SoC Fusion Estimation Based on Neural Network Long and Short Time Series

Abstract

Accurate prediction of state-of-charge (SoC) is critical to ensure battery performance, extend lifetime and ensure safety. Data-driven methods for SoC prediction are highly adaptable and generalizable. However, the current method of estimating SoC using a single model suffers from the difficulty of accommodating both global variations in the long time domain and local variations in the short time domain, which in turn leads to limited accuracy. Therefore, this paper proposes a dual-model fusion of Transformer and long short-term memory (LSTM) network for SoC estimation. Transformer and LSTM are used to capture the global change features of the battery in the long time domain and the local change features in the short time domain, respectively. First, we employ a single model to obtain separate SoC estimations for the long-term and short-term domains. Then, we fuse these long-term and short-term estimations using a neural network. Finally, we apply Kalman filtering to process the fused data and obtain the final SoC estimation. The proposed method is finally validated under different operating conditions and different temperatures, respectively. The results show that the root mean square error of the fused model is as low as 1.69%. This method can fully combine the advantages of LSTM for short-time sequences and Transformer for long-time sequence capture. The fused model is able to achieve satisfactory estimation accuracy under different temperatures and different working conditions with high accuracy and adaptability.

1. Introduction

Climate change induced by fossil fuel emissions has accelerated the global transition toward cleaner transportation solutions [1,2,3,4], with electric vehicles (EVs) emerging as a promising alternative due to their near-zero tailpipe emissions and superior energy efficiency. Lithium-ion batteries, which dominate the market owing to their exceptional energy density, power capacity, and cycling stability [5,6], constitute the core of EV performance. Within battery management systems, the State of Charge (SoC) serves as a critical parameter that directly influences charging strategies, battery lifespan, vehicle range, and system reliability [7]. However, the intricate electrochemical processes, multiphysics coupling phenomena, and varying operational conditions pose significant challenges for accurate real-time SoC estimation [8,9], making it a crucial research priority. Currently, SoC estimation methods can be broadly categorized into three primary approaches: definition-based methods, model-based methods, and data-driven methods.

Methods based on the definition of SoC include the Coulomb counting method and the open-circuit voltage method. The Coulomb counting method estimates SoC through continuous monitoring of battery current and voltage, integrating the charge flow over time to determine the cumulative charge transferred during charging and discharging processes. While this approach offers straightforward implementation, it is susceptible to cumulative errors arising from sensor inaccuracies and battery model uncertainties [10,11]. The open-circuit voltage method provides a relatively straightforward approach that determines SoC by correlating measured open-circuit voltage with established voltage-SoC characteristic curves. However, this technique necessitates extended battery relaxation periods to achieve equilibrium, precluding real-time monitoring capabilities and limiting its applicability to laboratory environments [12,13,14].

Model-based SoC estimation methods predict battery state by simulating electrochemical processes through battery modeling, parameter identification, and state estimation. The most prevalent approach establishes an equivalent circuit model (ECM) followed by parameter identification and Kalman filtering-based estimation [15,16]. Li et al. [17] developed a physically based ECM with improved electrochemical reaction modeling, achieving superior accuracy through Extended Kalman Filter (EKF) implementation. Zhang et al. [18] introduced an enhanced ECM incorporating battery hysteresis effects and adaptive unscented Kalman filtering, demonstrating high accuracy across diverse conditions. Buchicchio et al. [19] combined machine learning with ECM using electrochemical impedance spectroscopy data, achieving over 93% accuracy in experimental validation. While model-based approaches provide solid theoretical foundations and strong interpretability, they face challenges in model complexity, computational requirements, and parameter accuracy dependencies.

Data-driven SoC estimation methods establish nonlinear relationships between SoC and battery parameters (current, voltage, temperature) through extensive data training, independent of physical constraints. Common approaches include Artificial Neural Networks (ANN), Support Vector Machines (SVM), and Convolutional Neural Networks (CNN) [20,21,22]. Traditional Recurrent Neural Networks (RNNs) suffer from gradient vanishing/explosion issues during backpropagation with long sequences, limiting their ability to capture long-term dependencies critical for SoC prediction [23]. Long Short-Term Memory Networks (LSTM) address these limitations through gating mechanisms that regulate information flow. Tian et al. [24] integrated LSTM with adaptive cubature Kalman filter (ACKF), where LSTM captures long-term battery behavior while ACKF handles output uncertainty, demonstrating superior performance under dynamic conditions. Additionally, Transformer architectures leverage self-attention mechanisms to capture long-range dependencies in sequential data. Shen et al. [25] proposed KF-SA-Transformer, combining Kalman filtering for noise reduction, sparse autoencoder for feature extraction, and Transformer for dependency modeling, achieving enhanced SoC prediction accuracy and reliability. While data-driven methods offer high accuracy and adaptability, they require extensive training data and may lack physical interpretability.

