## 2. SOH Definition and Computation  
The SOH based on capacity degradation is usually defined as [14; 15]:  
\[SOH=\frac{Q_{i}}{Q_{C}}\times 100\% \tag{1}\]  
where, \(Q_{i}\) is the maximum available capacity at a certain time \(i\). It is defined in Equation (2). \(Q_{i}\) represents the total number of ampere-hours can be drawn from the fully charged battery at a specified current rate and ambient temperature. \(Q_{c}\) is the nominal capacity of the battery. \[Q_{i}=\frac{1}{3600}\int_{0}^{T_{i}}\eta\cdot i(t)dt \tag{2}\]  
where, time 0 means the initial discharge time and \(T_{i}\) means the end of the discharge time. \(\eta\) represents the coulombic efficiency and \(t\) is in seconds. At present, the mainstream methods of available capacity are as following [16]:  
(1) The methods based on OCV and more strictly based on the electro motive force (EMF) [17], that is, using the relationship between the EMF and the SOC to estimate the SOH of the battery while in idle or in operation. These methods are based on the following Equation:  
\[\frac{1}{3600}\int_{t_{1}}^{t_{2}}\eta\cdot i(t)dt=C\cdot(SOC(t_{2})-SOC(t_{1 })) \tag{3}\]  
An equivalent Equation to (3) is shown in (4):  
\[C=\frac{1}{3600}\int_{t_{1}}^{t_{2}}\eta\cdot i(t)dt/(SOC(t_{2})-SOC(t_{1})) \tag{4}\]  
where, SOC (\(t\)) means the SOC value at time \(t\). Upon measuring the OCV value of the certain time \(t_{1}\) and \(t_{2}\), the SOC value of certain times \(t_{1}\) and \(t_{2}\) can be calculated based on the OCV-SOC curve. Thus, the available capacity of the battery can be predicted according to the abovementioned Equation (4). After charging or discharging the battery, it needs to rest for a relatively long time. That is, to measure OCV precisely, the battery should be in a completely steady state [18]. Therefore, improvements to this type of methods are focused on how to calculate the OCV (or EMF) in a short relaxation time or without a relaxation time and how to improve the accuracy of the OCV-SOC curve [19; 20]. [PERSON] et al. [21] put forward a rapid OCV prediction method to predict the final static OCV using linear regression techniques, based on a novel mathematical model developed from an improvement on a second-order resistance-capacitance (RC) model [1]. [PERSON] et al. [22] proposed a novel OCV model which has a much better fitting accuracy for considering the staging phenomenon during the lithium intercalation/deintercalation process for LIB. [PERSON] et al. [23] proposed a SOH (SOC) correction as part of the battery equivalent circuit model (ECM) and on-line optimization of SOH (SOC) correlation impelled to optimize the OCV- SOC correlation and the capacity of a LIB. [PERSON] et al. [24] shows that the main factors influencing the OCV behavior of LIB are aging, temperature and working history of the battery. Furthermore, the paper investigated the impact of the abovementioned factors on OCVat different aging states using various active materials (C/NMC, C.LEP, LTO/NMC) over a wide temperature range (\(-20\)\({}^{\circ}\)C-\(45\)\({}^{\circ}\)C). (2) The methods based on incremental capacity analysis (ICA) and differential voltage analysis (DVA). These methods use the electrochemical characteristics of the battery. For ICA, the obtained curves _V-dQ/dV_ transform the plateau present in the cell voltage trend (representative of electrochemical equilibrium phases during the cell operation) into peaks [25; 26]. For DVA, the obtained trend _Q-dV/dQ_ presents, for each peak, the transition between two electrochemical equilibrium conditions during the battery operation conditions [27]. The locations and amplitudes of such peaks can reflect the deterioration of the battery. For the measured voltage contains trembling and noise, as a result, the perturbation is introduced into the IC or DV curves which make it difficult to identify the peaks. This kind of method makes full use of the electrochemical characteristics of the battery. However, it has strict requirements regarding the operating conditions.