Electric vehicles (EVs) represent a pivotal advancement in sustainable transportation, with power batteries serving as their core component. The accurate estimation of State of Charge (SOC) and State of Health (SOH) is crucial for optimizing battery performance, ensuring safety, and extending lifespan. However, traditional methods often suffer from inefficiencies, poor real-time performance, and low accuracy due to challenges like data anomalies, multidimensionality, and temporal dependencies. In this paper, we propose a novel approach based on the KA Informer model to address these limitations and achieve precise SOC and SOH estimation for China EV battery systems.
The growing adoption of EVs underscores the importance of reliable battery management systems (BMS). Power batteries, typically composed of numerous cells in series or parallel configurations, are susceptible to degradation from factors such as temperature fluctuations, charge-discharge rates, and aging. SOC indicates the remaining usable charge relative to the maximum capacity, while SOH reflects the battery’s current maximum capacity compared to its initial rated capacity. Accurate estimation of these parameters is essential for preventing issues like thermal runaway and optimizing user experience, such as mitigating range anxiety. Existing methods, including model-based approaches like equivalent circuit models and data-driven techniques using machine learning, often struggle with computational complexity and adaptability to real-world conditions. For instance, methods relying on fixed activation functions in autoencoders or attention mechanisms in transformers may not fully capture long-range dependencies in time-series data. Our work introduces the KA Informer model, which integrates a Kolmogorov-Arnold-based stacked denoising autoencoder (KASDAE) for data cleaning and a Fourier-mixed window attention (FMWA) mechanism for enhanced sequence modeling, leading to superior performance in estimating SOC and SOH for EV power battery systems.
In the context of China EV battery development, the need for efficient and accurate estimation methods is paramount. Data collected from sensors—such as voltage, current, and temperature—often contain noise, missing values, and anomalies due to sensor faults or environmental interference. Traditional data cleaning techniques, like 3σ outlier detection or regression imputation, are inadequate for handling the nonlinear and time-dependent nature of battery data. Similarly, models such as Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and standard Transformer networks may not efficiently process long sequences or capture global patterns. Our KA Informer model overcomes these issues by leveraging advanced deep learning components. The KASDAE component utilizes learnable B-spline activation functions based on Kolmogorov-Arnold theory to clean and reconstruct data, while the FMWA-enhanced Informer model improves the capture of both local and global temporal dependencies. This results in faster and more accurate estimations, as validated through experiments on multiple datasets, including those from real-world EV power battery applications.
The remainder of this paper is organized as follows: We first detail the methodology, including the KASDAE model for data cleaning and the FMWA Informer for SOC and SOH estimation. Next, we present experimental results demonstrating the model’s performance across various temperatures and cycling conditions. Finally, we conclude with insights and future directions for China EV battery management.
Methodology
Our approach consists of two main components: the KASDAE model for data preprocessing and the FMWA Informer model for sequence prediction. The overall framework is designed to handle the challenges of EV power battery data, such as anomalies and long-range dependencies, by integrating novel techniques from deep learning and approximation theory.
KASDAE Model for Data Cleaning
Sensor data from EV power battery systems often include outliers and missing values due to operational variances. Traditional stacked denoising autoencoders (SDAE) use fixed activation functions, limiting their ability to model complex nonlinear relationships. Inspired by the Kolmogorov-Arnold representation theorem, which states that any multivariate continuous function can be expressed as a finite composition of univariate functions, we reformulate the SDAE architecture. The KASDAE model replaces standard weights with learnable B-spline activation functions, allowing for adaptive feature extraction and improved data reconstruction.
