Accurate Multi-Step State of Charge Prediction for Electric Vehicle Batteries Using the Wavelet-Guided Temporal Feature Enhanced Informer

Abstract

The state of charge (SOC) serves as a critical indicator for evaluating the remaining driving range of electric vehicles (EVs), and its prediction is of significance for alleviating range anxiety and promoting the development of the EVs industry. This study addresses two key challenges in current SOC prediction technologies: (1) the scarcity of multi-step prediction research based on real driving conditions and (2) the poor performance in multi-scale temporal feature extraction. We innovatively propose the Wavelet-Guided Temporal Feature Enhanced Informer (WG-TFE-Informer) prediction model with two core innovations: a wavelet-guided convolutional embedding layer that significantly enhances anti-interference capability through joint time-frequency analysis and a temporal edge enhancement (TEE) module that achieves the collaborative modeling of local microscopic features and macroscopic temporal evolution patterns based on sparse attention mechanisms. Building upon this model, we establish a multidimensional SOC energy consumption prediction system incorporating battery characteristics, driving behavior, and environmental terrain factors. Experimental validation with real-world operating data demonstrates outstanding performance: 1-min SOC prediction accuracy achieves a mean relative error (MRE) of 0.21% and 20-min SOC prediction exhibits merely 0.62% error fluctuation. Ablation experiments confirm model effectiveness with a 72.1% performance improvement over baseline (MRE of 3.06%) at 20-min SOC prediction, achieving a final MRE of 0.89%.

1. Introduction

The rise of global environmental challenges has accelerated the adoption of sustainable energy solutions with electric vehicles (EVs) emerging as a key technology for the transition to cleaner transportation systems [1]. However, the well-documented issue of range anxiety [2,3] remains a major impediment to the broader adoption of EVs. The performance and lifespan of an EV are strongly influenced by the effective management of its energy storage system with the battery’s state of charge (SOC) estimation being a key parameter [4,5]. Leveraging the exponential growth of EVs data, research on real-world SOC prediction has become a key industry focus [6,7].

However, the inherent complexity from time-varying EVs data, coupled with sensor noise and highly dynamic driving conditions, poses significant challenges for accurate SOC estimation [8], highlighting the need for an SOC estimation model that can effectively extract latent temporal features while maintaining robustness across diverse operating conditions.

1.1. Literature Review

Researchers have extensively investigated and achieved significant progress in the estimation of battery state of charge (SOC). Broadly, SOC estimation methods can be classified into three main categories according to their underlying principles and practical applications: direct calculation methods, model-based methods, and data-driven methods [9], as summarized in Figure 1. The direct calculation methods primarily include the ampere-hour (Ah) integration method and the open-circuit voltage (OCV) method. Model-based approaches are mainly composed of electrochemical models and equivalent circuit models, whereas data-driven methods encompass machine learning and deep learning techniques. The first two categories rely on physical modeling and require accurate measurements of battery charge–discharge behavior to achieve precise estimation without depending on large-scale training data. In contrast, data-driven methods treat SOC estimation as a black-box learning problem, where predictive performance improves with the availability of substantial historical datasets. Accordingly, this study focuses on data-driven approaches with particular emphasis on the design of deep learning architectures for multi-step SOC prediction.

The data-driven approach primarily leverages machine learning and deep learning, which excel at processing high-dimensional, large-scale data and addressing complex non-linear problems. Moreover, with advancements in artificial neural networks, deep learning methods have been increasingly applied in the battery domain [10]. Compared to traditional machine learning approaches, deep learning excels at extracting hidden features, leading to improved model accuracy. For instance, Dong et al. [11] utilized a back-propagation (BP) neural network to predict the SOC of a battery using current, voltage, and temperature as inputs. However, their study only validated the model’s accuracy under constant current charging conditions. Ren et al. [12] utilized the particle swarm optimization (PSO) algorithm to optimize the key parameters of the LSTM-RNN, thereby enhancing the accuracy of SOC estimation. Additionally, they introduced random noise to the network’s input layer during the training process to improve its resistance to interference. Similarly, Jiao et al. [13] explored a momentum gradient method based on GRU-RNN and examined how factors such as momentum terms, noise variances, training epochs, and the number of neurons in the hidden layer influence the training speed and SOC estimation accuracy. Xie et al. [14] proposed an approach for SOC estimation using a multi-hidden-layer LSTM neural network combined with a suboptimal fading extended Kalman filter (EKF). Experimental results on training and testing datasets demonstrated that this method achieves high precision and robustness in SOC estimation. To mitigate the impact of measurement noise, a denoising autoencoder neural network was employed to reduce noise and enhance the dimensionality of battery measurement data by extracting key features. The study revealed that this method outperformed GRU and RNN neural networks in both accuracy and robustness [15]. Beyond RNN-based methods, Zou et al. [16] introduced a novel deterministic and probabilistic SOC estimation method utilizing a convolutional neural network (CNN) to extract spatial features from the original input data. This approach mapped high-dimensional data features to SOC values and effectively extracted feature information. The findings showed that the proposed model could accurately estimate SOC across various battery types and operating conditions. However, the experimental data did not validate its applicability for real-world driving conditions.