Despite promising performance, single-model data-driven SoC estimation approaches suffer from limited generalization and insufficient stability, motivating collaborative and ensemble frameworks. Hong et al. [26] proposed an LSTM-GRU multi-step prediction model achieving high accuracy and robustness in practical applications. Wang et al. [20] developed a Coulomb-counting-machine-learning hybrid using moving-average IRVM (movIRVM) to suppress noise and alternating estimators to reduce global error accumulation. Recently, physics-informed neural networks (PINNs) have emerged as a promising approach by explicitly incorporating governing physics into learning frameworks to enhance physical consistency and generalization. Li et al. [27] embedded electrochemical–mechanical coupling knowledge into a CNN-LSTM pipeline, using swelling displacement as key physical information to significantly reduce SoC estimation errors across multiple C-rates while maintaining computational efficiency. Wu et al. [28] comprehensively surveyed physics-based SoC estimation methods, identifying electrochemical-mechanism-driven algorithms as promising candidates for advanced battery management systems. While these collaborative approaches have improved stability and generalization, challenges remain in physics model selection, multi-scale feature fusion, and balancing accuracy with computational cost.

The primary challenges in SoC estimation can be summarized as follows: First, under diverse operating conditions, particularly extreme temperatures, intense electrochemical reactions within batteries pose significant modeling difficulties. Conventional models struggle to accommodate multiple operating scenarios, resulting in limited generalization capability. Second, models utilizing exclusively long-term time series data tend to prioritize overall trends while overlooking local detailed information, potentially missing critical short-term variations or anomalies essential for accurate SoC prediction. Third, models relying solely on short-term time series focus predominantly on local patterns and immediate trends, potentially failing to capture long-term dependencies necessary for robust predictive performance.

To overcome these limitations, we propose an adaptive LSTM–Transformer fusion strategy for data-driven SoC prediction. Unlike common static weighting or rule-based fusion schemes in the literature, we introduce a fully connected meta-learner to re-model the outputs of the LSTM and Transformer branches, together with Bayesian hyperparameter optimization for automatic tuning and efficient structure search. The strategy employs LSTM to model short- to medium-term dependencies—its gating mechanism enables robust local feature extraction and effective noise suppression [29]; meanwhile, the Transformer leverages self-attention to capture global temporal relations without stepwise recurrence, supports parallel computation, and alleviates vanishing gradients in very long sequences [30], and is therefore used for long-range dependency modeling. Compared with GRU—which reduces parameters but often sacrifices capacity for distant dependencies—and TCN—which benefits from dilated convolutions yet is constrained by a fixed receptive field—the Transformer exhibits stronger adaptability to variable dependency lengths. Building on this, the proposed strategy preserves the complementary strengths of LSTM (short-term dependencies) and the Transformer (global features) while learning, via a nonlinear mapping, condition-dependent optimal weights and cross-model interactions, thereby avoiding the limitations of hand-crafted fusion rules and, with Bayesian optimization, improving parameter and structure search efficiency.

2. Methodology

2.1. Fusion Model Overall Framework

Figure 1 presents the overall architecture of the proposed fusion model. The framework comprises three primary components: a long-term estimation model, a short-term estimation model, and a model fusion mechanism. The processing workflow operates as follows: voltage, current, and temperature signals are simultaneously input into LSTM and Transformer networks. LSTM networks process short-term time series information, whereas Transformer networks handle long-term time series information. Subsequently, outputs from both long-term and short-term models are fed into a fully connected layer for fusion processing, ultimately yielding SoC estimation results. This methodology leverages the complementary strengths of LSTM and Transformer architectures in short-term and long-term temporal prediction, respectively, thereby enhancing SoC estimation accuracy. All models in this study employ Bayesian hyperparameter optimization, which automatically identifies optimal neural network hyperparameters such as learning rate, node configurations, and dropout rates to ensure prediction accuracy [31].

