Prediction models based on AR only need battery degradation data and can predict the RUL of the battery. The method is simple and easy to be realized. However, vehicle lithium-ion batteries are influenced by many factors, including temperature, discharge current, and so on, which has led to a decline in accuracy. The neural network is often adopted to estimate the nonlinear degradation process due to its superior nonlinear approximation ability. The lithium battery degradation process is a strongly nonlinear process, so neural networks can be a good fit in this process. Min [

16] used a neural network to fit the relationship between open voltage, resistance, and discharge capacity at different depths of discharge (DOD). Min [

16] also proposed a fast battery capacity prediction method to assess the feasibility application of an artificial neural network in the lithium-ion battery discharge mass rapid prediction. However, the degradation process of lithium batteries is dynamic. In order to reflect the dynamic characteristics of the system, the dynamic recurrent neural network (El-man network) is optimal for describing the system. Wu [

17] proposed a method based on a modified Elman neural network to predict the lithium-ion battery remaining capacity and analyzed the relationship among the varying characteristics, internal resistance, and open-circuit voltage. It can be concluded that the network is not only a local generalization but also equipped with better dynamic performance and approximation capability. The network can effectively reduce the total prediction error. Given that the working state of the battery might change with the change course, Liu

et al. [

18] adopted an adaptive recurrent neural network aimed at using lithium battery impedance spectroscopy data to predict the RUL of lithium batteries. The method can be satisfied with the forecast results. However, compared with the SVM, the neural network requires a large amount of training data and is prone to fall into a local minimum. Therefore, many scholars use the SVM to estimate the RUL. Wang [

19] devised an iterative multi-step linear prognostics model based on the SVM. It used the energy efficiency and working temperature as input parameters and estimated the RUL of lithium-ion batteries at room temperature. Dong

et al. [

20] mathematically modeled the relationship among the battery cycle times, the capacity, and the internal resistance. They combined the SVM with the particle filter (PF) to achieve a parameter estimation and predict the RUL. Klass

et al. [

21] used several groups of battery degradation data at constant temperature to construct the vehicle battery degradation model based on the SVM and estimate the battery state of health (SOH). Nuhic

et al. [

22] used the SVM to study the battery capacity degradation to estimate the RUL. The SVM is a linear learning machine in high dimensional feature space. Compared with the linear model, it not only increases the complexity of computation, but also avoids the curse of dimensionality to a certain extent. However, the SVM has to choose the appropriate kernel function and only provides the point estimate values of the RUL. It is hard to reflect the uncertainty of estimation. RVM based on the Bayesian framework reduces the computation of the kernel function [

23]. The number of the association vectors of RVM is less than SVM, which has better generalization performance and can acquire point estimation and interval estimation. Zhang

et al. [

24] introduced the advantages of RVM and regarded it as one of the main potential methods for lithium-ion battery RUL estimation. Hu

et al. [

25] presented a sparse Bayesian learning method for Li-ion battery capacity estimation and trained an RVM regression model. The performance of the method is verified by 10 years of data. Xing

et al. [

26] proposed a naive Bayes (NB) model for the RUL prediction of batteries under different operating conditions. The results show that prediction performance surpasses that of SVM. Wang

et al. [

27] obtained the relevance vectors from the degradation of battery capacity and the number of cycles. The method is based on the RVM and uses the experiment data of multiple constant current discharge under constant temperature and constant load. They constructed an empirical degradation model using three parameters to estimate RUL, but their models lack the ability of dynamic updating. Therefore, Liu

et al. [

28] proposed an enhanced optimized RVM algorithm, which improved the ability of dynamic model updating and improved the prognostics accuracy of the lithium-ion battery RUL with the same data. Widodo

et al. [

29] predicted the RUL of the battery using the RVM algorithm and found that the long-term prediction performance is poor and not suitable for direct RUL prediction. In order to solve this problem, Zhou

et al. [

30] presented a novel dynamic gray RVM algorithm to achieve a lithium-ion battery RUL prediction. The result indicates that the multi-step prediction precision with fewer sample sizes could be improved. At the same time, in order to reduce the influence of noise on the prediction, Miao

et al. [

31] put forward a fault detection system based on a wavelet transform and hidden Markov model (HMM) modulus maximum distribution. This algorithm was validated by experimental data sets that achieved the classification of the two device statuses (normal and failure). However, the model cannot be directly used to predict the RUL and has certain limitations. Thus, Yuan

et al. [

32] proposed a training algorithm (Baum-Welch algorithm) based on an improved particle swarm optimization (MPSO)-amended hidden semi-Markov model (HSMM) to produce the RUL reliability function and the system failure rate, and finally acquire the RUL distribution of the equipment. Given that RUL prediction accuracy of the training algorithm is not high and applicability is not perfect, Zhang

et al. [

33] reduced noises in characteristic signals using wavelet decomposition and estimated the battery RUL, which was based on NASA’s lithium-ion battery data and used the RVM degradation model. The prediction methods based on RVM are the main methods for lithium-ion battery RUL estimation. However, the training time increases rapidly with the increase of the training sample. Other methods are also used in the parameter identification of the model. Tseng

et al. [

34] constructed three kinds of regression models based on the statistical data (N order polynomial regression model [

35], bivariate polynomial regression model, and the index regression model), and introduced the particle swarm optimization (PSO) algorithm to optimize the model parameters. Simulations indicate that the regression models using discharged voltage and internal resistance as aging parameters can more accurately build a state of health profile than those using cycle numbers. He

et al. [

36] proposed a double-index lithium battery degradation model and used the Dempster–Shafer theory (DST) to initialize the model parameters and the Bayesian Monte Carlo (BMC) method to update the model parameters, which are used to predict the battery RUL. Hu

et al. [

37] put forward a nonlinear kernel regression model of lithium battery degradation, obtained degradation parameters through the K-nearest neighbor, and used PSO to optimize the weight of the K-nearest neighbor regression model. Chen

et al. [

38] developed a quantitative approach for the battery RUL prediction based on an adaptive bathtub-shaped function and used the artificial fish swarm algorithm method to optimize the parameter model. This prognostic model can capture the dynamic behaviors of the battery capacity.