Leveraging attention mechanisms, Transformers efficiently capture long-term dependencies and identify key features in temporal sequences. Initially applied in fields like natural language processing and computer vision, they have shown great promise in battery applications. For example, Transformer-based frameworks achieve high accuracy in SOC estimation with one model reaching an MAE of 0.52% over a 6000-s discharge cycle across a temperature range of 0 °C to 50 °C [17]. These capabilities make Transformers a robust and efficient alternative for time series prediction tasks. However, in the context of SOC prediction, where data often exhibit long-range temporal dependencies and require accurate multi-step forecasting, standard Transformer models show limitations in both modeling capacity and efficiency. As pointed out by Zhou et al. [18], Transformers suffer from quadratic computational complexity and error accumulation in autoregressive decoding, making them less suitable for long-horizon time series prediction. They design the informer architecture, incorporating probabilistic self-attention and attention distillation mechanisms. These innovations significantly reduce computational costs while improving predictive performance for tasks involving long sequences. The sparsely optimized Informer is employed for the SOC estimation throughout the discharge process over 10,000 s. This optimization enhances the accuracy of the SOC estimation by 0.27% [19]. While the Informer model has demonstrated remarkable capabilities in time-series forecasting, its standard version primarily focuses on capturing dependencies between temporal points within sequences, thereby exhibiting limitations in extracting local sequence features. Although the model demonstrates relative insensitivity to localized environmental fluctuations, its feature extraction performance from historical data warrants further enhancement [20]. Studies have shown that Informer-based models are increasingly integrated with other techniques, demonstrating outstanding performance in battery SOC prediction. In lithium-ion and LFP battery SOC estimation, combining Informer with LSTM, CNN, or Hampel filters has significantly improved accuracy, enhancing robustness under diverse conditions [16,21,22].

1.2. Research Gap and Method Proposal

First, although numerous studies have focused on SOC estimation, many rely heavily on simulated datasets or controlled laboratory environments, which limits the applicability of their findings to real-world driving conditions [23]. Meanwhile, the current data-driven SOC prediction is only single-step prediction; it does not perform multi-step prediction. Finally, existing methods still require significant improvements in capturing the diversity and complexity of SOC data, which typically comprise short-term fluctuations, long-term trends, and periodic patterns. Most current approaches lack explicit mechanisms to model fine-grained and multi-scale temporal dependencies, resulting in suboptimal performance when faced with dynamic or irregular driving conditions. This limitation hinders their ability to generalize across different vehicle types, battery chemistry, and driving conditions, thereby reducing robustness under cross-domain deployment.

Based on the aforementioned analysis, this study adopts the Informer architecture as the core backbone network and selects wavelet convolutions as the embedding layer of the Informer architecture. This integration enhances the model’s sensitivity to frequency-domain features, enabling more effective feature extraction and a deeper understanding of complex signals [24]. In addition, we incorporate a LightGBM feature selector within the embedding pipeline to identify and retain the most informative input variables, thereby improving both model efficiency and interpretability [25]. Finally, inspired by edge enhancement techniques in 2D image processing [26], we propose a temporal edge enhancement (TEE) module, which is integrated into the sparse attention mechanism to emphasize critical fine-grained temporal variations. This design aims to improve the model’s sensitivity to subtle transitions in SOC dynamics, thereby enhancing the overall prediction accuracy.

1.3. Key Contribution and Paper Organization

The main contributions are as follows:

(1)

A novel SOC prediction model, the Wavelet-Guided Temporal Feature Enhanced Informer (WG-TFE-Informer), is proposed for multi-step forecasting tasks to enhance noise robustness and enable the efficient extraction of multi-scale temporal features.

(2)

A temporal edge enhancement (TEE) module is designed and integrated into the sparse attention mechanism to improve the model’s sensitivity to fine-grained temporal variations, thereby enhancing its ability to capture subtle sequential dynamics and improving overall prediction performance.

(3)

A comprehensive SOC prediction framework is constructed, which incorporates battery characteristics, driver behavior, and environmental factors such as terrain. The model achieves a mean relative error (MRE) of 0.21% for short-term predictions (1 min) and maintaining minimal error fluctuation at just 0.62% for long-term predictions (20 min), showcasing robust multi-scale prediction capability.

(4)

Ablation experiments are conducted to evaluate the contributions of the modules. Results show a significant improvement in prediction accuracy, with the MRE reduced from 3.06% to 0.89%, under 20-min SOC prediction, clearly outperforming baseline models and confirming the effectiveness and practical value of the proposed approach.

The rest of this paper is organized as follows: Section 2 describes the construction of the input features for the model. Section 3 presents the overall architecture of the model. Additionally, Section 4 indicates the results and discussion of research. Finally, Section 5 draws the conclusions.

2. SOC Estimation Factor

Given the complexity and diversity of the parameters involved in SOC prediction, achieving high accuracy necessitates a comprehensive consideration of the multiple factors that influence SOC. These influencing factors are systematically incorporated through the feature engineering process. This section introduces the multi-source dataset, describes the structure of the extracted variables, and outlines the data pre-processing pipeline employed in this study. The key features are categorized into four groups: battery system indicators, driver behavior characteristics, environmental conditions, and terrain-related factors. Furthermore, the SOC sequences are reconstructed to ensure the continuity, consistency, and completeness of the model inputs.

2.1. Vehicle Operating Data

This study utilizes real-world data from 1000 plug-in electric vehicles provided by an automaker in southern China. The dataset spans October 2024 to May 2025, which was collected via onboard acquisition systems following the GB/T 32960 standard protocol [27]. with a sampling frequency of 0.1 Hz. The collected data cover a wide range of operational and environmental conditions, making it highly representative of real-world electric vehicle usage patterns. For each vehicle, approximately 1.3 to 1.5 million data records were collected during the observation period.

According to the GB/T 32960 transmission protocol and its supplementary agreements, a total of 38 driving-related features are recorded. A representative subset of variables extracted from the original message frames is summarized in

Table 1. Categorized descriptions of main data fields collected during vehicle operation.