2.2. Fusion Methods

The fusion methodology employed in this study integrates outputs from two base models—Transformer and LSTM—encompassing both long-term and short-term temporal information. Long-term outputs effectively capture extended dependencies and global contextual information within time series data, while short-term outputs demonstrate enhanced sensitivity to immediate temporal variations and excel in detail processing. Both model outputs are processed through a four-layer fully connected network with Bayesian optimization. The first three layers utilize Bayesian hyperparameter optimization to automatically determine optimal node configurations and dropout rates, thereby enhancing network performance. The fourth layer functions as the output layer, and the final prediction results are obtained following Kalman filtering. Figure 2 illustrates the fusion module architecture, where the upper red arrow indicates input data flow and the lower red arrow represents output prediction results. This fusion approach effectively leverages the complementary advantages of both models—long-term sequence dependency modeling and short-term detail processing—thereby significantly enhancing prediction accuracy.

2.3. The Base Model

2.3.1. Transformer

The Transformer architecture, introduced by Ashish Vaswani et al. [30], was originally developed for natural language processing tasks and demonstrates exceptional proficiency in sequence data processing. The fundamental innovation of the Transformer lies in its self-attention mechanism, enabling parallel sequence processing, long-range dependency capture, and dynamic focus on different sequence segments through attention weight computation between queries, keys, and values. Since Transformer architectures lack recurrent structures and cannot inherently encode sequential order like RNNs or LSTMs, positional encoding becomes essential for providing positional information within sequences. Positional encoding approaches include sinusoidal functions, learnable positional embeddings, and relative positional encoding. Sinusoidal positional encoding, characterized by its simplicity, deterministic nature, periodicity, and capability to capture long-range dependencies, represents an effective positional encoding strategy for Transformers [30,32]. The sinusoidal positional encoding formula is expressed as follows:

$$PE\left(pos,2i\right)=\mathrm{s}\mathrm{i}\mathrm{n}({\displaystyle \frac{pos}{{\mathrm{10,000}}^{\frac{2i}{d_{model}}}}})$$

(1)

$$PE\left(pos,2i+1\right)=cos({\displaystyle \frac{pos}{{\mathrm{10,000}}^{\frac{2i}{d_{model}}}}})$$

(2)

where $pos$ denotes the position of the word, $i$ denotes the dimension index, and $d_{model}$ is the dimension of the model. In this way, each position is uniquely encoded and the model can understand the order of the word in the sequence by the position encoding.

This experiment utilizes only the encoder component of the Transformer architecture, as illustrated in Figure 3a. For regression tasks, the encoder effectively captures long-range dependencies through its attention mechanism, enabling efficient processing of long sequential data without requiring the step-by-step generation process inherent in decoders, thereby enhancing prediction efficiency. The encoder comprises multiple identical layers (typically 6) stacked sequentially, with each layer containing two primary components: a self-attention mechanism and a feed-forward neural network. The encoder’s function is to transform input sequences into contextual representations. The self-attention mechanism enables the model to simultaneously consider information from all sequence elements when processing each individual element. The core attention formula is expressed as follows:

$$Attention\left(Q,K,V\right)=softmax\left({\displaystyle \frac{Q{K}^T}{\sqrt{d_k}}}\right)V$$

(3)

where $Q$, $K$ and $V$ represent Query, Key and Value, respectively, and $d_k$ denotes the dimensionality of the key vectors. This formula computes attention scores between each sequence element and all other elements, and then performs a weighted aggregation of value vectors based on these scores to produce the final output representation.

The feed-forward network consists of two linear transformations with a ReLU activation function applied between them. The mathematical formulation is expressed as follows:

$$FFN\left(x\right)=\max \left(0,x{W}_1+b_1\right)W_2+b_2$$

(4)

where $x$ is the input, $W_1$ and $W_2$ are the weight matrices, and $b_1$ and $b_2$ are the bias terms.

2.3.2. LSTM

Long short-term memory (LSTM) networks represent a specialized variant of recurrent neural networks (RNNs) introduced by Hochreiter and Schmidhuber in 1997 [29]. The fundamental innovation of LSTM lies in its gating mechanism, which regulates information flow through three distinct gates: the forget gate, input gate, and output gate [29].

The forget gate determines which information should be removed from the cell state. Its mathematical formulation is expressed as:

$$f_t=\sigma (W_f·\left[h_{t-1},x_t\right]+b_f)$$

(5)

where $f_t$ is the output of the forgetting gate, $\sigma$ is the sigmoid activation function, $W_f$ and $b_f$ are the weight and bias of the forgetting gate, respectively, $h_{t-1}$ is the hidden state of the previous time step, and $x_t$ is the input of the current time step.