The Kolmogorov-Arnold theorem can be mathematically expressed as:
$$f(x_1, x_2, \ldots, x_n) = \sum_{q=1}^{2n+1} \Phi_q \left( \sum_{p=1}^{n} \phi_{q,p}(x_p) \right)$$
where $\Phi_q$ and $\phi_{q,p}$ are univariate functions. In the KASDAE, we implement this by decomposing the encoding and decoding processes using B-spline curves. For a given input $X = (x_1, x_2, \ldots, x_n)$ with added noise $\tilde{X}$, the encoding step is defined as:
$$H_{DE} = \sigma_{DAE} \left( W_{encoder} \tilde{x} + b_{encoder} \right)$$
where $W_{encoder}$ and $b_{encoder}$ are replaced by B-spline-based functions. The decoding step reconstructs the input as:
$$\hat{X} = \sigma_{DAE} \left( W_{decoder} H_{DE} + b_{decoder} \right)$$
To enhance model capacity, we employ grid expansion techniques during training. Initially, B-spline curves are defined with a coarse grid width $G_1$, and later refined to $G_2$ ($G_2 > G_1$) for finer granularity. This allows the model to progressively learn complex patterns without initial over-parameterization. The effectiveness of KASDAE in cleaning voltage data, for example, is demonstrated through reduced reconstruction errors compared to traditional methods, as summarized in Table 1.
| Method | MAE (%) | RMSE (%) | Time (s) |
|---|---|---|---|
| Traditional SDAE | 0.91 | 1.12 | 107 |
| KASDAE (Proposed) | 0.24 | 0.37 | 30 |
This table highlights the superiority of KASDAE in handling anomalies and missing data, which is critical for reliable SOC and SOH estimation in China EV battery applications.
FMWA Informer Model for SOC and SOH Estimation
The Informer model, a variant of the Transformer, addresses long-sequence prediction challenges but its multi-head ProbSparse self-attention (MPSSA) mechanism may overlook global dependencies. We propose the Fourier-mixed window attention (FMWA) to replace MPSSA, enhancing the model’s ability to capture both local and global temporal patterns in EV power battery data.
The FMWA consists of two modules: windowed self-attention and Fourier mixing. The windowed self-attention divides the input sequence $X \in \mathbb{R}^{L \times d_{model}}$ into $N$ segments, where $L$ is the sequence length and $d_{model}$ is the model dimension. For each segment, attention is computed as:
$$\text{Attention}(Q_i, K_i, V_i) = \text{Softmax}\left(\frac{Q_i K_i^T}{\sqrt{d_k}}\right) V_i$$
where $Q_i$, $K_i$, and $V_i$ are the query, key, and value matrices for the $i$-th segment. The outputs are concatenated to form the windowed attention score. The Fourier mixing module applies a Fourier transform along the time and model dimensions to capture global interactions, taking the real part of the result to maintain computational efficiency. The combined FMWA mechanism is integrated into the Informer’s encoder and decoder, resulting in the FMWA Informer model.
The overall computation for the FMWA Informer can be summarized as:
$$Y = \text{FMWAInformer}(X) = f_{decoder} \left( f_{MHSA} \left( f_{FM} \left( f_{WA}(X) \right) \right) \right)$$
where $f_{WA}$ denotes windowed attention, $f_{FM}$ is Fourier mixing, and $f_{MHSA}$ is multi-head self-attention. This structure enables efficient processing of long sequences, which is essential for real-time SOC and SOH estimation in EV power battery systems.
Experimental Results and Analysis
We evaluated the KA Informer model on multiple datasets, including the University of Maryland PL sample battery dataset, Oxford University battery dataset, and Beijing Institute of Technology Nature dataset. These datasets cover various temperatures (-40°C to 50°C) and cycling conditions, reflecting real-world scenarios for China EV battery operations. Performance metrics included Mean Absolute Error (MAE) and Root Mean Square Error (RMSE), defined as:
$$\text{MAE} = \frac{1}{m} \sum_{i=1}^{m} |y_i – \hat{y}_i|$$
$$\text{RMSE} = \sqrt{\frac{1}{m} \sum_{i=1}^{m} (y_i – \hat{y}_i)^2}$$
where $y_i$ is the actual value, $\hat{y}_i$ is the predicted value, and $m$ is the number of samples.
