# State of Health Prediction for Lithium-Ion Batteries Using Transformer-LSTM Fusion Model
## 1 Introduction  
Lithium-ion batteries are essential energy storage technologies in modern applications, renowned for their high energy density, long lifespan, and low self-discharge rate. They are increasingly used in electric vehicles and energy storage devices [1, 2]. However, with long-term use, battery performance gradually degrades due to internal chemical reactions and external environmental factors, impacting its lifespan and potentially causing failure [3, 4, 5]. As batteries age, thermal runaway can occur, leading to rapid temperature increases that may result in combustion, posing significant safety risks [6, 7]. Therefore, accurate evaluation of the SOH of lithium batteries has become a key factor in ensuring their safe and stable operation. Battery SOH is a key indicator to measure the current health level of the battery, which reflects the performance changes and degradation of the battery during use [8, 9]. SOH is usually expressed as the ratio between the current maximum available capacity of the battery and its initial rated capacity, and the calculation method is as follows:  
\[\text{SOH}=\frac{C_{max}(n)}{C(0)}\times 100\% \tag{1}\]  
where \(C_{max}(n)\) is the maximum available capacity of the battery at the \(n\)-th charge and discharge cycle, and \(C(0)\) is the initial rated capacity of the battery. As the battery is used,the maximum available capacity of the battery gradually decreases, resulting in a decrease in SOH. The battery management system (BMS) is a crucial component of modern battery-driven devices, such as electric vehicles, battery energy storage systems, and mobile devices. Its primary responsibilities include ensuring the safety, efficiency, and long-term performance of the battery. SOH prediction plays a vital role in this [10; 11]. By monitoring the battery health in real time, the BMS can provide early warning if the battery is nearing failure and detect abnormal signs of battery degradation timely, thereby effectively reducing the risk of thermal runaway and ensuring that the battery operates within a safe operating range. However, implementing SOH prediction in a BMS is challenging. First, SOH is influenced by a variety of factors, including environmental conditions like temperature and humidity, usage patterns such as charge and discharge rates and depth of discharge, material properties, and the complex changes in the internal chemical reactions of the battery, making the battery degradation process highly complex and nonlinear. This complexity makes predicting battery degradation difficult. Second, SOH prediction depends on multi-dimensional data, such as a battery's charge and discharge history, voltage, current, and temperature information. In practical applications, however, the quality and uncertainty of data often pose significant challenges to achieving accurate prediction. Finally, the SOH prediction model needs robust generalization capabilities to be effective across different battery types, brands, and working conditions. The degradation process of lithium batteries is affected by multiple factors, such as charging and discharging cycles, temperature fluctuations, and material aging. These factors cause the battery to exhibit different degradation characteristics at different stages of use and working conditions. Therefore, it is particularly important to identify key features related to battery aging. It is worth noting that the battery degradation process usually exhibits obvious nonlinear characteristics. Especially after extended use, the degradation rate tends to accelerate, which poses significant challenges to accurately predicting SOH [12; 13; 14]. Research on lithium battery SOH prediction can be divided into two categories: physical model-based methods and data-driven model-based methods. Physical model-based methods focus on in-depth exploration of the dynamic process of electrochemical reactions inside batteries by establishing equivalent circuits and electrochemical models of batteries.