Field Name	Description	Example
Battery and Power System
batt_SOC	Battery state of charge (%)	72
batt_vol	Total battery voltage (V)	558.2
main_batt_cur	Main motor battery current (A)	135.6
cell_vol_min	Minimum cell voltage (V)	3.251
cell_vol_max	Maximum cell voltage (V)	3.497
cell_temp_min	Minimum battery cell temperature (°C)	21
cell_temp_max	Maximum battery cell temperature (°C)	35
main_motor_temp	Main motor temperature (°C)	56
main_motor_rs	Main motor rotational speed (rpm)	1840
Driver Behavior Features
acc_pedal	Accelerator pedal position (%)	43
brake_pedal	Brake pedal engagement status	1
turn_sharp_freq	Frequency of sharp turns (times/min)	3
Terrain and Spatial Context
elevation	Vehicle elevation (m)	135
direction	Driving direction angle (°)	185

. In addition to capturing indicators directly related to the battery’s state of charge (SOC), such as voltage and current, the dataset also includes features that reflect driver behavior—such as accelerator pedal position and brake pedal engagement—as well as directional changes used to construct indicators like sharp turn frequency. Moreover, positional and elevation data are incorporated to provide a more comprehensive spatial and contextual understanding of vehicle operation.

2.2. Environmental Data

Previous studies have demonstrated that warm air generates lower aerodynamic drag compared to cold air [28], which is often associated with increased electrical losses. We examined the dependence of the battery’s SOC decline rate on ambient temperature using one year of data from a single vehicle, as shown in Figure 2. The results indicate that the SOC drops more rapidly under cooler conditions. However, excessively high perceived temperatures may lead to the activation of air conditioning systems, thereby reducing overall energy efficiency. Furthermore, related research has indicated that the driver’s line of sight can significantly influence braking and acceleration performance [29]. Given these observations, it is essential to account for environmental factors in energy consumption analysis. The weather data used in this study, comprising 18 distinct features, were sourced from the Visual Crossing platform (https://www.visualcrossing.com, accessed on 15 July 2025).

Table 2. Descriptions of partial environmental weather-related data fields.

Field Name	Description	Example
temp	Ambient temperature (°C)	24.6
dew	Dew point temperature (°C)	18.3
humidity	Relative humidity (%)	76
precip	Precipitation amount (mm)	1.2
windspeed	Wind speed (km/h)	13.5
winddir	Wind direction (°)	220
visibility	Visibility (km)	10.0
feelslike	Feels-like temperature (°C)	26.1

presents a selected subset of these variables.

2.3. Data Pre-Processing

After acquiring the raw data, data pre-processing becomes a fundamental step to ensure the reliability of subsequent analyses and the stability of model performance. In real-world driving conditions, raw data are highly susceptible to disturbances caused by terminal device malfunctions, bus signal faults, or communication errors. Additionally, the sensors themselves may introduce non-linear distortions, calibration biases, or response delays, which further exacerbate temporal drifts and degrade data accuracy. During storage and transmission, data distortion, loss, and format corruption are also inevitable due to various external and internal factors [30]. Such multi-source disturbances result in highly heterogeneous data quality. Particularly for modeling tasks involving neural networks—where input sensitivity is critical—poor-quality data can significantly impair both convergence and generalization capabilities.

Therefore, before proceeding to the modeling stage, a systematic pre-processing strategy is applied based on data transmission protocols and acquisition specifications. The detailed process is described as shown in Figure 3.

Step 1: Data Cleaning

Raw message data are first converted into a decimal format suitable for subsequent processing. Given that noise and errors may be introduced during data acquisition and transmission, data cleaning is a critical step to ensure data quality and the reliability of subsequent analysis. The cleaning process includes removing duplicate records, detecting and correcting outliers, and imputing missing values.

Step 2: Segmentation of Continuous Driving

Based on the vehicle status and charging status fields, only records where the vehicle is in a started state and not undergoing charging are selected for further analysis and model development. A continuous driving segment is defined as one in which the time gap between consecutive records is less than 60 s, and the segment contains at least 100 data points. Data points with vehicle speed lower than 10 km/h are removed, as they typically correspond to idling, parking, or crawling and introduce noise into the analysis.

Step 3: Environmental Data Alignment

Simultaneously, hourly weather data were obtained from the Visual Crossing platform (https://www.visualcrossing.com, accessed on 15 July 2025) and temporally aligned with the vehicle timestamp data to facilitate an integrated analysis of environmental influences. To be consistent with the 10-s sampling interval of driving data, the Lagrange interpolation method is used to interpolate it. Since the weather rarely fluctuates significantly in such a short time of one day, the interpolation results are sufficiently accurate to fulfill the research objectives and effectively capture the essential characteristics of the actual weather patterns [31].

Step 4: Characteristic variable selection

To reduce the computational burden while keeping the estimation accuracy, based on the pre-filtered dataset, Pearson correlation analysis was first employed to identify optimal input features that exhibit a significant linear relationships with SOC. The Pearson correlation coefficient is defined as

$$r={\displaystyle \frac{{\sum }_{i=1}^n(x_i-\overline{x})(y_i-\overline{y})}{\sqrt{{\sum }_{i=1}^n{(x_i-\overline{x})}^2}·\sqrt{{\sum }_{i=1}^n{(y_i-\overline{y})}^2}}}$$

(1)

where n is the number of observations, $x_i$ is the value of variable x at the i-th observation, and $y_i$ is the value of variable y at the i-th observation.

However, Pearson analysis is limited in its ability to capture potential non-linear or monotonic associations within the data. To address this limitation, Spearman correlation analysis was further introduced as a complementary approach. The Spearman rank correlation coefficient is defined as

$$\rho =1-{\displaystyle \frac{6\sum d_i^2}{n(n^2-1)}}$$

(2)

where $d_i$ is the difference between the ranks of each observation in the two variables, and n is the number of observations.

Spearman analysis is capable of revealing monotonic trends between variables and SOC regardless of whether the relationships are linear.

