Abstract
Accurate State of Charge (SOC) estimation is critical for optimizing the performance and safety of LiFePO4 battery, particularly in applications such as electric vehicles and grid energy storage. However, the inherent voltage plateau characteristic of LiFePO4 battery introduces significant challenges due to voltage signal insensitivity and noise susceptibility. To address this limitation, we propose a novel data-driven approach that integrates mechanical expansion force signals with electrical and thermal parameters to enhance SOC estimation accuracy. A hybrid Convolutional Neural Network-Bidirectional Long Short-Term Memory (CNN-BiLSTM) architecture is developed to simultaneously capture local temporal patterns and long-term dependencies within sequential battery data. Experimental validation under four environmental temperatures (−0°C, 10°C, 25°C, and 40°C) and two dynamic load profiles (FUDS and US06) demonstrates that the inclusion of expansion force signals reduces the root-mean-square error (RMSE) by an average of 43.82% compared to conventional voltage-temperature models. The CNN-BiLSTM framework further outperforms standalone neural networks, achieving a maximum RMSE reduction of 53.88%. These results highlight the synergistic benefits of multi-physics signal fusion and advanced deep learning architectures for robust SOC estimation in LiFePO4 battery systems.
1. Introduction
LiFePO4 battery has become a cornerstone of modern energy storage technologies due to their thermal stability, long cycle life, and cost-effectiveness. Despite these advantages, their flat open-circuit voltage (OCV)-SOC relationship (Figure 1) introduces substantial uncertainty in SOC estimation, particularly during the mid-SOC range (20%–80%). Traditional model-based methods, such as Kalman filters and equivalent circuit models, struggle to adapt to the nonlinear dynamics of LiFePO4 battery under varying operating conditions.
Recent advancements in data-driven techniques, including recurrent neural networks (RNNs) and convolutional neural networks (CNNs), have shown promise in addressing these challenges. However, their performance remains constrained by reliance on voltage and temperature signals alone, which lack discriminative power during the voltage plateau phase.
This study introduces expansion force as a complementary mechanical signal to augment SOC estimation. During charge/discharge cycles, LiFePO4 battery exhibit measurable mechanical deformation due to lithium-ion intercalation-induced stress in electrode materials. We demonstrate that this force signal exhibits a monotonic relationship with SOC across the entire operational range, providing critical information that voltage signals cannot resolve. A hybrid CNN-BiLSTM model is designed to exploit both local features and temporal dependencies within multi-sensor data streams, enabling high-precision SOC estimation under diverse environmental and load conditions.
2. Methodology
2.1 Experimental Setup
Experiments were conducted on commercial 50 Ah LiFePO4 prismatic cells (Table 1). A multi-physics testing platform (Figure 2) integrated the following components:
- Neware BTS-5V300A cycler for applying dynamic current profiles.
- SWE2100 in-situ expansion analyzer for measuring mechanical force (resolution: ±5 N).
- K-type thermocouples for surface temperature monitoring.
- Environmental chamber for temperature control (±0.5°C).
Table 1: LiFePO4 Battery Specifications
| Parameter | Value |
|---|---|
| Cathode Material | LiFePO4 |
| Anode Material | Graphite |
| Nominal Capacity | 50 Ah |
| Nominal Voltage | 3.2 V |
| Charge Cut-off Voltage | 3.65 V |
| Discharge Cut-off Voltage | 2.5 V |
| Dimensions | 185 × 135 × 29.3 mm |
| Weight | 1395 ± 50 g |
Dynamic discharge tests were performed at −0°C, 10°C, 25°C, and 40°C using FUDS and US06 profiles. Expansion force, voltage, current, and temperature data were sampled at 1 Hz.
2.2 Data Preprocessing
Input features included normalized sequences of voltage V(t), current I(t), accumulated charge Q(t), temperature T(t), and force F(t):X(t)=V(t)I(t)Q(t)T(t)F(t),X′(t)=Xmax−XminX(t)−Xmin
Sliding windows of 90 timesteps were used to construct input-output pairs for training.
