# Online State of Health Estimation for Lithium-Ion Batteries Based on Support Vector Machine
## 2 Definition and Description of State of Health  
In this paper, the SOH of the lithium-ion battery is described by the loss of rated capacity, which can be furnished as,  
\[SOH=\frac{C_{bat}}{C_{nom}}\times 100\%, \tag{1}\]  
where \(C_{nom}\) and \(C_{bat}\) denote the nominal and actual battery capacity, respectively. For the sake of accurate SOH estimation, the extraction of characteristic variables is pivotal. Due to complexity of the battery inner structure and materials, it is difficult to extract efficient features from the data under a static condition. Based on this, data from charge/discharge test are more feasible for the SOH study. The offline discharge test is a common method for the measure of battery capacity, in which the battery is discharged by a constant rate at a certain temperature; however, this method would accelerate the battery degradation and its whole test time is relatively long. In addition, focusing on on-road application, the lithium-ion battery pack in EVs is irregularly discharged under different driving conditions, leading to difficulty estimating the SOH online. Instead, the charging process is more applicable for the SOH estimation, owing to its constant current (CC), as shown in Figure 1. Moreover, in practice, when EVs are charged, the battery charging data are easy to acquire and the BMS has enough capability to handle the SOH estimation. Considering this, the data during the CC charge process are selected for the SOH estimation. In this paper, the battery cycling data are collected from a public source [28], which records the voltage, current, temperature and capacity for each charge and discharge cycle [28; 29]. After screening all the operation process, the charging data of two batteries (called Cell 1 and Cell 2 hereinafter) by the CC method are analyzed and main parameters are listed in Table 1. They are 18,650-size lithium-ion cells with 2.0 Ah nominal capacity, and LiNi\({}_{0.8}\)Co\({}_{0.15}\)Al\({}_{0.05}\)O\({}_{2}\) was applied as the main positive electrode material. The battery is charged under the CC mode first until the battery voltage reaches 4.2 V, and then sustains under the CV mode until the charging current drops to 20 mA. The capacity and the internal resistance are commonly selected to characterize the lithium-ion battery degradation. Actually, the battery internal parameters vary slowly with increase of cycle numbers. The external measured signals can be affected by variation of internal parameters, and thus the shape of externally measured voltage curve would also be changed. Based on this, we can employ the regular charge pattern variation of external signals to depict the variation of SOH. The battery partial voltage variation profile under the CC mode with different cycle numbers is shown in Figure 2, based on which we can find that the tendency of three charge curves are obviously different. From this point, we can extract proper vectors from the CC charging voltage curve to estimate the SOH. However, when the batteries in EVs are charged for daily use, the initial SOC is rarely the same due to random driving conditions. Moreover, to achieve a uniform SOH estimation based on the charging data, the data region should be defined properly. In addition, the BMS needs to store and process large data for the SOH estimation. Thus, we can say that the prerequisite of selecting all CC charging data for the SOH estimation cannot make sense. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Battery Number** & **Charge Current (A)** & **Discharge Current (A)** & **Ending Discharge Voltage (V)** & **Temperature (\({}^{\circ}\)C)** \\ \hline Cell 1 & 1.5 & 2 & 2.7 & 24 \\ Cell 2 & 1.5 & 2 & 2.2 & 24 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of batteries with their operating parameters. Figure 1: Charge process of battery.