## 2 Remaining Useful Life (RUL) Prognostics Methodologies
### RUL Prognostics Methodologies Based on Artificial Intelligence  
Methodologies based on artificial intelligence usually use the monitoring data to fit the variable degradation model and calculate the RUL by extrapolating the variables to the failure threshold. Methods such as the AutoRegressive (AR) model [12], neural network [13; 14; 15; 16; 17; 18], support vector machine (SVM) [19; 20; 21; 22], and relevance vector machine (RVM) [23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33] are used. Prediction models based on AR only need battery degradation 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. [PERSON] [16] used a neural network to fit the relationship between open voltage, resistance, and discharge capacity at different depths of discharge (DOD). [PERSON] [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. [PERSON] [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, [PERSON] _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. [PERSON] [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. [PERSON] _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. [PERSON] _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). [PERSON] _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