As shown in Figure 4, the top 10 features with the highest Pearson and Spearman correlations with SOC are presented. Figure 4a illustrates the Spearman correlation heatmap of the top 10 variables, reflecting monotonic relationships among features. Figure 4b shows the Pearson correlation heatmap of the top 10 variables, capturing linear dependencies. By jointly analyzing the results of both correlation methods, the most important input features were selected for model development.

By integrating the results from both methods and screening out variables with low correlation coefficients (<0.3), a more representative and computationally efficient set of input features was ultimately determined for the dataset. Based on the selection outcome, for example, vehicle HYBABA140M1000018 yielded 12 selected driving-related variables and 5 weather-related variables as the final input features.

2.4. SOC Reconfiguration

Due to the limited precision of onboard sensors, most of the collected SOC values are integers, which inevitably contain sensor acquisition errors and battery model uncertainties. To enable high-precision SOC estimation, Kalman filtering is applied to post-process the raw SOC data. At each sampling time, the filter adjusts the SOC estimate by comparing the predicted voltage with the observed voltage.

The Kalman filter is a widely used state estimation algorithm and has been successfully applied in the real-time SOC estimation for electric vehicles [32]. One of its most significant advantages is its self-correcting nature, allowing it to tolerate high current fluctuations during dynamic operating conditions. The general form of the KF is expressed as

$$\begin{array}{cc}\hfill & {\widehat{x}}_{k|k-1}=A{\widehat{x}}_{k-1}+B{u}_{k-1}\hfill \end{array}$$

(3)

$$\begin{array}{cc}\hfill & P_{k|k-1}=A{P}_{k-1}{A}^T+Q\hfill \end{array}$$

(4)

$$\begin{array}{cc}\hfill & K_k=P_{k|k-1}{H}^T{(H{P}_{k|k-1}{H}^T+R)}^{-1}\hfill \end{array}$$

(5)

$$\begin{array}{cc}\hfill & {\widehat{x}}_k={\widehat{x}}_{k|k-1}+K_k(y_k-H{\widehat{x}}_{k|k-1})\hfill \end{array}$$

(6)

$$\begin{array}{cc}\hfill & P_k=(I-K_{k}H)P_{k|k-1}\hfill \end{array}$$

(7)

where ${\widehat{x}}_{k|k-1}$: predicted state, A: state transition matrix, B: control matrix, $u_{k-1}$: control input, $P_{k|k-1}$: predicted covariance, Q: process noise, $K_k$: Kalman gain, H: observation matrix, R: measurement noise, $y_k$: measurement, ${\widehat{x}}_k$: updated state, $P_k$: updated covariance, I: identity matrix.

The results after Kalman filtering are illustrated in Figure 5, and it can be observed that the reconstructed SOC values align more closely with the actual vehicle operation patterns. This alignment corresponds to the input feature scale, enabling subsequent models to capture finer details more effectively.

3. Proposed Framework

Following the dataset construction in Section 2, integrating the correlations between variables and extracting multi-scale temporal features from dynamic driving environments are foundational for achieving high-accuracy SOC predictions. Therefore, this section presents our enhanced forecasting framework, which builds upon the Informer architecture. By incorporating LightGBM and wavelet convolutions, the model strengthens multi-scale feature extraction and temporal representation. The extracted features are then integrated into the improved Informer framework, where a TEE block is combined with the ProbSparse self-attention mechanism to highlight temporal edge information. Finally, the refined features are processed through the encoder–decoder structure to generate multi-step SOC predictions. A detailed explanation of each component in the proposed model is provided in the following subsections.

3.1. Informer

Based on the preceding analysis, there has been limited research on the multi-step forecasting of SOC, and given the superior capability of the Informer model in long-sequence prediction tasks [18], we adopt the Informer model as the baseline architecture to address the challenge of multi-step SOC forecasting for long time series data. The Informer model enhances long input–output sequence prediction through its probabilistic sparse self-attention mechanism and self-attention distillation approach. Its architecture is illustrated in Figure 6.

In this study, the Informer model serves as the foundation due to its established proficiency in capturing long-term dependencies in time series. Building upon this robust baseline, we propose further enhancements aimed at improving predictive performance for SOC forecasting tasks.

3.1.1. ProbSparse Self-Attention

To address the quadratic computational complexity of standard dot-product self-attention, the Informer model introduces a novel ProbSparse self-attention mechanism. This mechanism significantly reduces computational and memory costs by selecting only the most “informative” query vectors for full attention calculation. The informativeness of each query is measured by its sparsity score, which evaluates the divergence between the query’s maximum attention and its average attention across all keys.

Formally, the sparsity measurement function is defined as

$$\begin{array}{c}\hfill \overline{M}(q_i,K)=\underset{j}{max}\left\{{\displaystyle \frac{q_i{k}_j^{\top }}{\sqrt{d}}}\right\}-{\displaystyle \frac{1}{L_K}}\sum _{j=1}^{L_K}{\displaystyle \frac{q_i{k}_j^{\top }}{\sqrt{d}}}\end{array}$$

(8)

where $q_i$ is the i-th query vector, $k_j$ is the j-th key vector, $L_K$ is the length of the key sequence, and d is the dimension of the queries and keys.

Based on Equation (8), only the top-u query vectors with the highest sparsity scores are retained and denoted as $\overline{Q}$. The remaining less informative queries are approximated by assigning them their average attention values, thus avoiding full dot-product computations. The resulting attention output is computed as

$$\begin{array}{c}\hfill A(Q,K,V)=\mathrm{Softmax}\left({\displaystyle \frac{\overline{Q}{K}^{\top }}{\sqrt{d}}}\right)V\end{array}$$

(9)

where K and V represent the key and value matrices, respectively.

To ensure numerical stability and minimize information loss, the discarded queries are filled with zero attention scores. Since $\overline{M}(q_i,K)$ is insensitive to zero values, this approximation is stable and effective. In practice, the length of the queries and keys is usually equal, i.e., $L=L_Q=L_K$. Under this mechanism, the time and space complexity of self-attention is reduced from $𝒪\left(L^2\right)$ to $𝒪(L_{K}log{L}_Q)$, enabling efficient long-sequence modeling in SOC estimation while preserving critical long-range dependencies.