2.3 CNN-BiLSTM Architecture
The hybrid model (Figure 3) combines:
- 1D Convolutional Layers: Extract local spatial features through cascaded convolutions (kernel sizes: 32 and 64).
- Bidirectional LSTM Layers: Capture long-term dependencies via forward-backward hidden states (128 units per direction).
- Fully Connected Layers: Map BiLSTM outputs to SOC estimates.
The loss function minimizes mean squared error (MSE):L=N1t=1∑N(SOCpred(t)−SOCtrue(t))2
2.4 Performance Metrics
- RMSE: N1∑t=1N(SOCpred(t)−SOCtrue(t))2
- MAE: N1∑t=1N∣SOCpred(t)−SOCtrue(t)∣
- Max Error: max(∣SOCpred(t)−SOCtrue(t)∣)
3. Results and Discussion
3.1 Impact of Expansion Force Signals
The inclusion of force signals significantly improved SOC estimation accuracy across all temperatures (Table 2). At 10°C under FUDS cycling, RMSE decreased by 73.02% (from 4.41% to 1.19%) when force data were incorporated. This enhancement is attributed to the force-SOC relationship’s monotonicity (Figure 4), which mitigates voltage plateau ambiguities.
Table 2: SOC Estimation Errors with/without Force Signals (FUDS Profile)
| Temperature | RMSE (%) | MAE (%) | Max Error (%) |
|---|---|---|---|
| 0°C (With Force) | 2.76 | 2.17 | 15.61 |
| 0°C (Without Force) | 4.78 | 3.88 | 16.38 |
| 10°C (With Force) | 1.19 | 0.73 | 7.80 |
| 10°C (Without Force) | 4.41 | 3.28 | 14.12 |
| 25°C (With Force) | 2.07 | 1.48 | 10.81 |
| 25°C (Without Force) | 4.05 | 2.60 | 26.45 |
| 40°C (With Force) | 2.18 | 2.26 | 8.14 |
| 40°C (Without Force) | 4.90 | 3.65 | 23.64 |
3.2 Model Comparison
The CNN-BiLSTM model outperformed standalone LSTM, CNN, and feedforward neural networks (Table 3). For US06 cycles at 25°C, the hybrid architecture achieved an RMSE of 1.77%, compared to 3.79% for LSTM. This superiority stems from the model’s ability to jointly learn localized force-voltage correlations and temporal current-temperature dynamics.
Table 3: Performance Comparison of Neural Networks (25°C, US06)
| Model | RMSE (%) | MAE (%) | Max Error (%) |
|---|---|---|---|
| CNN-BiLSTM | 1.77 | 1.25 | 5.10 |
| LSTM | 3.79 | 2.30 | 19.10 |
| CNN | 2.95 | 1.89 | 12.33 |
| FNN | 4.12 | 2.98 | 21.45 |
3.3 Generalization Across Dynamic Profiles
The model maintained robust performance under unseen load conditions (Figure 5). For example, training on FUDS and testing on US06 yielded an RMSE of 2.18% at 40°C, demonstrating effective generalization. Transient errors at SOC ≈ 70% (attributable to force-SOC hysteresis during rapid lithiation) were contained within 8.14%, validating the framework’s stability.
4. Conclusion
This work establishes a paradigm for high-accuracy SOC estimation in LiFePO4 battery by integrating mechanical expansion force signals with a CNN-BiLSTM deep learning architecture. Key contributions include:
- Multi-Physics Signal Fusion: Force signals resolve ambiguities caused by voltage plateaus, reducing RMSE by 43.82% on average.
- Hybrid Deep Learning: The CNN-BiLSTM model synergizes spatial feature extraction and temporal dependency modeling, achieving a 53.88% RMSE improvement over conventional networks.
- Environmental Robustness: Consistent performance across −0°C to 40°C ensures applicability in real-world scenarios.
Future work will explore real-time deployment on embedded systems and the integration of aging-induced force-SOC relationship shifts. These advancements position the proposed framework as a cornerstone for next-generation battery management systems in LiFePO4-dominated applications.