Accurate estimation of the State of Health (SOH) for lithium-ion batteries is critical for ensuring the reliability and safety of energy storage systems in applications such as electric vehicles and portable electronics. This study proposes a novel framework that combines multi-health factor selection with an Improved Particle Swarm Optimization-Long Short-Term Memory (IPSO-LSTM) model to achieve precise SOH prediction. By focusing on measurable operational parameters—voltage, current, and temperature—we address the limitations of conventional methods that rely on complex electrochemical models or indirect feature extraction.
1. Health Factor Extraction and Correlation Analysis
Lithium-ion battery degradation manifests through changes in operational parameters. From voltage, current, and temperature profiles, we extract 13 candidate health factors (HFs) to characterize aging:
- Constant Voltage Charging Time (HF1)
- Constant Current Charging Time (HF2)
- Maximum Charging Time (HF3)
- Maximum Discharging Time (HF4)
- Time to Minimum Voltage During Discharge (HF5)
- Voltage Drop Duration (3.8 V to 3.5 V) (HF6)
- Maximum Charging Temperature (HF7)
- Minimum Charging Temperature (HF8)
- Average Charging Temperature (HF9)
- Maximum Discharging Temperature (HF10)
- Minimum Discharging Temperature (HF11)
- Average Discharging Temperature (HF12)
- Temperature Rise Time (33°C to 36°C) (HF13)
To identify the most relevant features, we compute the Pearson correlation coefficient (r) between each HF and SOH:r=n1i=1∑n(σXXi−Xˉ)(σYYi−Yˉ)
where Xi and Yi represent the HF and SOH values, Xˉ and Yˉ are their means, and σX, σY are standard deviations.
Table 1: Top Correlated Health Factors
| Health Factor | Correlation (r) |
|---|---|
| HF13 | 0.92 |
| HF4 | 0.89 |
| HF5 | 0.85 |
| HF6 | 0.82 |
HF13 (temperature rise time) exhibits the strongest correlation with SOH, reflecting the impact of thermal dynamics on battery aging. These four factors are selected as inputs for the IPSO-LSTM model.
2. IPSO-LSTM Framework
2.1 LSTM Architecture
The LSTM network addresses the vanishing gradient problem in traditional RNNs through gated mechanisms:
- Forget Gate: Decides which information to discard.
- Input Gate: Updates cell state with new information.
- Output Gate: Controls the exposure of cell state.
The hidden state ht and cell state ct are computed as:ft=σ(Wf⋅[ht−1,xt]+bf)it=σ(Wi⋅[ht−1,xt]+bi)c~t=tanh(Wc⋅[ht−1,xt]+bc)ct=ft⊙ct−1+it⊙c~tot=σ(Wo⋅[ht−1,xt]+bo)ht=ot⊙tanh(ct)
where ft, it, and ot are gate activations, ⊙ denotes element-wise multiplication, and W and b are weights and biases.
2.2 Improved PSO Algorithm
Traditional PSO suffers from premature convergence and local optima. We enhance PSO through:
- Chaotic Initialization:
Using Circle chaotic mapping to generate uniformly distributed initial populations:xi+1=mod(xi+0.2−2π0.5sin(2πxi),1) - Asymmetric Learning Factors:
Adjust C1 (cognitive) and C2 (social) dynamically:C1=2−1.5⋅tmaxt,C2=1+1.5⋅tmaxt - Nonlinear Inertia Weight:
Exponentially decay inertia to balance exploration and exploitation:w=0.1+0.6⋅e−0.3⋅(t/tmax)
2.3 IPSO-LSTM Training
- Data Preprocessing:
Normalize HFs and SOH to [0, 1] using min-max scaling. - Hyperparameter Optimization:
IPSO optimizes LSTM neurons (10–200), learning rate (0.001–0.01), and dropout rate (0.1–0.4). - Fitness Function:
Minimize the root mean squared error (RMSE) over 3 training runs:Fitness=1+RMSE1,RMSE=31k=1∑3n1i=1∑n(yi−y^i)2
3. Experimental Results
3.1 Performance Metrics
Model accuracy is evaluated using:
- Mean Absolute Error (MAE):MAE=n1i=1∑n∣yi−y^i∣
- Root Mean Squared Error (RMSE):RMSE=n1i=1∑n(yi−y^i)2
- Mean Absolute Percentage Error (MAPE):MAPE=n100%i=1∑nyiyi−y^i
Table 2: Comparison of SOH Estimation Errors
| Model | MAE (%) | RMSE (%) | MAPE (%) |
|---|---|---|---|
| LSTM | 1.30 | 1.70 | 1.60 |
| PSO-LSTM | 0.93 | 1.20 | 1.07 |
| IPSO-LSTM | 0.68 | 0.93 | 0.82 |
IPSO-LSTM reduces MAE by 48% and RMSE by 45% compared to vanilla LSTM, demonstrating superior optimization of network hyperparameters.
3.2 Generalization Across Datasets
Training data ratios (50%, 60%, 70%) are tested on NASA’s B0005, B0006, and B0007 lithium-ion battery datasets.
Table 3: Generalization Performance (B0005 Battery)
| Training Data | Model | MAE (%) | RMSE (%) | MAPE (%) |
|---|---|---|---|---|
| 50% | IPSO-LSTM | 0.14 | 0.18 | 0.21 |
| PSO-LSTM | 0.18 | 0.23 | 0.26 | |
| 60% | IPSO-LSTM | 0.13 | 0.17 | 0.20 |
| PSO-LSTM | 0.16 | 0.19 | 0.24 | |
| 70% | IPSO-LSTM | 0.11 | 0.13 | 0.16 |
| PSO-LSTM | 0.15 | 0.18 | 0.22 |
IPSO-LSTM maintains robust performance even with limited training data, achieving <1% MAPE across all cases.
3.3 Feature Selection Impact
Table 4: Feature Set Comparison
| Input Features | MAE (%) | RMSE (%) | MAPE (%) |
|---|---|---|---|
| 13 HFs | 1.11 | 1.23 | 1.38 |
| 1 HF (HF13) | 1.63 | 1.64 | 1.99 |
| 4 HFs (HF4,5,6,13) | 0.68 | 0.93 | 0.82 |
The selected four HFs reduce noise and computational complexity while preserving critical aging information.
4. Comparative Analysis with Existing Models
Table 5: Benchmarking Against State-of-the-Art Methods
| Model | MAE (%) | RMSE (%) | MAPE (%) |
|---|---|---|---|
| SFFS-LSTM [24] | 0.53 | 0.69 | 0.73 |
| BiGRU-Transformer [25] | 0.82 | 0.99 | 0.65 |
| VMD-CNN-AttBiGRU [26] | 1.75 | 2.17 | – |
| IPSO-LSTM | 0.11 | 0.13 | 0.16 |
IPSO-LSTM outperforms existing methods in MAE and RMSE, highlighting its effectiveness in capturing nonlinear capacity regeneration phenomena.
5. Conclusion
This study presents a data-driven framework for lithium-ion battery SOH estimation that integrates multi-health factor selection with an enhanced PSO-LSTM model. By leveraging measurable operational parameters and optimizing network hyperparameters through IPSO, we achieve MAE, RMSE, and MAPE below 1%. The framework’s robustness is validated across diverse training scenarios and benchmark datasets, demonstrating its potential for real-time battery management systems. Future work will explore adaptive feature selection and multi-battery transfer learning to further improve generalizability.