Multiphysics Feature-Based State-of-Energy Estimation for LiFePO4 Batteries Using Bidirectional Long Short-Term Memory and Particle Swarm-Optimized Kalman Filter
Abstract
:1. Introduction
- A sliding window is proposed to make full use of past measurements containing voltage, temperature, current, and mechanical force.
- A BiLSTM with four multiphysics feature inputs is used to obtain preliminary estimation of SOE. The PSO algorithm is introduced to optimize the noise covariance of the KF, thereby minimizing manual parameter adjustments. The optimized KF algorithm then smooths the outputs of BiLSTM, achieving enhanced estimation precision and effectively mitigating noise interference.
- A test bench is established to acquire multiphysics features, including current, voltage, temperature, and mechanical force. The force signal is introduced as a model input feature, which significantly improves the estimation accuracy of SOE during the voltage plateau period.
- The validity of the proposed model and mechanical force signals in high-precision SOE prediction is verified by applying the proposed method to different operating conditions and temperatures. In addition, the comparison of BiLSTM, PSO, and KF (BiLSTM–PSO–KF) with other networks and the prediction results under different preload forces further validate the robustness and generalization performance of the proposed model.
2. Experimental Data Analysis
2.1. Text Platform
2.2. Data Acquisition
2.3. Data Analysis
- The voltage and temperature exhibit a strong dependence on the periodically varying current. Both parameters fluctuate significantly with the current within a localized range. In contrast, the mechanical force remains relatively stable in both local variations within a single operating condition and overall variations across different operating conditions.
- Conventional methods utilize voltage, current, and temperature as model inputs to predict the SOE of LFP batteries. However, similar to SOC estimation, these methods suffer from the issue of the voltage plateau, which leads to reduced estimation accuracy. Figure 3(a2–d2) show the overall trend of voltage with a slow decrease in the range of 0.3 to 0.9 SOE, although it fluctuates periodically with the current. In contrast, the curve of mechanical force shows a significant change with an overall decreasing trend, but a reverse peak occurs in the range of 0.3 to 0.6 SOE.
3. Methodology
3.1. BiLSTM
3.2. KF
- Initialization process
- 2.
- Prediction progress
- 3.
- Correction process
3.3. PSO
3.4. Training and Evaluation
3.4.1. Model Setup
3.4.2. Evaluation Criteria
3.5. The Fusion Model Framework
4. Results and Discussion
4.1. Comparison of SOE Estimation with Different Operating Conditions
4.2. Comparison of SOE Estimation at Different Temperatures
4.3. Comparison of SOE Estimation of Different Models
4.4. Comparison of SOE Estimation Under Different Preload Forces
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Item | LFP Battery |
---|---|
Cathode | LiFePO4 |
Anode | Graphite |
Nominal capacity | 10 Ah |
Nominal voltage | 3.2 V |
Charge cutoff voltage/discharge voltage | 3.65 V/2.5 V |
Size (H/W/L) | 135/68/13 mm |
Brand | Dingshan New Energy Co., Ltd., Guiyang, China |
Model code | 1368135-10 Ah |
Production date | 13 January 2024 |
Training Data | Test Data | RMSE% | MAXE% | MAE% |
---|---|---|---|---|
DST, BJDST (without force) | FUDS | 2.35 | 5.34 | 2.06 |
US06 | 2.02 | 5.62 | 1.50 | |
DST, BJDST (with force) | FUDS | 0.64 | 1.64 | 0.53 |
US06 | 0.56 | 2.22 | 0.39 |
Training Data | Test Data | RMSE% | MAXE% | MAE% |
---|---|---|---|---|
DST, BJDST (without force) | US06 (15 °C) | 1.85 | 7.32 | 1.58 |
US06 (35 °C) | 2.65 | 7.25 | 1.84 | |
DST, BJDST (with force) | US06 (15 °C) | 0.89 | 2.10 | 0.71 |
US06 (35 °C) | 0.76 | 2.58 | 0.69 |
Model | Training Data | Test Data | RMSE% | MAXE% | MAE% |
---|---|---|---|---|---|
LSTM | DST, BJDST (without force) | FUDS | 4.20 | 15.70 | 3.28 |
BiLSTM | 3.20 | 15.18 | 2.51 | ||
Proposed | 2.29 | 6.67 | 1.73 | ||
LSTM | DST, BJDST (with force, 500 N) | FUDS | 2.34 | 9.33 | 1.74 |
BiLSTM | 1.69 | 6.05 | 1.27 | ||
Proposed | 0.62 | 2.66 | 0.48 |
Model | Training Data | Test Data | RMSE% | MAXE% | MAE% |
---|---|---|---|---|---|
LSTM | DST, BJDST (1000 N) | US06 | 1.86 | 7.78 | 1.44 |
BiLSTM | 1.16 | 3.51 | 0.93 | ||
Proposed | 0.59 | 1.09 | 0.46 | ||
LSTM | DST, BJDST (1500 N) | US06 | 2.38 | 8.34 | 1.85 |
BiLSTM | 1.65 | 6.70 | 1.28 | ||
Proposed | 0.95 | 2.48 | 0.70 |
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Wu, Z.; He, X.; Chen, H.; Lv, L.; Jiang, J.; Wang, L. Multiphysics Feature-Based State-of-Energy Estimation for LiFePO4 Batteries Using Bidirectional Long Short-Term Memory and Particle Swarm-Optimized Kalman Filter. Appl. Sci. 2025, 15, 5003. https://doi.org/10.3390/app15095003
Wu Z, He X, Chen H, Lv L, Jiang J, Wang L. Multiphysics Feature-Based State-of-Energy Estimation for LiFePO4 Batteries Using Bidirectional Long Short-Term Memory and Particle Swarm-Optimized Kalman Filter. Applied Sciences. 2025; 15(9):5003. https://doi.org/10.3390/app15095003
Chicago/Turabian StyleWu, Zhengpu, Xu He, Haisen Chen, Lu Lv, Jiuchun Jiang, and Lujun Wang. 2025. "Multiphysics Feature-Based State-of-Energy Estimation for LiFePO4 Batteries Using Bidirectional Long Short-Term Memory and Particle Swarm-Optimized Kalman Filter" Applied Sciences 15, no. 9: 5003. https://doi.org/10.3390/app15095003
APA StyleWu, Z., He, X., Chen, H., Lv, L., Jiang, J., & Wang, L. (2025). Multiphysics Feature-Based State-of-Energy Estimation for LiFePO4 Batteries Using Bidirectional Long Short-Term Memory and Particle Swarm-Optimized Kalman Filter. Applied Sciences, 15(9), 5003. https://doi.org/10.3390/app15095003