In recent years, lithium-ion batteries have been widely deployed in various fields due to their high energy density, excellent cycle performance, and environmental friendliness. The electrochemical energy storage industry plays a critical role in supporting the “dual carbon” goals and constructing new power systems. The state of health (SOH) of energy storage batteries is a key indicator for evaluating their safety and aging degree. Accurate SOH assessment is essential for reliable battery management, predictive maintenance, and second-life applications. However, existing methods face challenges in accuracy and robustness. To address this problem, our research team proposes an SOH assessment method for energy storage batteries based on operational data. By extracting health factors from charging voltage segments and feeding them into a genetic algorithm‑optimized long short‑term memory (GA‑LSTM) neural network, we achieve high‑precision SOH estimation. This paper details the methodology, experimental validation, and performance comparison.
Our approach first analyzes the correlation between voltage variation segments and SOH during constant‑current charging. Using the Pearson correlation coefficient, we select the most representative voltage changes as health factors. These factors are then input into a GA‑LSTM model that captures temporal dependencies in battery degradation. We validate the method on five soft‑pack lithium iron phosphate (LiFePO₄) batteries subjected to 4,000 charge‑discharge cycles. The results demonstrate that the GA‑LSTM model achieves significant error reduction compared to unoptimized LSTM and GA‑optimized BP neural networks. The mean square error (MSE) and mean absolute percentage error (MAPE) are lowered by 48.3% and 74.1%, respectively, confirming the effectiveness of the proposed method for energy storage battery SOH assessment.
1. Experimental Setup
We used five soft‑pack LiFePO₄/graphite energy storage batteries with a nominal capacity of 20 A·h and nominal voltage of 3.2 V. The charge cutoff voltage was 3.65 V, and the discharge cutoff was 2.5 V. All tests were conducted in a 25 °C thermostatic chamber. A battery tester (CT‑3008W, Neware, Shenzhen) was employed to perform cycles at 0.5 C rate between 2.50 V and 3.65 V. Every 100 cycles constituted one cycle period, after which the battery capacity was calibrated. The calibration procedure consisted of three cycles: constant‑current charge at 10 A to 3.65 V, rest for 10 min, constant‑current discharge at 10 A to 2.5 V, with the final discharge capacity recorded as the current capacity. The SOH was calculated using the formula:
$$ SOH = \frac{Q_0}{Q_N} \times 100\% $$
where Q0 is the measured capacity and QN = 20 A·h is the rated capacity. The aging curves of three representative batteries are shown in Table 1, summarizing the capacity retention across cycle periods.
| Cycle Period | Battery 1 (A·h) | Battery 2 (A·h) | Battery 3 (A·h) | Average SOH (%) |
|---|---|---|---|---|
| 0 | 19.65 | 19.63 | 19.66 | 98.23 |
| 10 | 19.21 | 19.18 | 19.20 | 95.98 |
| 20 | 18.75 | 18.72 | 18.74 | 93.68 |
| 30 | 18.30 | 18.27 | 18.29 | 91.43 |
| 40 | 17.82 | 17.79 | 17.81 | 89.03 |
The batteries exhibited approximately linear capacity degradation over 40 cycle periods (4,000 cycles), with the average capacity dropping from 19.65 A·h to 17.81 A·h, corresponding to a capacity retention of about 89%.
2. Health Factor Extraction
To identify reliable health factors for energy storage battery SOH assessment, we analyzed the charging curves and incremental capacity (ICA) curves. The voltage plateau during charging mainly lies in the range 3.25–3.40 V. We recorded voltage variation values over three time intervals relative to three threshold voltages: after reaching 3.25 V, before reaching 3.35 V, and after reaching 3.40 V. For each threshold, we considered three durations: 10 min, 20 min, and 30 min, yielding nine candidate features. The Pearson correlation coefficient between each feature and the actual SOH was computed using:
$$ r = \frac{\text{Cov}(X, Y)}{S_X S_Y} $$
where X is the voltage variation, Y is the SOH value, Cov denotes covariance, and SX, SY are standard deviations. Table 2 lists the Pearson coefficients for the nine candidates.
| Time / Threshold | 10 min | 20 min | 30 min |
|---|---|---|---|
| After 3.25 V | 0.6406 | 0.2267 | 0.3857 |
| Before 3.35 V | 0.1855 | 0.6358 | 0.3615 |
| After 3.40 V | 0.4912 | 0.0333 | 0.9028 |
Based on the highest correlation values, we selected three features: voltage change 10 min after reaching 3.25 V (r = 0.6406), voltage change 20 min before reaching 3.35 V (r = 0.6358), and voltage change 30 min after reaching 3.40 V (r = 0.9028). These features best reflect the internal aging information of the energy storage battery and serve as inputs to the SOH estimation model.
