, the corresponding weight will increase.
训练的目标是使最大似然估计最小化。当 σ 增加时，相应的权重将减少。相反，当 σ 减少时，相应的权重将增加。

3. Experimental verification
3. 实验验证

3.1. Experimental data description
3.1. 实验数据描述

The experimental data used in this study comes from Huazhong University of Science and Technology [37]. It consists of life cycle data for 77 LFP/graphite A123 APR18650M1A cells. These batteries have a nominal capacity of 1.1 Ah and a standard voltage of 3.3 V. All cells were charged and discharged at a constant temperature of 30 °C. While all batteries used the same fast charging scheme, each battery had a different discharge protocol.
本研究中使用的实验数据来自华中科技大学[37]。它包括 77 个 LFP/石墨 A123 APR18650M1A 电池的寿命周期数据。这些电池的标称容量为 1.1 Ah，标准电压为 3.3 V。所有电池均在 30°C 的恒定温度下充电和放电。虽然所有电池都使用了相同的快速充电方案，但每个电池的放电协议不同。
  • (1)
    Charging scheme: 5C constant current (CC) charging is adopted from 0 % to 80 % state of charge (SOC). 1C constant current charging is adopted from 80 % SOC to 3.6 V. Then constant–voltage (CV) charge until 100 % SOC with a current cutoff of C/20.
    充电方案：从 0%至 80%充电状态（SOC）采用 5C 恒定电流（CC）充电。从 80% SOC 至 3.6 V 采用 1C 恒定电流充电。然后以 C/20 电流截止值进行恒定电压（CV）充电，直至 100% SOC。
  • (2)
    The discharge scheme consists of four stages. Stage 1 is from 100 % to 60%SOC. Stage 2 is from 60 % to 40%SOC. Stage 3 is from 40 % to 20%SOC. Stage 4 is from 20 % to 0 % SOC, which is discharged by 1C CC with a cut-off voltage of 2 V. The specific discharge scheme of each battery is shown in Table 1. NO. Represents the number of the battery, Life represents the battery life, and the unit is cycle. S1-S4 represents the four stages of discharge. For example, the 4 stages of No. 1 battery respectively adopt 5C-1C-1C-1C CC discharge.
    放电方案分为四个阶段。第一阶段从 100%到 60%SOC。第二阶段从 60%到 40%SOC。第三阶段从 40%到 20%SOC。第四阶段从 20%到 0%SOC，由 1C CC 以 2V 的截止电压放电。每个电池的具体放电方案如表 1 所示。NO.代表电池编号，Life 代表电池寿命，单位为循环。S1-S4 代表放电的四个阶段。例如，No.1 电池的 4 个阶段分别采用 5C-1C-1C-1C CC 放电。