3.1.2. Encoder Distillation Mechanism

The encoder architecture of Informer, as shown in the left part of Figure 6, is designed to capture long-range dependencies and deep temporal features. Following the ProbSparse mechanism, query vectors deemed unimportant are not explicitly used in attention computation but are approximated through averaging. To further emphasize the dominant attention features and suppress noise, convolutional and pooling operations are integrated between encoder layers to distill feature maps.

This distillation enhances salient patterns and reduces redundancy, thereby improving the model’s capacity to represent informative temporal features. The transformation from encoder layer j to layer $j+1$ is defined in Equation (10):

$$\begin{array}{c}\hfill X_{j+1}^t=\mathrm{MaxPool}\left(\mathrm{ELU}\left(\mathrm{Conv}1\mathrm{d}\left({\left[X_j^t\right]}_{AB}\right)\right)\right)\end{array}$$

(10)

3.2. Improved Encoding Structure

To overcome the limitations of conventional encoding strategies in modeling complex temporal dependencies and feature interactions, we propose an enhanced encoding framework that replaces the original value encoding, positional encoding, and temporal encoding in the Informer architecture. This redesigned structure is tailored to better capture multi-scale temporal variations and domain-specific non-linear relationships inherent in SOC sequences in large-scale data scenarios.

3.2.1. LightGBM

Given the large-scale nature of the SOC dataset used in this study, it is essential to adopt an encoding method that balances both training efficiency and effective temporal feature extraction. LightGBM (Light Gradient Boosting Machine) is an efficient gradient boosting framework that is well suited for large-scale datasets, offering high training speed and strong predictive performance [33]. It improves upon traditional GBDT by adopting a histogram-based algorithm for split point selection and a leaf-wise growth strategy with depth control, thereby accelerating training and reducing overfitting.

LightGBM discretizes continuous feature values into k bins, transforming the range $[X_{min},X_{max}]$ into equal-width intervals of size

$$\begin{array}{cc}\hfill w& ={\displaystyle \frac{X_{max}-X_{min}}{k}}\hfill \end{array}$$

(11)

where w denotes the bin width. Each input value $X_i$ is then assigned to its corresponding bin as

$$\begin{array}{cc}\hfill \mathrm{bucket}\left(X_i\right)& =min\left\{k-1,⌊{\displaystyle \frac{X_i-X_{min}}{w}}⌋\right\}\hfill \end{array}$$

(12)

ensuring that values at the upper boundary ($X_i=X_{max}$) are consistently mapped to the last bin ($k-1$).

This histogram-based discretization substantially reduces both memory consumption and computational overhead. By shifting the computation from the raw data level to the bin level, the overall complexity is reduced from $O(\mathrm{data}\times \mathrm{features})$ to $O(k\times \mathrm{features})$, thereby achieving superior scalability. A schematic illustration of this optimization process is provided in Figure 7.

Building upon this efficient binning mechanism, LightGBM further enhances tree construction through a leaf-wise growth strategy. Unlike conventional level-wise approaches, which expand all nodes at the same depth simultaneously, the leaf-wise strategy prioritizes the leaf that yields the highest potential gain, thus improving both training efficiency and predictive accuracy:

$$\begin{array}{cc}\hfill G_{\mathrm{leaf}}& =max\left(\sum _{i\in \mathrm{leaf}}\mathrm{gain}\left(X_i\right)\right)\hfill \end{array}$$

(13)

Here, $G_{\mathrm{leaf}}$ represents the maximum aggregated gain among candidate leaves. The term leaf denotes a terminal node within the decision tree, while $i\in \mathrm{leaf}$ indexes the samples contained in that leaf. The function $\mathrm{gain}\left(X_i\right)$ measures the information gain associated with feature value $X_i$, which is typically computed from gradient and Hessian statistics. The $max(·)$ operator ensures that the split offering the largest overall gain is selected.

To avoid overfitting caused by excessively deep trees, LightGBM enforces a maximum tree depth constraint:

$$\begin{array}{cc}\hfill \mathrm{Depth}\mathrm{of}\mathrm{tree}& \le d_{\max }\hfill \end{array}$$

(14)

Here, $\mathrm{depth}\mathrm{of}\mathrm{tree}$ denotes the current depth of the decision tree (i.e., the number of levels from the root to the leaf), and $d_{\max }$ is a user-defined hyperparameter that limits tree depth. This constraint effectively balances model expressiveness with generalization capability, thereby stabilizing performance on unseen data.

Overall, the combination of histogram-based binning and leaf-wise tree growth allows LightGBM to achieve both high computational efficiency and strong predictive performance, making it particularly well suited for large-scale machine learning tasks.

Prior studies have demonstrated LightGBM’s utility in sequence modeling. Yang et al. [34] combined Transformer with LightGBM for mid-term load forecasting, while Hao et al. [35] integrated wavelet features with LSTM and LightGBM to improve water demand prediction. Inspired by these studies, we employ LightGBM as a data-driven temporal encoder, which is capable of capturing trends and periodicity in time-series data.

Formally, the LightGBM-based feature encoding is defined as

$$\begin{array}{c}\hfill X_{\mathrm{LG}}=\mathrm{LightGBMEncoder}\left(X\right)\end{array}$$

(15)

where $X_{\mathrm{LG}}$ represents temporal features extracted by LightGBM, capturing essential patterns such as trend and seasonality.

