## 2 Remaining Useful Life (RUL) Prognostics Methodologies
### RUL Prognostics Methodologies Based on Artificial Intelligence
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methodology** & **Advantages** & **Disadvantages** & **Main Relevant References** \\ \hline \multirow{4}{*}{\begin{tabular}{c} Artificial \\ intelligence \\ \end{tabular} } & (a) Does not need a data model & & \\  & (b) The algorithms are simple & (a) The point estimated value of RUL & \\  & and feasible & (b) Does not describe the uncertainty & [12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 26; 27; 28; 29; 30; 31; 32; 33] \\  & (c) The algorithms are the best & of measurement results & \\  & solution for non-linear systems & & \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} Filtering \\ techniques \\ \end{tabular} } & (a) Can be used in any form of & (a) Needs data mode & \\  & state-space model & (state-space model) & [34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45] \\  & Gaussian, and non-Gaussian systems & (b) The point estimated value of RUL & \\ \hline \multirow{4}{*}{
\begin{tabular}{c} Stochastic \\ process \\ \end{tabular} } & (a) Considers the time-dependence of & & \\  & the degradation process & (a) Higher calculation complexity & [46; 47; 48; 49] \\ \cline{1-1}  & (b) Describes the uncertainty of & (b) Considers uncertain factors & [46; 48; 49] \\ \cline{1-1}  & predictable results & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of RUL prognostics of vehicle lithium-ion batteries using data-driven methodologies. 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. [PERSON] _et al._[24] introduced the advantages of RVM and regarded it as one of the main potential methods for lithium-ion battery RUL estimation. [PERSON] _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. [PERSON] _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. [PERSON] _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, [PERSON] _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. [PERSON] _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, [PERSON] _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, [PERSON] _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.