    Table 1. Battery discharge scheme.
    表 1. 电池放电方案。

    No. 没有。Life 生命S1S2S3S4No. 没有。Life 生命S1S2S3S4
    115045C1C1C1C4019084C4C2C1C
    226785C1C2C1C4118044C4C3C1C
    318585C1C3C1C4217174C4C4C1C
    415005C1C4C1C4321784C4C5C1C
    519715C1C5C1C4424684C5C1C1C
    611435C2C1C1C4524504C5C3C1C
    716785C2C2C1C4616904C5C4C1C
    822855C2C3C1C4720304C5C5C1C
    926515C2C5C1C4812953C1C1C1C
    1017515C3C1C1C4913933C1C2C1C
    1114995C3C2C1C5018753C1C3C1C
    1213865C3C3C1C5114193C1C4C1C
    1315725C3C4C1C5216853C1C5C1C
    1422025C3C5C1C5319383C2C1C1C
    1514815C4C1C1C5413083C2C2C1C
    1619385C4C2C1C5520413C2C3C1C
    1722835C4C3C1C5622903C2C4C1C
    1816495C4C4C1C5718853C2C5C1C
    1917665C4C5C1C5813483C3C1C1C
    2026575C5C1C1C5923653C3C2C1C
    2124915C5C2C1C6020473C3C3C1C
    2224795C5C3C1C6116793C3C4C1C
    2323425C5C4C1C6220573C3C5C1C
    2422175C5C5C1C6321433C4C1C1C
    2517824C1C1C1C6419053C4C2C1C
    2611424C1C2C1C6519753C4C3C1C
    2714914C1C3C1C6621683C4C4C1C
    2815614C1C4C1C6717423C4C5C1C
    2913804C1C5C1C6820123C5C1C1C
    3022164C2C1C1C6923083C5C2C1C
    3117064C2C2C1C7017023C5C3C1C
    3225074C2C3C1C7116973C5C4C1C
    3319264C2C4C1C7218483C5C5C1C
    3426894C2C5C1C7318112C4C1C1C
    3519624C3C1C1C7420302C5C2C1C
    3615834C3C2C1C7522852C3C3C1C
    3724604C3C3C1C7617832C2C4C1C
    3814484C3C4C1C7714002C1C5C1C
    3916094C4C1C1C
Table 1 shows a total of 77 discharge protocols. During the battery life cycle experiment, voltage, current, and capacity data were collected until the maximum capacity of the battery reached 80 % of its nominal capacity (the failure threshold).
表 1 显示了总共 77 个放电协议。在电池寿命周期实验中，收集了电压、电流和容量数据，直到电池的最大容量达到标称容量的 80%（失效阈值）。

3.2. Data processing 3.2. 数据处理

In this study, we selected two data types - charging voltage and capacity - as training samples for our proposed network. To reduce the amount of training data, we selected data from 80 % state of charge (SOC) to the first 3.6 V as our sample sequence. Each cycle sample was uniformly interpolated to a fixed length of 100 points to standardize the data length. We used a sliding window technique to take 30 consecutive cycles of data as a single sample. To reduce the amount of computation, we sampled one cycle every three cycles, resulting in a total of 10 cycles of data being sampled. This means that the shape of each sample is 2 × 100 × 10 (i.e., 2 features, 100 sampling points, and 10 cycles). The discharge capacity of the 10 cycles and the remaining useful life (RUL) of the last cycle in the sequence were used as labels.
在此研究中，我们选择了两种数据类型——充电电压和容量——作为我们提出网络的训练样本。为了减少训练数据量，我们选择了从 80%的充电状态（SOC）到第一个 3.6V 的数据作为样本序列。每个循环样本被均匀插值到 100 个固定点以标准化数据长度。我们使用滑动窗口技术将 30 个连续循环的数据作为一个样本。为了减少计算量，我们每三个循环采样一个循环，从而总共采样了 10 个循环的数据。这意味着每个样本的形状为 2×100×10（即 2 个特征，100 个采样点，和 10 个循环）。使用 10 个循环的放电容量和序列中最后一个循环的剩余使用寿命（RUL）作为标签。
We randomly selected 55 cells from the 77 available cells to use as training data and used the remaining 22 cells as test data. In this study, the test data consisted of cells #1, #2, #4, #9, #10, #12, #13, #15, #18, #19, #20, #23, #24, #36, #39, #44, #57, #65, #66, #71, #73 and #75. The remaining 55 cells were used as training data.
我们从 77 个可用的细胞中随机选择了 55 个作为训练数据，剩余的 22 个细胞作为测试数据。在本研究中，测试数据包括细胞编号#1、#2、#4、#9、#10、#12、#13、#15、#18、#19、#20、#23、#24、#36、#39、#44、#57、#65、#66、#71、#73 和#75。其余 55 个细胞用作训练数据。
To illustrate the impact of discharge protocols on battery health status, we plotted curves showing the discharge protocol, capacity change, and capacity degradation distribution for cells 1, 2, 29, and 68 (as shown in Fig. 2). These curves show that different discharge protocols result in different degradation trends for battery capacity and corresponding differences in distribution curves. This indicates that the usage scenario of a battery has a significant impact on its health status.
为了说明放电协议对电池健康状况的影响，我们绘制了显示放电协议、容量变化和容量退化分布曲线的图表，涉及 1 号、2 号、29 号和 68 号电池（如图 2 所示）。这些曲线表明，不同的放电协议会导致电池容量退化趋势不同，以及分布曲线的相应差异。这表明电池的使用场景对其健康状况有重大影响。
Fig. 2
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Fig. 2. Discharge scheme and capacity distribution.
图 2. 排放方案和容量分布。