3.2.2. Wavelet Convolutions

While LightGBM demonstrates excellent performance in capturing global patterns and conducting effective feature selection—particularly for identifying trend-related components in large-scale SOC data—it lacks the capacity to learn localized, high-frequency temporal variations due to its tree-based structure. These finer-grained dynamics, however, are often crucial in characterizing the transient behaviors and non-linear shifts inherent in SOC sequences.

To address this limitation, we introduce a wavelet-based convolutional module [36] that complements LightGBM by enabling multi-scale temporal feature extraction. Unlike standard convolutional layers, wavelet convolutions leverage predefined basis functions to decompose input sequences across various temporal resolutions, thus capturing both long-term and short-term SOC dynamics with reduced computational overhead. This design enhances the model’s ability to recognize intricate temporal features that may be overlooked by gradient-boosting methods alone.

To construct a comprehensive temporal representation, we define two key components. First, $X_{\mathrm{WTconv}}$ represents the output from the wavelet convolutions module, which captures multi-resolution temporal features through wavelet-guided filtering. Then, this is combined with the previously defined $X_{\mathrm{LG}}$ to form a fused representation:

$$\begin{array}{c}\hfill X_{\mathrm{en}}=X_{\mathrm{WTconv}}+X_{\mathrm{LG}}\end{array}$$

(16)

This fused representation ($X_{\mathrm{en}}$) is then passed to the encoder, providing a multi-perspective temporal feature space that enhances forecasting performance. Notably, this design effectively replaces and extends beyond the conventional positional, value, and temporal embeddings (PE, VE, TE).

3.3. TEE Block

In SOC time-series data, critical transition points—such as sudden rises, sharp drops, or inflection segments—often encapsulate essential information related to battery dynamics, anomalies, or operational state changes. These “edges” in the temporal domain are crucial for accurate modeling and prediction. However, conventional time-series modeling approaches, particularly standard convolutional operations, inherently perform smoothing due to their sliding-window nature. As a result, they tend to attenuate these abrupt transitions, thereby limiting the model’s ability to capture such high-value features under rapidly changing conditions.

To address this challenge, we draw inspiration from edge enhancement techniques in image processing, particularly the method proposed in [26], where image boundaries are emphasized to preserve fine-grained spatial details. Analogously, we posit that enhancing edge-like features in SOC sequences can improve the model’s temporal sensitivity and predictive accuracy.

As shown in Figure 8, we propose a temporal edge enhancement module (TEE), which explicitly extracts and integrates edge features along the temporal axis to amplify critical transitions in SOC sequences, thereby enhancing the representational capacity of the network for downstream time-series tasks.

3.3.1. Edge Feature Extraction

In time-series data processing, edge features refer to the rapid changes in the signal, such as abrupt jumps or spikes. The first step in the TEE module is to extract these edge features by applying an average pooling layer to the input features. This smoothing operation captures the local temporal trends. Specifically, an average pooling layer is applied along the time dimension to extract the local mean. Next, the module computes the difference between the original input and the smoothed version, which highlights the rapid changes and produces the edge features.

3.3.2. Edge Enhancement Convolution

After extracting the edge features, a $1\times 1$ convolution layer is applied to process the edge features. The purpose of this convolution is to perform a weighted sum of the features across the channel dimension, effectively fusing information from different channels. This operation enhances the edge features without altering the time step length, thereby amplifying the expression of the edge features.

3.3.3. Residual Connection and Output

To avoid losing the original information during the enhancement process, the TEE module employs a residual connection. The edge-enhanced features are added to the original input features, allowing the model to use both the original and enhanced features simultaneously. This structure, similar to the residual connections in ResNet architectures, helps stabilize training and accelerates convergence.

To validate the efficiency of the proposed TEE module in enhancing the representation of temporal edge information, we conducted a visual comparison between the original attention heatmap and the enhanced attention heatmap, as shown in Figure 9. It is evident that the introduction of the TEE module leads to significant changes in the attention heatmap. The enhanced heatmap (Figure 9 right) shows higher attention values distributed more cohesively, indicating that the model can now consider a broader range of contextual information for predictions. In contrast, the original attention heatmap (Figure 9 left) displays a more confined and less intense distribution of attention, suggesting a relatively limited understanding of temporal features by the model.

This visualization strongly demonstrates the benefits of incorporating the TEE module into the model architecture. It not only improves the model’s ability to capture changes in temporal features but also enhances its understanding of complex patterns, thereby contributing to an overall improvement in model performance.

3.4. WG-TFE-Informer Network

We propose an improved version of the original Informer model, named WG-TFE-Informer, as illustrated in Figure 10. The WG-TFE-Informer architecture consists of three main components. In the encoding layer, we incorporate both Wtconv encoding and LightGBM encoding to extract implicit temporal features and construct the inputs for the encoder and decoder. Additionally, the embedding output is projected to a channel dimension of 512 to enhance feature representation.

In the encoder module, we integrate the TEE block with ProbSparse Self-Attention, which selectively retains the most influential attention weights. This design significantly reduces computational complexity while focusing on the most relevant interactions, thereby improving model efficiency without compromising performance. To further enhance feature compactness, we introduce a distillation operation within the encoder, which is aimed at extracting core features and effectively compressing the temporal dimension of the input. This distillation process involves applying a 1D convolution across each time step, followed by Batch Normalization, and finally using a MaxPooling layer to reduce the sequence length by half. This results in a more compact and efficient representation of temporal data.

In the decoder module, historical target information is provided as input to the ProbSparse Self-Attention mechanism to ensure that future data remain inaccessible during prediction. Subsequently, a cross-attention layer attends to the encoder outputs, allowing the decoder to condition its predictions on the encoded input features. When processing long sequences, the model adapts dynamically during training, enabling it to capture essential underlying patterns that are critical for accurate SOC prediction. After several layers of attention processing, the decoder produces the final output corresponding to future time steps.