The input gate comprises two components: a sigmoid layer that determines which values require updating and a tanh layer that generates candidate values for potential addition to the cell state. The corresponding formulations are:

$$i_t=\sigma (W_i·\left[h_{t-1},x_t\right]+b_i)$$

(6)

$$\widetilde{C_t}=\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{h}(W_c·\left[h_{t-1},x_t\right]+b_C)$$

(7)

where $i_t$ is the output of the input gate and $\widetilde{C_t}$ is the candidate memory cell state.

The cell state constitutes the fundamental component of LSTM networks, serving as the repository for long-term memory information. Its update mechanism is governed by the following formula:

$$C_t=f_t*C_{t-1}+i_t*{\tilde{C}}_t$$

(8)

where $C_t$ is the cell state at the current time step.

The output gate regulates the proportion of cell state information that is transmitted to the hidden state. This mechanism is mathematically expressed as:

$$o_t=\sigma (W_o·\left[h_{t-1},x_t\right]+b_o)$$

(9)

where $o_t$ is the output of the output gate.

Subsequently, the hidden state is computed, which represents the network’s output at each time step and encapsulates the processed cell state information. This computation follows the equation:

$$h_t=o_t*\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{h}\left(C_t\right)$$

(10)

where $h_t$ is the hidden state of the current timestep.

LSTM networks exhibit temporal sensitivity, enabling them to extract intricate patterns and features from sequential data. This characteristic confers significant advantages in applications such as time series forecasting and signal processing, particularly for short-duration sequences where rapid adaptation to data variations is crucial. The architectural structure of LSTM is illustrated in Figure 3b.

2.4. Dataset Description

Two datasets are employed in this experimental study. The first comprises publicly available data from the Centre for Advanced Life Cycle Engineering (CALCE) database at the University of Maryland [33], while the second consists of synthetically generated data derived from model predictions, as detailed in Section 4.1.

The experimental validation employs an open dataset of A123 LiFePO4 (lithium iron phosphate) batteries. To comprehensively assess the adaptability and accuracy of the proposed approach, three dynamic driving profiles are utilized: the Dynamic Stress Test (DST), the Federal Urban Driving Scheme (FUDS), and the Highway Driving Scheme (US06). These driving profiles are sourced from the publicly available datasets of the University of Maryland Center for Advanced Life Cycle Engineering (CALCE) database. The experimental conditions encompass multiple temperature scenarios, with data from three representative conditions selected for analysis: low temperature (0 °C), room temperature (25 °C), and high temperature (40 °C). Battery units 7 and 8 serve as the primary datasets for this investigation. The voltage and current profiles of battery unit 7 at 25 °C, along with detailed cycle information, are presented in Figure 4.

The Dynamic Stress Test (DST) represents a comprehensive evaluation protocol designed to simulate battery performance in electric vehicles across diverse operational scenarios. This assessment incorporates various dynamic current profiles to characterize battery behavior under fluctuating conditions. The Federal Urban Driving Scheme (FUDS) emulates urban transportation patterns, encompassing acceleration, deceleration, and steady-state operations. In contrast, the Highway Driving Scheme (US06) replicates highway driving scenarios with elevated speeds and accelerations characteristic of motorway environments. DST serves as the training dataset for this investigation due to its comprehensive characterization of battery dynamics across multiple operational regimes. Conversely, US06 and FUDS function as validation datasets, representing distinct driving paradigms that differ from the training protocol. US06 emphasizes high-speed operation, while FUDS concentrates on urban mobility patterns. This testing framework enables comprehensive evaluation of the model’s generalization capabilities across diverse real-world driving scenarios.

3. Experimental Setup

3.1. Experimental Environment

The neural network architecture is implemented using the TensorFlow framework, with hyperparameter optimization performed through Bayesian optimization to enhance training performance. Unlike model parameters derived during training, hyperparameters constitute predefined configuration settings that significantly influence prediction accuracy in deep learning models. Traditional manual tuning approaches often rely on heuristic methods and may converge to suboptimal solutions. Bayesian optimization provides a more efficient exploration of the hyperparameter space, thereby reducing computational overhead and training time while achieving superior model performance. The optimization process targets three key hyperparameters: the number of hidden units, learning rate, and dropout rate. Experimental validation is conducted on a workstation equipped with an Intel Core i9-12900K CPU and NVIDIA RTX 3090Ti GPU. The software environment comprises TensorFlow 2.3.0, CUDA 10.1.243, cuDNN 7.6.5.32, and Python 3.7.12.