3.3. Network configuration
3.3. 网络配置

The proposed network framework and related parameter settings are shown in Table 2. The discharge capacity and remaining useful life (RUL) of cells in the source domain are used as corresponding labels. Labeled source domain data and unlabeled target domain data are input into the network for training. First, the feature extraction module is trained using the MK-MMD loss function. The goal is to extract features from the source and target domains that are as close as possible to a common distribution space. Then, the capacity prediction module and RUL prediction module are trained using the extracted source domain features.
建议的网络框架和相关参数设置显示在表 2 中。源域中电池的放电容量和剩余使用寿命（RUL）用作相应的标签。标记的源域数据和未标记的目标域数据被输入到网络中进行训练。首先，使用 MK-MMD 损失函数训练特征提取模块。目标是提取源域和目标域的特征，使其尽可能接近一个公共分布空间。然后，使用提取的源域特征训练容量预测模块和 RUL 预测模块。

Table 2. The proposed network and parameter configuration.
表 2. 建议的网络和参数配置。

Module 模块Layer 层Parameter configuration 参数配置Shape 形状
Input 输入––(2,1000)
Feature extraction 特征提取Conv1d 卷 1din_channels = 2, out_channels = 8, kernel_size = 400
in_channels = 2, out_channels = 8, kernel_size = 400		(8, 601)
LeakyReLU 漏激活函数–(8, 601)
Conv1d 卷 1din_channels = 8, out_channels = 16, kernel_size = 400
in_channels = 8, out_channels = 16, kernel_size = 400		(16, 202)
Dropout 弃用p = 0.3(16, 202)
LeakyReLU 漏激活函数–(16, 202)
Conv1d 卷 1din_channels = 16, out_channels = 32, kernel_size = 202
in_channels = 16, out_channels = 32, kernel_size = 202		(32,1)
ReLU–(32, 1)
Capacity prediction 容量预测Flatten 展平–32
Linear 线性in_features = 32, out_features = 64
in_features = 32, out_features = 64		64
ReLU–64
Linear 线性in_features = 64, out_features = 10
in_features = 64, out_features = 10		10
RUL prediction RUL 预测Linear 线性in_features = 10, out_features = 1
in_features = 10, out_features = 1		1

3.4. Evaluation index 3.4. 评估指标

In this study, we used three evaluation metrics to assess the prediction results: root mean square error (RMSE), coefficient of determination (R2), and symmetric mean absolute percentage error (SMAPE). Suppose ŷi represents the predicted value, yirepresents the actual value, and y¯ denotes the average of the actual sample. The specific formulas for calculating each metric are as follows:
在此研究中，我们使用了三个评估指标来评估预测结果：均方根误差（RMSE）、确定系数（ R2 ）和对称平均绝对百分比误差（SMAPE）。假设 ŷi 代表预测值， yi 代表实际值， y¯ 表示实际样本的平均值。计算每个指标的具体公式如下：
  • (1)
    Root mean square error. 均方根误差。
(10)RMSE=1n∑i=1nyi−ŷi2
The result range is [0,+∞]. When the predicted value is exactly consistent with the real value, it is equal to 0, that is, the model is perfect. The larger the error, the larger the value.
结果范围是[0,+∞]。当预测值与真实值完全一致时，它等于 0，即模型是完美的。误差越大，值就越大。
  • (2)
    Coefficient of determination
    决定系数
(11)R2=∑i=1nŷi−y¯2∑i=1nyi−y¯2
The higher the coefficient of determination is, the closer it is to 1, indicating that the prediction effect of the model is better.
系数决定性越高，越接近 1，表示模型的预测效果越好。
  • (3)
    Symmetric mean absolute percentage error
    对称平均绝对百分比误差
(12)SMAPE=100%n∑i=1nŷi−yiŷi+yi/2
When the predicted value is exactly consistent with the real value, it is equal to 0, that is, the model is perfect. The larger the error, the larger the value.
当预测值与真实值完全一致时，它等于 0，即模型是完美的。误差越大，值就越大。