4. Experiments Design

In this section, we establish a comprehensive experimental framework to evaluate the effectiveness of the proposed WG-TFE-Informer model. First, we validate the model’s performance on publicly available benchmark datasets, covering both short- and long-term forecasting horizons. This step lays a solid foundation for subsequent evaluations on real-world SOC prediction tasks.

Second, extensive comparative experiments are conducted using real SOC datasets under varying prediction lengths with multiple baseline models incorporated for reference. The results demonstrate the superior forecasting performance of our model across different temporal resolutions. To ensure consistency and interpretability, six representative electric vehicles are selected for detailed result presentation.

Finally, ablation studies are performed to assess the individual contributions and effectiveness of key modules within the proposed architecture, particularly in capturing critical SOC-related temporal features.

4.1. Assessment of Model Validity

To validate the effectiveness of the proposed WG-TFE-Informer architecture, we first conducted experiments on the Panasonic 18650PF Li-ion Battery dataset. The dataset is a benchmark dataset that contains detailed data related to the internal charging and discharging behavior of lithium-ion batteries. Each data point includes the time, current, voltage, temperature and SOC, and it encompasses nine driving cycles. These driving cycles accurately reflect real-world driving conditions, making the dataset highly suitable for the preliminary validation of our proposed model. To provide a comprehensive comparison, both deep learning and classical machine learning models were included in our experiments under the same training, validation, and testing protocols as described in the referenced benchmark study [37]. The comparison results are summarized in

Table 3. Comparison of estimation performance on Panasonic 18650PF dataset.

Algorithm	MAE (%)	MAX (%)
ANN [38]	4.505	–
LR [39]	3.916	–
SVR [39]	3.273	–
DNN [40]	2.502	–
LSTM [41]	1.606	–
SBLSTM [42]	1.20	6.00
BLSTM-ED [43]	1.07	4.62
SPA-ED [37]	0.77	1.98
WG-TFE-Informer	0.28	0.54

.

Since the aforementioned methods primarily focus on single-step prediction, we further evaluate the multi-step forecasting capability of the proposed model using the public Weather dataset. Although SOC and weather prediction differ in physical dynamics, both are representative long-range time series tasks, and this auxiliary test helps evaluate the model’s temporal generalization ability. The performance evaluation metrics are illustrated in Figure 11.

Experimental results demonstrate that the proposed WG-TFE-Informer model exhibits significant performance advantages in both single-step and multi-step prediction tasks. Compared with baseline models, it achieves notably higher prediction accuracy. These results validate the effectiveness of the proposed wavelet-guided temporal feature extraction module and the enhanced attention mechanism. Specifically, the wavelet-guided module enables a more precise capture of both local and global dependencies in time series data, while the improved attention mechanism further enhances the model’s capability to model long-term dependencies. The validation results on public benchmark datasets confirm the applicability and effectiveness of WG-TFE-Informer for SOC prediction, establishing a solid foundation for subsequent experiments.

4.2. Multi-Step SOC Forecasting and Model Comparison on Real-World Data

We propose an WG-TFE-Informer architecture for the multi-step prediction of SOC in electric vehicles, which was designed for real-world driving conditions. Unlike conventional methods that focus on estimating the current SOC, our approach aims to forecast future SOC trajectories over extended horizons, thereby enabling proactive energy management. This directly addresses the gap in existing studies that predominantly rely on short-term or single-step estimation [40,44].

To assess model performance across different forecast horizons, we compare multiple deep learning models under consistent experimental settings, focusing on prediction window sizes (PWSs) of $\{6,30,60,120\}$, which span from short-term control to long-term energy management.

In addition to the proposed Informer, the evaluation includes several baseline models widely adopted in SOC estimation research, such as the GRU [45], and hybrid variants including LSTM-GRU [46] and LSTM-Transformer [47].

All models are trained and validated using one-year real-world operational data, as detailed in Section 2. The dataset is split into training, validation, and testing sets in a ratio of 8:1:1. The mean relative error (MRE) is employed as the primary evaluation metric:

$$\mathrm{MRE}={\displaystyle \frac{1}{n}}\sum _{t=1}^n\left|{\displaystyle \frac{{\mathrm{SOC}}_{pt}-{\mathrm{SOC}}_{rt}}{{\mathrm{SOC}}_{rt}}}\right|\times 100\%$$

(17)

where n denotes the number of samples, ${\mathrm{SOC}}_{pt}$ represents the predicted state of charge (SOC) at time t, and ${\mathrm{SOC}}_{rt}$ represents the corresponding true (measured) SOC at time t.

To comprehensively evaluate the predictive performance of various models across different temporal scales, this study first presents in Figure 12 a large-scale comparison involving 1000 real-world electric vehicles. The figure summarizes the mean relative error (MRE) across four prediction window sizes (PWS = 6, 30, 60, 120), corresponding to 1-min, 5-min, 10-min, and 20-min horizons, respectively. As shown in Figure 12, the proposed model exhibits significantly more stable prediction performance across all forecasting horizons. Specifically, its MRE increases only modestly from 0.37% at PWS = 6 to 0.95% at PWS = 120, reflecting a total increase of just 0.58 percentage points. In contrast, models such as GRU and LSTM-GRU experience much steeper error growth. For example, GRU’s MRE rises from 1.98% to 4.43%, with an increase of 2.45 percentage points, while LSTM-GRU grows by 0.81 percentage points (from 0.85% to 1.66%).

This clearly demonstrates that the proposed WG-TFE-Informer maintains superior prediction stability under increasing time uncertainty. Its ability to effectively model long-range temporal dependencies allows it to outperform conventional architectures, particularly in long-horizon scenarios where error accumulation typically poses a challenge.

