## 1 Introduction
Nevertheless, it is more difficult to develop a precise battery degradation model because the electrochemical model is dynamic and nonlinear. The above model-based methods provide an accurate representation of the external dynamic characteristics of the battery. However, a substantial amount of prior knowledge is required to use the method, and frequent adjustments to the model according to the specific type of lithium-ion battery and varying operating conditions are needed, making it unsuitable for real-time forecasting [20]. In contrast, data-driven methods do not require intensive examination of the battery's aging mechanism, but battery performance parameters are directly extracted, such as voltage, current, resistance, temperature, and other data as health features. The health feature parameters are analyzed and modeled with the trend of capacity degradation to estimate the internal state and performance of the batteries. Data-driven methods offer the advantages of efficiency, simplicity, and ease of use, and have attracted extensive attention in various fields [21]. [PERSON] et al. [22] used the rate of temperature change associated with capacity degradation as input to time convolution networks and SOH as output, achieving good prediction accuracy. [PERSON] et al. [23] implemented RUL prediction by analyzing the change rule of the terminal voltage curve during battery charging and extracting degradation features as inputs to the feed-forward neural network. [PERSON] et al. [24] introduced an application of deep neural networks to extract eight features from charge-discharge curves to predict SOH and RUL, with better results. [PERSON] et al. [25] used capacity and equal voltage drop discharge time as health features, preprocessed health features using ensemble empirical mode decomposition (EEMD), introduced phase space reconstruction to optimize input sequences, and finally combined it with support vector regression (SVR) to complete the prediction of RUL. [PERSON] et al. [26] combined partial incremental capacity with an artificial neural network for estimating battery status under constant current discharge conditions. [PERSON] et al. [27] used constant current charging time and capacity, as well as constant voltage charging time, as features for training the SVR model to predict SOH. [PERSON] et al. [28] advanced a hybrid model combining a modified adaptive noise algorithm for performing EEMD decomposition of capacity data, predicting each decomposition component separately using LSSVR. [PERSON] et al. [29] investigated changes in battery charging status under various health conditions. The particle swarm algorithm was employed to optimize the kernel function of the support vector machine for the joint estimation of SOC and SOH. Experimental results show that the method is remarkably adaptable and feasible. [PERSON] et al. [30] used support vector machines to predict trends in capacity degradation by extracting health features from the temperature differential curve during constant current battery charging. [PERSON] et al. [31] extracted features from charging capacity and incremental capacity data to model battery aging through ridge regression. Experimental results showed that compared to SVR and Gaussian process regression, more reliable estimates with a simpler structure and lower computational cost were provided by ridge regression using selected features. The data-driven methods mentioned above are simple to implement and achieve high prediction accuracy when reliable training sets are used. However, due to dynamic changes in electrochemical reactions within the battery. This includes factors such as fine-tuning the electrode material structure, electrolyte redistribution, and repair of the solid electrolyte interface layer, which can lead to a phenomenon of capacity regeneration in the battery within a short time [32]. The existence of this capacity regeneration phenomenon can lead to a situation where the battery has the same SOH but different RUL in two different cycles.