3.5. Prediction result 3.5. 预测结果

The charging data from 22 test cells were used as target domains and input into the proposed network for training and prediction. Fig. 3 shows the predicted results. For clarity, the graph displays the value of one cycle every 30 cycles. Even when the target domain is not labeled, the proposed method can accurately reflect the degradation trend of battery discharge capacity. The RUL prediction results follow a linear degradation law and become more accurate as the number of cycles increases.
从 22 个测试单元的充电数据被用作目标域并输入到所提出的网络中进行训练和预测。图 3 显示了预测结果。为了清晰起见，图表每 30 个周期显示一个周期的值。即使目标域未标记，所提出的方法也能准确反映电池放电容量的退化趋势。RUL 预测结果遵循线性退化规律，并且随着循环次数的增加而变得更加准确。
Fig. 3
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Fig. 3. Prediction results of capacity and RUL.
图 3. 容量和 RUL 预测结果。

To demonstrate the effectiveness of the proposed method, it was compared with several commonly used methods. The specific comparison metrics are presented in Table 3.
为了展示所提方法的有效性，它被与几种常用方法进行了比较。具体的比较指标见表 3。

Table 3. Comparison between the common methods and the proposed method.
表 3. 常规方法与所提方法的比较。

Methods 方法Capacity (mAh) 容量（mAh）RUL (cycles) RUL（循环）
RMSER2SMAPE(%)RMSER2SMAPE(%)
LSTM [38]48.620.633.86322.530.6162.31
DCNN [34]41.320.723.21292.640.6567.87
Adversarial Transfer [35]
对抗迁移 [35]		27.160.882.56288.280.6969.93
Our method 我们的方法14.670.961.16255.220.7578.32
Each task with the same weight
每个具有相同权重的任务		22.230.921.76270.340.7272.21
The bold font indicates the optimal value for the column.
粗体字表示该列的最佳值。
We compared the proposed method with three commonly used methods: LSTM, DCNN, and adversarial transfer learning. As shown in Table 3, the proposed method outperforms the others. LSTM and DCNN lack a transfer learning module, limiting their effectiveness for batteries with dispersed degradation data. The adaptive transfer learning method is effective when the source domain data has the same feature distribution. However, in this experiment, the battery discharge data in the source domain is dispersed and the domain discriminator could not distinguish between source and target domain data, resulting in suboptimal prediction performance.
我们比较了所提出的方法与三种常用方法：LSTM、DCNN 和对抗性迁移学习。如表 3 所示，所提出的方法优于其他方法。LSTM 和 DCNN 缺乏迁移学习模块，限制了它们在具有分散退化数据的电池上的有效性。当源域数据具有相同特征分布时，自适应迁移学习方法有效。然而，在本实验中，源域的电池放电数据分散，域判别器无法区分源域和目标域数据，导致预测性能次优。
The multi-task loss function weight adaptive optimization method proposed in this work also contributes to the effectiveness of the proposed method. To demonstrate its efficacy, the weights of the three loss functions were set to 1 and a prediction experiment was conducted. The results, shown in the last row of Table 3, indicate that using the same weight for all functions is not optimal. Since the cell degradation data in the target domain is dispersed, the weights of the three loss functions for each test cell vary. Fig. 4 shows the weight coefficients of the loss functions for all 22 test cells.
该工作中提出的多任务损失函数权重自适应优化方法也有助于提高所提方法的有效性。为了证明其有效性，将三个损失函数的权重均设为 1，并进行了预测实验。结果如表 3 最后一行所示，表明对所有函数使用相同的权重并非最佳。由于目标域中的细胞退化数据分散，每个测试单元的三个损失函数的权重各不相同。图 4 显示了所有 22 个测试单元的损失函数权重系数。
Fig. 4
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Fig. 4. Weight coefficients of the loss function.
图 4. 损失函数的权重系数。

