Accurate state-of-charge (SOC) estimation for lithium iron phosphate (LiFePO4) batteries remains challenging due to their characteristic voltage plateau and complex electrochemical dynamics. This study proposes a novel data-driven framework that integrates mechanical expansion force signals with conventional electrical-thermal parameters, coupled with a hybrid CNN-BiLSTM neural architecture, to achieve high-precision SOC estimation across diverse operating conditions.
Experimental Design and Signal Analysis
Comprehensive testing was conducted on LF50F LiFePO4 battery cells under four temperature conditions (0°C, 10°C, 25°C, 40°C) and two dynamic profiles (FUDS/US06). The experimental setup captured synchronized measurements of voltage, current, temperature, and expansion force at 1Hz sampling frequency. Key battery specifications are summarized in Table 1.
| Parameter | Value |
|---|---|
| Nominal Capacity | 50 Ah |
| Voltage Range | 2.5-3.65 V |
| Charge Temperature | 0-55°C |
| Discharge Temperature | -20-55°C |
The characteristic evolution of voltage and expansion force during discharge reveals complementary information patterns:
$$V(t) = f_{electro}(SOC,T,I)$$
$$F(t) = f_{mech}(SOC,T,\dot{I})$$
Where $V(t)$ represents terminal voltage, $F(t)$ denotes expansion force, $T$ is temperature, and $I$ indicates current.
Hybrid CNN-BiLSTM Architecture
The proposed model architecture combines temporal feature extraction and sequential dependency learning through:
- Input Layer: Normalized multi-dimensional signals
$$x’ = \frac{x – \min(x)}{\max(x) – \min(x)}$$ - 1D Convolutional Layers: Local pattern recognition
$$c_i = \text{ReLU}(W_{conv} \ast x_i + b_{conv})$$ - Bidirectional LSTM: Temporal dependency modeling
$$h_t = \text{BiLSTM}(c_t, h_{t-1}, h_{t+1})$$ - Dense Layers: Non-linear regression
$$\widehat{SOC} = \sigma(W_{dense}h_t + b_{dense})$$
| Layer | Parameters |
|---|---|
| CNN | 32-64 filters, kernel=3 |
| BiLSTM | 128 units, 2 layers |
| Optimizer | Adam (lr=0.0005) |
Performance Evaluation
The framework demonstrates significant improvement over conventional approaches through multi-signal fusion:
| Method | RMSE (%) | MAE (%) |
|---|---|---|
| Electrical-only | 4.21 | 3.18 |
| Force-Electric-Thermal | 2.05 | 1.49 |
Key findings demonstrate:
- Expansion force signals reduce voltage plateau errors by 43.8%
- CNN-BiLSTM achieves 53.9% lower RMSE than single LSTM
- Cross-temperature validation maintains <3% RMSE
$$Error_{reduction} = \frac{RMSE_{base} – RMSE_{proposed}}{RMSE_{base}} \times 100\%$$
Mechanistic Interpretation
The enhanced performance stems from:
- Mechanical-electrochemical coupling in LiFePO4 batteries
$$\Delta F \propto \frac{\partial SOC}{\partial t} \cdot \frac{\partial \epsilon_{Li}}{\partial SOC}$$ - Multi-scale feature learning:
$$\mathcal{F}_{total} = \alpha\mathcal{F}_{local} + \beta\mathcal{F}_{temporal}$$
This methodology establishes a new paradigm for LiFePO4 battery management systems, particularly effective in voltage plateau regions where traditional electrical-based methods typically fail. The integration of mechanical signals with advanced deep learning architectures enables robust SOC estimation across diverse operating scenarios.