## 1 Introduction  
Due to the global energy shortage and environmental pollution, countries around the world have attached great importance to the development of electric vehicles. The lithium-ion battery is considered to be an ideal electric vehicle power battery with high safety, large discharge power, environmental protection, less pollution, and long cycle life [1; 2]. However, the increase in energy density and electrochemical performance of the battery often means a decrease in safety performance, which is prone to safety accidents. In the process of use, because of the side reaction of the electrolyte and the interface between the positive and negative electrodes, the thermal and electrical properties of the aged lithium-ion battery will be significantly changed and, therefore, the thermal stability of the lithium-ion battery will inevitably change as it ages [3]. In [4], the differences in the safety behavior between un-aged and aged high-power 18650 lithium-ion cells were investigated at the cell and material level by accelerating rate calorimetry (ARC) and simultaneous thermal analysis (STA). The results show that the aging of the battery will lead to the mechanical deformation of the jelly roll and lithium plating on the anode, which has a great impact on battery safety. The cyclic stability and thermal runaway characteristics of four commercially available cylindrical batteries under three different states-of-charge (0, 50%, and 100%) were investigated in [5]. Abuse testing (crush and nail penetration tests) was also performed at 100% SOC. It is not difficult to see from the analysis of the article that the SOC of the battery is related to the thermal stability of the battery. The higher the SOC, the worse the thermal stability of the battery, and the lower the temperature of the thermal runaway. In actual practice, lithium-ion batteries need to be well monitored, judged, and controlled by the battery management system (BMS). An accurate battery state estimation is one of the most basic functions of the BMS. The state of the battery includes state-of-charge (SOC), state-of-health (SOH), and state-of-function (SOF). SOC refers to the battery's remaining capacity and is one of the main parameters describing the state of the battery. An accurate estimation of the SOC can effectively prevent battery overcharge and over discharge, extend battery life, and provide drivers with accurate cruising range information. SOC of the battery cannot be directly measured by the instrument and can only be estimated from other measurable parameters. However, external factors and internal factors, such as ambient temperature, self-discharge, and cycle life, can affect the estimation of the battery's SOC. How to accurately estimate the battery capacity is a worldwide problem. With the development of technology, a series of battery SOC estimation algorithms have been proposed; each has its advantages and disadvantages. The common battery SOC estimation methods include: (1) the residual capacity method [6]; (2) the open circuit voltage (OCV) method [7]; (3) the ampere-hour integration method [8]; (4) the Kalman filter method [9]; (5) the deep learning algorithm [10]; (6) the neural network method [11]; and (7) hybrid techniques [9]. The residual capacity method calculates the SOC by discharging the battery to a lower cut-off voltage in the controlled test equipment [6] and the OCV method is based on the relationship between the open circuit voltage of the battery and the SOC [7]. The results obtained by the two methods in the laboratory are very reliable, but both require a large amount of measurement time and are not suitable for online monitoring of the BMS. The ampere-hour integration method estimates the SOC by integrating the inflow and outflow currents of the battery. The method is easily calculated online and the cost is low. However, this method cannot correct the cumulative error caused by the drift of the current measurement sensor. In addition, the accuracy of the estimation depends on the initial SOC [8].