# Online State of Health Estimation for Lithium-Ion Batteries Based on Support Vector Machine
## 1 Introduction  
Nowadays, oil crisis and environmental pollution bring increasing concern to our daily life. Vehicle electrification can effectively mitigate their influences. Among all the solutions, the most popular manner is electric vehicles (EVs), which employ the energy storage system and one or two motors to power the vehicle [1; 2; 3]. In an EV, hundreds to thousands of cells connected in series/parallel topologies enable powering the EV for the maximum range of 100-500 km. Consequently, it is necessary to manage the battery pack to ensure safe and proper operations by a so-called battery management system (BMS). With increase of cycle numbers of lithium-ion batteries, the electrode materials gradually become inactive, leading to the performance degradation of the battery. The battery state of health (SOH) is an estimation to evaluate the battery capability status, by which the battery related inner parameters including state of charge (SOC) and remaining driving range can be accessed with higher precision. Actually, the battery aging rate depends on the battery operation state, including charging and discharging rates, depth of discharge, and the external environment such as ambient temperature and storage conditions. Gaining more knowledge about battery aging can potentially bring improvement of the battery life and avoid occurrence of safety hazard [4; 5; 6], and thus it motivates researchers to conduct the SOH estimation for lithium-ion batteries. Currently, various studies on the SOH estimation have been put forward [7; 8], which can be classified into the physical-based method, the parameter variation method of the equivalent circuit model (ECM), the data-driven method and the fusion method [9]. The physical-based method considers the physical degradation of the battery and includes the electro-chemical based model and external characteristic model. The model based electro-chemical property is extensively investigated for the SOH estimation [10; 11]. The electro-chemical based methods establish the model based on the internal specific physical and chemical reaction of the battery during the charge and discharge process. However, the complex modeling process and excessive computation intensity limit its wide application. An external characteristic model was introduced [12] to discover the relationship among capacity,charge and discharge current rate, discharge depth and temperature, and was validated to be suitable under fixed battery operation conditions. The ECM is a widely employed method for the SOH estimation [13]. In [13], the Thevenin ECM and the genetic algorithm (GA) are implemented together to identify the parameter variation, and the results show that it can achieve reliable SOH estimation. To sum up, for physical-based approaches and the ECM based method, various complex equations with considerable parameters are required for the accurate SOH prediction, and thus it is difficult to achieve the online prediction due to complex computation. The data-driven approach is an efficient and effective method [14; 15; 16], which typically includes neural networks (NN), support vector machines (SVMs), Gaussian regression process (GRS), relevance vector machine (RVM), autoregressive and moving average (ARMA), etc. [17; 18; 19; 20; 21]. In [16], a SOH estimation method is proposed based on the ARMA model. [PERSON], D et al. [21] predicted battery degradation trend using GRS model. Considering the possibility analysis, the Dempster-Shafer theory (DST) and the Bayesian Monte Carlo (BMC) method are integrated together to realize battery capacity forecasting [22]. However, these models can only be applied in fixed discharging and charging operations, implying that they are inadequate for real-time application. To conduct better performance for SOH prediction, fusion methods attract much attention. They employ two or more approaches to operate together thereby achieving the estimation, e.g., ARMA, NN, fuzzy logic, etc. [23].