The remaining useful life (RUL) prognostic of lithium-ion batteries (LIBs) is important in the reliability of electric vehicles. The degradation state of LIBs is related to the current moment and historical data, which is a non-Markovian process with long-term dependence. This manuscript proposes a RUL prognostic approach based on a non-Markovian process, which uses a fractional Brownian motion (FBM) model. Firstly, a nonlinear FBM model is established to describe the battery non-Markovian capacity fading process. The drift parameter of the FBM model and degradation states are updated by an online Kalman filter when a new measurement value arrives. Then the maximum likelihood estimation approach is introduced to obtain the other undecided fixed parameters. This approach is based on off-line battery degradation historical data. According to the first hitting time, the probability distribution function is derived to quantify the uncertainty of the RUL prognostic results. Finally, two datasets are used to verify the effectiveness of the proposed method. For the NASA dataset battery #5, the relative errors of the RUL prediction results of the proposed method are 2.941 and 2.083 when the starting points of the predictions are 60 cycles and 80 cycles, respectively. Thus, the proposed method is superior to other methods.

锂离子电池 (LIB) 的剩余使用寿命 (RUL) 预测对于电动汽车的可靠性非常重要。锂离子电池的退化状态与当前时刻和历史数据有关，是一个具有长期依赖性的非马尔可夫过程。本手稿提出了一种基于非马尔可夫过程的 RUL 预测方法，该过程使用分数布朗运动 (FBM) 模型。首先，建立非线性FBM模型来描述电池的非马尔可夫容量衰减过程。当新的测量值到达时，FBM 模型的漂移参数和退化状态由在线卡尔曼滤波器更新。然后引入最大似然估计方法来获得其他未定的固定参数。该方法基于离线电池退化历史数据。根据首次命中时间推导概率分布函数，量化RUL预测结果的不确定性。最后，使用两个数据集验证所提方法的有效性。对于 NASA 数据集电池 #5，当预测起点为 60 个循环和 80 个循环时，所提出方法的 RUL 预测结果的相对误差分别为 2.941 和 2.083。因此，所提出的方法优于其他方法。083 当预测的起点分别为 60 个周期和 80 个周期时。因此，所提出的方法优于其他方法。083 当预测的起点分别为 60 个周期和 80 个周期时。因此，所提出的方法优于其他方法。