To enhance the interpretability of model behavior over different time horizons, Figure 13 further selects six representative vehicles for detailed comparison. These subfigures illustrate the MRE performance of each model under the same four prediction windows. Additionally, Figure 14 provides an in-depth visualization of prediction trajectories and corresponding absolute errors for Car1 under varying forecast lengths. Each subplot adopts a dual-panel design: the upper panel compares the predicted SOC trajectories of all models against ground truth, while the lower panel depicts the absolute prediction errors.

As shown in the figures, all models perform best at short-term forecasting (PWS = 6, equivalent to 1 min) with WG-TFE-Informer achieving the lowest MRE of just 0.21% on Car4. However, as the prediction horizon increases, a consistent degradation in model performance is observed. This is primarily attributed to reduced information density and increased temporal uncertainty in longer sequences, which complicates accurate learning. In particular, traditional recurrent models (e.g., LSTM-GRU and GRU) exhibit significant error accumulation over extended prediction horizons. For example, on Car1, increasing the PWS from 6 to 120 leads to MRE increases of 0.75% and 2.5% for LSTM-GRU and GRU, respectively. In contrast, attention-based models demonstrate superior stability in capturing long-range dependencies. Notably, WG-TFE-Informer maintains exceptional robustness, with its MRE increasing only marginally from 0.45% to 1.02%—a gap of just 0.62%—as the prediction window expands from 1 min to 20 min. Collectively, these results confirm that WG-TFE-Informer consistently outperforms baseline models in both short- and long-term forecasting tasks. Its ability to accurately track dynamic SOC trajectories across complex real-world scenarios highlights its robustness, generalization capability, and strong potential for practical deployment in electric vehicle battery management systems.

It is worth noting that as shown in Figure 14, the peak in the absolute error observed at certain stages is mainly caused by a sudden change in the battery state, where the vehicle temporarily switched from discharging to charging. This transition, coupled with specific driving behaviors, leads to a short-term mismatch between the model and the actual SOC. Since the proposed model is primarily aimed at predicting the discharging state for remaining range estimation, such transient deviations do not affect the overall accuracy. The model rapidly restores its prediction performance in the subsequent discharging period, indicating strong robustness under dynamic operating conditions.

4.3. Modular Ablation Study

To evaluate the effectiveness and robustness of each component in the proposed model, we conducted ablation studies. This ensures that the observed improvements are not specific to a single vehicle but rather hold across different driving conditions.

Table 4. The impact of different modules on estimation accuracy.

Model	Wavelet Convolutions	LightGBM	TEE	$\overline{\mathbf{MRE}}$ (%)
Informer	✗	✗	✗	3.06
Model1	✓	✗	✗	2.59
Model2	✗	✓	✗	3.03
Model3	✗	✗	✓	2.27
Model4	✓	✓	✗	1.98
Model5	✓	✗	✓	1.56
Model6	✗	✓	✓	2.23
WG-TFE-Informer	✓	✓	✓	0.89

reports the performance metrics of the full model and its ablated variants across the selected vehicles under PWS = 120.

As shown in Table 4, the complete model achieves an MRE of 0.89%, representing a 72.1% improvement over the baseline model (3.06%). The novel improved encoding structure, consisting of Wavelet Convolution and LightGBM, demonstrates its effectiveness in time-frequency feature extraction and feature selection by reducing the MRE by 35.3% (to 1.98%) when used independently (Model4). The TEE module, serving as an enhancement component for sparse attention mechanisms, validates its capability in capturing temporal edge information by achieving a 25.8% MRE reduction (to 2.27%) when operating alone (Model3). Notably, the synergistic operation of the novel embedding layer and TEE module further reduces the MRE to 0.89%, representing an additional 45.1% improvement over improved encoding structure, which fully demonstrates the advantages of cooperative optimization between feature embedding and attention mechanisms. These results confirm that the proposed WG-TFE-Informer framework can effectively improve the SOC prediction accuracy.

5. Conclusions

This paper proposes a multi-step forward prediction method for electric vehicle battery state of charge (SOC) based on an improved WG-TFE-Informer model. The goal is to enhance SOC prediction accuracy under complex driving conditions and thereby alleviate users’ range anxiety. The proposed framework comprehensively incorporates vehicle parameters, environmental conditions, and individual driving styles to construct a deep time-series prediction model with strong generalization capability.

To validate the model performance, we trained the WG-TFE-Informer model using one year of real-world operational data from 1000 electric vehicles with multiple PWS values. The experimental results demonstrate that the WG-TFE-Informer model exhibits outstanding performance advantages in SOC prediction. The model achieved the lowest MRE of 0.21% in short-term prediction (PWS = 6), while showing only a 0.62% error increase in long-term prediction (PWS = 120), consistently outperforming mainstream traditional energy consumption prediction models. Through training with large-scale real-world operational data and multi-prediction-dimension comparisons, the model demonstrates exceptional prediction accuracy and robustness.

To further assess the contribution of model components, ablation studies were conducted. The results show that the proposed enhancements significantly improve the model’s ability to capture long-term dependencies and subtle short-term variations in time series data. The model maintained stable prediction performance across datasets of varying sizes, confirming its superiority over the original Informer architecture in both scalability and accuracy.

Future work will focus on the following aspects:

• Incorporation of battery health (SOH): With the continuous accumulation of vehicle operation data, SOC prediction will be extended to include battery degradation effects by integrating SOH into the modeling framework. This will allow dynamic model updates across the battery’s life cycle.
• Multi-vehicle generalization evaluation: More electric vehicles with diverse driving behaviors and environmental conditions will be involved to assess the model’s adaptability and robustness across different geographies and user profiles.
• Federated learning deployment: A federated learning framework will be adopted to aggregate local model weights from individual vehicles, enabling cross-vehicle knowledge sharing and improving overall model generalization and security.

In conclusion, the proposed approach achieves significant improvements in SOC prediction accuracy, real-time performance, and scalability, laying a solid foundation for the development of next-generation intelligent battery management systems.