Where λ1 represents the weight of the discharge capacity prediction loss, λ2 represents the weight of the RUL prediction loss, and λ3 represents the weight of the MK-MMD loss between the source and target domains. Different cells have different optimal weight coefficients, indicating that using the same weight for all tasks does not produce optimal prediction results.
λ1 代表放电容量预测损失权重， λ2 代表 RUL 预测损失权重， λ3 代表源域和目标域之间 MK-MMD 损失的权重。不同单元格有不同的最优权重系数，表明对所有任务使用相同的权重不会产生最优预测结果。

4. Conclusion 4. 结论

This work proposes an adaptive transfer learning and prediction method for cross-domain health status prediction of lithium-ion batteries under different usage scenarios. When the target domain is not labeled, we established a training network with a self-supervision function. The network comprises three modules: feature extraction, discharge capacity prediction, and Remaining Useful Life (RUL) prediction, corresponding to three training tasks. To achieve the best prediction results, we proposed an automatic weight optimization method for multi-task training. The optimal weight is automatically assigned based on the dispersion of test and training data to improve prediction accuracy. To demonstrate the effectiveness of the proposed method, we compared it with several typical battery health status prediction methods using experimental data from Huazhong University of Science and Technology. The results show that the proposed method is superior. It should be noted that this work only studied transfer prediction when the source domain has labels and the target domain does not. If the target domain has partially labeled data, the model trained in this work can be fine-tuned for potentially more accurate predictions. Fine-tuning of deep learning models has been extensively researched and will not be discussed further in this work.
这项工作提出了一种针对不同使用场景下锂离子电池跨域健康状况预测的自适应迁移学习和预测方法。当目标域未标记时，我们建立了一个具有自监督功能的训练网络。该网络包括三个模块：特征提取、放电容量预测和剩余使用寿命（RUL）预测，对应三个训练任务。为了实现最佳的预测结果，我们提出了一种多任务训练的自动权重优化方法。最优权重根据测试和训练数据的分散性自动分配，以提高预测精度。为了证明所提出方法的有效性，我们使用华中科技大学提供的实验数据，将其与几种典型的电池健康状况预测方法进行了比较。结果表明，所提出的方法更优。需要注意的是，这项工作仅研究了当源域有标签而目标域没有标签时的迁移预测。 如果目标域有部分标记数据，本工作中训练的模型可以进行微调以实现更准确的预测。深度学习模型的微调已经得到了广泛研究，本工作中将不再进一步讨论。

Declaration of competing interest
声明利益冲突

The authors declared that they have no conflicts of interest to this work.
作者声明他们与这项工作无利益冲突。

Acknowledgements 致谢

This work was supported in part by the Suzhou Science and Technology Foundation of China under Grant SYG202021, Jiangsu Provincial Natural Science Research Foundation of China under Grant 21KJA510003, Jiangsu Key Laboratory for Elevator Intelligent Safety under Grant JSKLESS202101.
这项工作部分得到了中国苏州科学技术基金会的支持，项目编号 SYG202021，江苏省自然科学研究基金会支持，项目编号 21KJA510003，以及江苏省电梯智能安全重点实验室支持，项目编号 JSKLESS202101。

Data availability 数据可用性

Data will be made available on request.
数据将在请求后提供。

References 参考文献

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