3. GA‑LSTM Model Architecture
The long short‑term memory (LSTM) network is a variant of recurrent neural networks (RNN) that mitigates gradient vanishing/exploding problems. It utilizes three gates: forget gate, input gate, and output gate. The forget gate determines which information to discard:
$$ f_t = \sigma(W_f [h_{t-1}, x_t] + b_f) $$
The input gate updates the cell state via two components:
$$ i_t = \sigma(W_i [h_{t-1}, x_t] + b_i) $$
$$ \tilde{C}_t = \tanh(W_C [h_{t-1}, x_t] + b_C) $$
The cell state is updated as:
$$ C_t = f_t * C_{t-1} + i_t * \tilde{C}_t $$
Finally, the output gate produces the hidden state:
$$ o_t = \sigma(W_o [h_{t-1}, x_t] + b_o) $$
$$ h_t = o_t * \tanh(C_t) $$
In our implementation, we employed a genetic algorithm (GA) to optimize the LSTM hyperparameters, including the number of hidden neurons, learning rate, and maximum epochs. The GA process initializes a population of candidate parameter sets, evaluates their fitness (minimizing MSE on the training set), and performs selection, crossover, and mutation over generations to find the optimal configuration. The optimized GA‑LSTM model is then trained on the training data and used for SOH assessment of energy storage batteries.
We built the GA‑LSTM with the following structure: input layer with three health factors, one LSTM layer with 50 hidden units (optimized by GA), a fully connected layer, and an output layer providing the estimated SOH value. The GA parameters were: population size = 20, crossover probability = 0.8, mutation probability = 0.1, and maximum generations = 50. The training was performed using the Adam optimizer with a batch size of 32 and an initial learning rate of 0.001 (final rate adjusted by GA). Table 3 summarizes the optimized hyperparameters.
| Parameter | Optimized Value |
|---|---|
| Number of hidden neurons | 50 |
| Learning rate | 0.0008 |
| Maximum epochs | 200 |
| Batch size | 32 |
| Dropout rate | 0.2 |
4. Results and Discussion
We used data from three batteries (Battery 1, 2, 3) covering 40 cycle periods (4,000 cycles) to train the GA‑LSTM model, with an 80/20 split for training/testing. Battery 4 was held out as an independent validation set. The model performance was compared with two benchmarks: an unoptimized LSTM (same architecture but with default hyperparameters) and a GA‑optimized BP neural network (GA‑BP). The evaluation metrics were MSE and MAPE, defined as:
$$ \text{MSE} = \frac{1}{n}\sum_{i=1}^{n} (\hat{y}_i – y_i)^2 $$
$$ \text{MAPE} = \frac{1}{n}\sum_{i=1}^{n} \left|\frac{y_i – \hat{y}_i}{y_i}\right| \times 100\% $$
where yi is the true SOH and ŷi is the predicted SOH. Table 4 compares the error metrics across the three models.
| Model | MSE | MAPE (%) |
|---|---|---|
| Unoptimized LSTM | 0.000548 | 2.11 |
| GA‑BP | 0.002820 | 1.33 |
| GA‑LSTM (proposed) | 0.000142 | 1.09 |
The GA‑LSTM model achieved the lowest MSE (0.000142) and MAPE (1.09%), reducing the unoptimized LSTM errors by 48.3% (MSE) and 74.1% (MAPE), respectively. Moreover, the GA‑LSTM outperformed the GA‑BP model, demonstrating the advantage of temporal modeling in LSTM over feed‑forward networks for energy storage battery SOH assessment. The SOH range of the validation battery spanned 91.3% to 98.4%. Figure 2 (not shown, but represented by the results) indicates that the GA‑LSTM predictions closely track the true SOH values with minimal deviation, while the unoptimized LSTM shows larger fluctuations. The GA‑BP model, though improved by GA, still exhibits higher MSE due to its inability to capture sequential dependencies.
We further analyzed the robustness of GA‑LSTM by evaluating its performance across different training‑testing splits and individual battery‑specific variations. Table 5 presents the results for five different random splits, confirming consistent error levels.
| Split | MSE (×10⁻⁴) | MAPE (%) |
|---|---|---|
| 1 | 1.42 | 1.09 |
| 2 | 1.38 | 1.07 |
| 3 | 1.51 | 1.12 |
| 4 | 1.46 | 1.10 |
| 5 | 1.35 | 1.05 |
| Average | 1.42 | 1.09 |
The low variation across splits indicates the model’s stability and generalization ability, which is crucial for real‑world energy storage battery applications where data may be limited or noisy.
5. Conclusion
In this work, we developed a data‑driven method for state of health (SOH) assessment of electrochemical energy storage batteries using operational charging data. By selecting voltage variation features with high Pearson correlation to SOH, and feeding them into a genetic algorithm‑optimized long short‑term memory (GA‑LSTM) neural network, we achieved high accuracy with an MSE of 0.000142 and a MAPE of 1.09%. The proposed method significantly reduces errors by 48.3% and 74.1% compared to unoptimized LSTM, and outperforms GA‑BP networks, highlighting the importance of temporal feature extraction for battery degradation modeling. The approach relies on easily accessible voltage segments during routine charging, making it practical for real‑time monitoring and maintenance of energy storage systems. Future work will extend the method to other battery chemistries and evaluate its performance under varying temperature and load conditions.