SOC and SOH Estimation Under Varied Temperatures
The KA Informer model demonstrated robust performance across different temperatures, which is critical for EV power battery reliability in diverse climates. For instance, at -40°C, the model achieved SOC MAE and RMSE values of 0.27% and 0.36%, respectively, and SOH MAE and RMSE of 0.51% and 0.65%. Similar results were observed at higher temperatures, such as 40°C and 50°C, as shown in Table 2.
| Temperature (°C) | Battery Cell | SOC MAE (%) | SOC RMSE (%) | SOH MAE (%) | SOH RMSE (%) |
|---|---|---|---|---|---|
| -40 | Cell7 | 0.27 | 0.36 | 0.51 | 0.65 |
| 20 | Cell3 | 0.25 | 0.35 | 0.54 | 0.60 |
| 50 | Cell8 | 0.29 | 0.38 | 0.55 | 0.67 |
These results indicate that the model maintains high accuracy even under extreme conditions, making it suitable for China EV battery applications where temperature variations are common.
Comparative Analysis with Baseline Models
We compared the KA Informer with state-of-the-art models, including standard Informer, Transformer, LSTM, GRU, and ELM. The KA Informer consistently outperformed these models in terms of accuracy and computational efficiency. For example, on the Oxford dataset, the KA Informer achieved SOC MAE and RMSE of 0.24% and 0.37%, respectively, while the next best model (Informer) had errors of 0.49% and 0.61%. A summary of the comparison is provided in Table 3.
| Model | SOC MAE (%) | SOC RMSE (%) | SOH MAE (%) | SOH RMSE (%) | Training Time (s) |
|---|---|---|---|---|---|
| ELM | 1.04 | 1.12 | 1.14 | 1.25 | 2100 |
| LSTM | 0.77 | 0.86 | 0.94 | 1.11 | 1974 |
| GRU | 0.75 | 0.83 | 0.92 | 1.05 | 1824 |
| Transformer | 0.64 | 0.76 | 0.82 | 0.94 | 1518 |
| Informer | 0.49 | 0.61 | 0.72 | 0.81 | 906 |
| KA Informer (Proposed) | 0.24 | 0.37 | 0.51 | 0.64 | 492 |
The KA Informer’s efficiency stems from its optimized architecture, which reduces parameter count and computational time while improving accuracy. This is particularly beneficial for real-time BMS in China EV battery systems, where quick and reliable estimations are essential.
Ablation Studies
To validate the contributions of individual components, we conducted ablation studies by incrementally adding KASDAE and FMWA to the base Informer model. Results showed that KASDAE alone reduced SOC MAE by 16% and SOH MAE by 11.4%, while FMWA alone reduced SOC MAE by 32% and SOH MAE by 17.1%. The combined KA Informer model achieved the highest improvements, with SOC MAE reduced by 52% and SOH MAE by 28.6%, confirming the synergy between data cleaning and enhanced attention mechanisms for EV power battery estimation.
Conclusion
In this paper, we presented the KA Informer model for accurate and efficient estimation of SOC and SOH in electric vehicle power batteries. By integrating KASDAE for data cleaning and FMWA for sequence modeling, our approach addresses key challenges in China EV battery management, such as data quality issues and long-range dependencies. Experimental results demonstrate superior performance across diverse conditions, with SOC and SOH errors significantly lower than those of existing methods. The model’s ability to handle real-time data makes it practical for deployment in EV BMS, aiding in range prediction and battery health monitoring.
Future work will explore the impact of user driving patterns, road conditions, and emerging battery technologies on SOC and SOH estimation. Additionally, we plan to extend the model to other aspects of battery management, such as thermal runaway prediction, to further enhance the safety and reliability of China EV battery systems. The KA Informer framework sets a foundation for advanced, data-driven solutions in the evolving landscape of electric mobility.