## 1 Introduction
proposed a deep fully convolutional neural network (FCNN) model to estimate SOC under different driving cycles at constant and varying environmental temperatures. This model uses batch processing operations and constructs a data window to accelerate model training [16]. [PERSON] et al. used the time convolutional network (TCN) method to estimate SOC, using time-series data to capture temporal changes in data and reduce prediction time [17]. [PERSON] et al. proposed a TCN-based method for estimating the SOC of lithium-ion batteries. The TCN directly reflects the voltage, current, and temperature of the battery SOC and demonstrates superior ability in processing lithium-ion battery timing data through a specially designed extended causal convolution structure [18]. [PERSON] et al. proposed a fusion convolutional neural network (FCNN) algorithm to estimate battery SOC. The experimental results showed that it can improve the accuracy of SOC estimation [19]. [PERSON] et al. proposed a method based on a CNN-GRU hybrid network to accurately estimate the battery SOC in low-temperature environments. The network exhibits strong generalization ability, high estimation accuracy, and robustness in learning feature parameters and adjusting weights [20]. [PERSON] et al. proposed an SOC estimation method based on the U-Net architecture, processing variable-length input data to output SOC estimates of equal lengths. A symmetrical padding convolutional layer was also proposed to solve the boundary effect of convolutional neural networks (CNNs) and improve the accuracy of edge SOC estimation. Experimental results indicated that the average absolute error of this method was within 1.1% under isothermal conditions [21]. [PERSON] et al. compared four different RNN models for battery SOC estimation to help battery management engineers develop the most appropriate estimation methods [22]. [PERSON] et al. proposed a co-estimation model to estimate battery SOC and capacity. The model uses the least-squares support vector machine (LSSVM) to estimate capacity, thereby inputting the capacity estimation results into the RNN. The moving window method solves the long-term dependency problem in RNN, and the results indicated that the model performs well [23]. [PERSON] et al. proposed a battery SOC estimation method based on voltage and stress measurements combined with the LSTM neural network, achieving a maximum absolute error (MAE) and root mean square error (RMSE) within 0.34% and 0.45%, respectively [24]. [PERSON] et al. proposed a dual-input neural network that combines the GRU and fully connected layers for battery SOC estimation. Experiments showed that this network can provide a more accurate SOC estimation throughout the battery life cycle [25]. [PERSON] et al. applied a three-dimensional CNN algorithm (3 DCNN) for the first time for battery SOC estimation. They further introduced the FCNN algorithm, which improves the accuracy of the SOC estimation by considering the degree of battery aging [26]. [PERSON] et al. proposed a series of intelligent SOC estimation methods using GA and particle swarm optimization (PSO) algorithms to optimize BP based on the Levenberg-Marquardt (L-M) algorithm, demonstrating an accuracy and robustness higher than those of the EKF method [27]. [PERSON] et al. proposed a model-based battery SOC estimation method using an adaptive genetic algorithm (AGA) for parameter identification and a fractional unscented Kalman filter (FOUKF) for state estimation. The experimental results showed that the AGA-FOUKF algorithm improves the accuracy of SOC estimation [28]. [PERSON] et al. proposed an efficient method to estimate battery SOC using a BP neural network optimized by a multi-population genetic algorithm (MPGA) to compensate for the nonlinear error of the EKF [29]. [PERSON] et al. proposed an SOC estimation method using the fireworks elite genetic algorithm (FEG-BP) to optimize the BP neural network to solve the problems of traditional BP networks, which are prone to falling into local optima and have low accuracy.