3.2. Evaluation Index

Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) are widely adopted metrics for evaluating regression model performance. MAE is defined as the mean of the absolute differences between predicted and actual values. This metric provides a clear measure of average error magnitude and is robust to outliers, as it employs absolute values rather than squared terms. Conversely, RMSE is calculated as the square root of the mean of the squared residuals. By emphasizing larger deviations through squaring, RMSE assigns greater weight to significant errors, making it particularly sensitive to substantial discrepancies. In this study, MAE and RMSE are employed as the primary evaluation indices to assess the performance of the proposed fusion model for state-of-charge (SoC) estimation.

$$MAE={\displaystyle \frac{1}{N}}{\sum }_{k=1}^N\left|y_k-y_k^{*}\right|$$

(11)

$$RMSE=\sqrt{{\displaystyle \frac{1}{N}}\sum _{k=1}^N{(y_k-y_k^{*})}^2}$$

(12)

where $y_k$ represents the true SoC and $y_k^{*}$ represents the predicted SoC.

3.3. Sequence-Length Selection for Different Networks

The Transformer, with its self-attention mechanism, can directly relate any positions within a sequence in a single computation, effectively capturing long-range dependencies while supporting highly parallel computation. This avoids the vanishing-gradient and information-dissipation issues that recurrent architectures typically encounter on long sequences, thereby enabling superior contextual modeling for long-horizon time series. In contrast, the LSTM propagates and updates information step-by-step through gated recurrence. Although it performs well for short- and medium-term dependencies, its recursive nature can still lead to gradient decay or explosion on very long sequences, degrading its ability to model distant dependencies. Therefore, in theory, Transformers are better suited to long-sequence prediction tasks, whereas LSTMs have advantages in short sequences or scenarios dominated by strong local dependencies.

To substantiate the aforementioned analysis, we conducted a controlled study where the sole varying factor was the input sequence length, using the 25 °C DST7-US067 condition as a representative case. The results are depicted in Figure 5: Figure 5a illustrates the state-of-charge (SoC) prediction error of the LSTM across various sequence lengths, with the minimum error occurring at 40–50 time steps; Figure 5b displays the Transformer’s SoC prediction error, which achieves its optimal performance at approximately 100 time steps. Guided by both theoretical considerations and these empirical results, we adopted an LSTM window length of 40 and a Transformer window length of 100 as the foundational configurations for subsequent training and prediction experiments.

4. Experimental Results and Analysis

4.1. Base Model Training Results

This section outlines the process of constructing the dataset and its associated details. Initially, Long Short-Term Memory (LSTM) and Transformer models are employed independently to generate SoC estimation results for the dataset described in Section 2.4. These models produce two sets of SoC estimates with differing sequence lengths, as the LSTM is configured to prioritize short-term temporal dependencies, while the Transformer emphasizes long-term dependencies. By leveraging the strengths of both models in their respective domains, enhanced prediction accuracy is achieved. Subsequently, the resulting estimates are aligned and concatenated to ensure consistent data dimensions, thereby forming the new test set. Figure 6a illustrates the test set for the US06 condition at 25 °C. For the training set, LSTM and Transformer models are trained independently on the Dynamic Stress Test (DST) condition. The resulting data undergo the same alignment and concatenation process to create the new training set, as depicted in Figure 6b for the DST condition at 25 °C. Figure 6c,d present the RMSE values for the training and test sets, respectively. This process is applied to data from each operating condition to construct a comprehensive dataset for SoC estimation.

4.2. Fusion Model Prediction Results

In this subsection, the results of the fusion model are compared and analyzed against those of the individual models, taking the 25 °C US06 operating conditions as a representative example. Figure 7 illustrates the comparison: Figure 7a presents the LSTM prediction results, Figure 7b shows the Transformer prediction results, Figure 7c displays the fusion model predictions, and Figure 7d depicts the estimation errors of both the single models and the fusion model in the form of a histogram.

Each subfigure contains two curves: the orange curve represents the true SoC value, while the blue curve shows the value predicted by the corresponding model, namely the LSTM, Transformer, or fusion model. The MAE and RMSE for the LSTM network are 1.96% and 2.47%, respectively, whereas those for the Transformer network are 2.26% and 2.66%. In comparison, the fusion model achieves lower MAE and RMSE values of 1.42% and 1.78%, respectively, indicating improved prediction accuracy. As illustrated in the prediction curves, the LSTM output exhibits significant fluctuations in the mid-time region. This is likely due to the nonlinear relationship between battery voltage and SoC: during discharge, the voltage characteristic curve forms a plateau in the mid-SoC range where voltage is relatively insensitive to SoC variations, amplifying estimation errors and resulting in pronounced fluctuations. By contrast, the Transformer prediction is smoother and avoids such large oscillations, owing to its attention mechanism, which effectively captures long-range dependencies in sequential data [34]. However, the Transformer is less capable of modeling local details with high sensitivity. The fusion model combines the strengths of both the LSTM and Transformer networks. As shown in Figure 7c, its prediction curve avoids the pronounced fluctuations observed in the LSTM output while retaining the Transformer’s smoothing effect, and it captures local features more effectively.

4.3. Results at Different Temperatures and Under Different Operating Conditions

In this subsection, the prediction results of the model at 0 °C, 25 °C, and 40 °C are presented and evaluated. Figure 8a–d illustrate the fusion model predictions under the US06 and FUDS conditions, where each subfigure displays two curves: the orange curve represents the true SoC at the given time, while the blue curve shows the corresponding value estimated by the fusion model. The MAE and RMSE values for different operating conditions are summarized as histograms in Figure 9a–d. The histogram indicates that the model has the highest error at 40 °C, with the Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) reaching 2.31% and 2.87%, respectively.

The MAE and RMSE for all other conditions remain below 3%, and the fusion model demonstrates higher accuracy compared to the individual models. It is observed that the FUDS conditions at 0 °C and 40 °C exhibit pronounced fluctuations in the mid-time region, resulting in reduced prediction accuracy. This can be attributed to the fact that, under low-temperature conditions, the battery’s chemical reaction rate decreases and internal resistance increases, which lowers its discharge capacity. Conversely, at elevated temperatures, the reaction rate accelerates, potentially causing overheating and adversely affecting the battery’s stability and lifespan. Consequently, the battery’s dynamic response under extreme temperatures, such as 0 °C and 40 °C, may differ significantly, resulting in larger oscillations under FUDS operating conditions, while such oscillations are not evident under US06 conditions. Despite these challenges, the fusion model consistently improves prediction performance across various operating conditions, demonstrating its capability to deliver reliable SoC estimation under diverse temperatures and driving profiles.

5. Conclusions

This study presents an innovative fusion model that integrates LSTM and Transformer frameworks to predict the SoC of lithium-ion batteries. By combining the LSTM’s sensitivity to short-term temporal features with the Transformer’s capacity to capture long-range dependencies, a hybrid model capable of delivering accurate SoC estimations is developed. Initially, the SoC is predicted using individual models on a separate test set; subsequently, the trained models are employed to generate an augmented training set under DST operating conditions. The enhanced dataset is subsequently fed into a fully connected layer for fusion processing, and the final SoC estimation value is generated through Kalman filtering. Throughout this process, Bayesian optimization is applied to automatically tune hyperparameters, ensuring optimal predictive performance. The proposed fusion model is validated under various operating conditions (DST, FUDS, and US06). Results indicate an average RMSE of 2.1%, with prediction accuracies consistently surpassing those of the individual models, demonstrating the fusion model’s high accuracy and strong generalization capability under diverse temperatures and driving scenarios.

The main contributions of this work are as follows:

1.

A data-driven SoC estimation framework is developed by integrating LSTM and Transformer networks, with hyperparameter tuning automated through Bayesian optimization, achieving high-precision SoC predictions across varying temperatures and operating conditions.

2.

The SoC predictions from the LSTM and Transformer models are fused using a neural network, enabling the integration of features across multiple temporal scales. This nonlinear mapping enhances model representation and prediction accuracy.

3.

The complementary strengths of the Transformer’s global context awareness and the LSTM’s responsiveness to short-term variations are effectively combined, improving adaptability to diverse conditions and strengthening the model’s generalization performance.

The proposed approach not only improves prediction accuracy but also enhances generalizability under different operating conditions and temperatures, offering new perspectives and solutions for SoC estimation in lithium-ion batteries. Future work may extend this fusion strategy to explore alternative hybrid architectures and further applications such as battery fault diagnosis and energy management systems.