In my research on energy storage systems, I have concentrated on developing a robust methodology for assessing the state of health (SOH) of electrochemical energy storage cells. The accurate evaluation of SOH is critical for ensuring the safe and efficient operation of energy storage cells in practical applications. Over the years, I have observed that traditional methods often suffer from limited accuracy due to the complex aging mechanisms inside energy storage cells. To address this challenge, I proposed a data-driven approach that leverages fragmentary charging data combined with a genetic algorithm optimized long short-term memory neural network, which I refer to as GA-LSTM throughout this work.
The core idea of my methodology is to extract health factors from routine charging processes that strongly correlate with the internal degradation of energy storage cells. Instead of relying on full charge-discharge cycles, which are time-consuming and impractical in real-world scenarios, I selected specific voltage variation intervals during charging as input parameters. These fragments are easy to obtain and contain rich information about the aging state of the energy storage cell. By feeding these health factors into a GA-LSTM model, I achieved highly accurate SOH estimations with minimal computational overhead.
In this article, I will systematically present my experimental design, the theoretical foundation of the algorithms, the process of health factor extraction, model construction, and a comprehensive comparison of results. The findings demonstrate that the proposed method significantly outperforms conventional approaches, making it highly suitable for practical engineering deployment in energy storage systems.
Experimental Setup and Data Collection
To validate my proposed methodology, I conducted extensive cycling aging experiments on five pouch-type lithium iron phosphate (LiFePO4) energy storage cells. These cells are widely used in stationary energy storage applications due to their excellent safety characteristics and long cycle life. The key parameters of the tested energy storage cells are summarized in Table 1.
Table 1: Specifications of the tested energy storage cells
| Parameter | Value |
|---|---|
| Electrode Materials (Cathode / Anode) | LiFePO4 / Graphite |
| Rated Capacity | 20 Ah |
| Rated Voltage | 3.2 V |
| Charge Cut-off Voltage | 3.65 V |
| Discharge Cut-off Voltage | 2.5 V |
| Form Factor | Pouch Cell |
| Test Temperature | 25 °C (Constant Temperature Chamber) |
| Charge / Discharge Rate | 0.5C (10 A) |
I performed charge-discharge cycling experiments using a battery tester (model CT-3008W, manufactured by Neware Corporation in Shenzhen). Each cycle consisted of a constant current charge at 10 A up to 3.65 V, followed by a constant current discharge at 10 A down to 2.5 V. Every 100 cycles, I designated one cycle as a aging cycle, during which I recorded the full charge-discharge data and measured the actual capacity to calculate the SOH value. The entire experiment spanned 4000 cycles, and the capacity degradation trajectory is shown in a consistent downward trend across all tested cells.
The SOH of an energy storage cell at any given cycle is defined as the ratio of the current measured capacity to the rated capacity. The formula I used for SOH calculation is:
$$
SOH = \frac{Q_{current}}{Q_{rated}} \times 100\%
$$
where Qcurrent represents the actual capacity measured during the calibration process at the end of each aging cycle, and Qrated = 20 Ah is the nominal capacity of the fresh energy storage cell. The calibration process involved three consecutive charge-discharge cycles at 0.5C, and I recorded the last discharge capacity as the true capacity for SOH computation.
Figure 1 illustrates the capacity retention decay curves of three representative energy storage cells over 4000 cycles. The initial capacity before cycling was approximately 19.65 Ah, and after 4000 cycles, the capacity dropped to around 17.80 Ah, corresponding to a capacity retention rate of about 90.5%. The degradation was nearly linear, and the three parallel cells exhibited very similar aging trajectories, confirming the reproducibility of the experimental data.
During the cycling process, I observed that the charging curves shifted gradually with the accumulation of cycles. The plateau voltage region consistently remained within 3.25 V to 3.40 V, even as the cell aged. This observation motivated me to explore the voltage variations within this specific region as potential health indicators for SOH estimation.
Health Factor Extraction and Correlation Analysis
One of the most critical steps in building an accurate SOH estimation model is to identify features that are sensitive to the aging state of energy storage cells. In my study, I focused on the incremental voltage changes during constant current charging. By analyzing the voltage profiles at different aging stages, I hypothesized that the rate of voltage change in specific time windows could reflect the internal electrochemical dynamics and thus correlate with SOH.
To further investigate the aging characteristics, I performed differential analysis on the charging curves to obtain the incremental capacity (ICA) curves. The ICA curves of the energy storage cell at different cycle intervals revealed three distinct peaks within the voltage range of 3.25 V to 3.40 V. This indicates that the primary electrochemical reactions during charging occur predominantly in this voltage window, thereby confirming the feasibility of collecting voltage data within this region as health factors.
I defined nine candidate health factors by computing the voltage variation over fixed time intervals before and after certain voltage thresholds. Specifically, I considered the following time windows:
- 10 minutes, 20 minutes, and 30 minutes after the voltage reached 3.25 V
- 10 minutes, 20 minutes, and 30 minutes before the voltage reached 3.35 V
- 10 minutes, 20 minutes, and 30 minutes before the voltage reached 3.40 V
For each of these nine intervals, I calculated the voltage change value and then computed the Pearson correlation coefficient with the corresponding SOH values measured during the calibration cycles. The Pearson correlation coefficient is defined as:
$$
r_{XY} = \frac{Cov(X, Y)}{S_X S_Y}
$$
where Cov(X, Y) is the covariance between the voltage change (X) and SOH (Y), while SX and SY are the standard deviations of X and Y, respectively. The value of r ranges from -1 to 1, with values closer to 1 indicating a strong positive linear correlation, and values closer to -1 indicating a strong negative linear correlation.
Table 2 presents the computed Pearson correlation coefficients for all nine candidate health factors.
Table 2: Pearson correlation coefficients between voltage variation features and SOH
| Time Window | After reaching 3.25 V | Before reaching 3.35 V | Before reaching 3.40 V |
|---|---|---|---|
| 10 minutes | 0.6406 | 0.1855 | 0.4912 |
| 20 minutes | 0.2267 | 0.6358 | 0.0333 |
| 30 minutes | 0.3857 | 0.3615 | 0.9028 |
Based on the correlation results, I selected the three features with the highest absolute correlation values as the final health factors for model input:
- Factor 1: Voltage variation in 10 minutes after reaching 3.25 V (Pearson r = 0.6406)
- Factor 2: Voltage variation in 20 minutes before reaching 3.35 V (Pearson r = 0.6358)
- Factor 3: Voltage variation in 30 minutes before reaching 3.40 V (Pearson r = 0.9028)
The high correlation values confirm that these three features effectively capture the internal aging information of the energy storage cell. Factor 3, with a correlation coefficient of 0.9028, is particularly strong, indicating that the voltage behavior in the 30-minute window before reaching 3.40 V is highly indicative of the overall SOH. I therefore adopted these three features as the input parameters for my GA-LSTM model.
Theoretical Foundation of the GA-LSTM Model
To perform the SOH estimation, I employed a long short-term memory (LSTM) neural network, which is a specialized recurrent neural network architecture designed to handle sequential data. The LSTM model is well-suited for this task because the aging process of an energy storage cell is inherently a time-dependent phenomenon, and the health factors extracted from consecutive cycles form a natural time series.
Compared to a standard RNN, the LSTM introduces gating mechanisms that effectively mitigate the vanishing and exploding gradient problems. Each LSTM unit comprises three gates: the forget gate, the input gate, and the output gate. The mathematical formulations are as follows.
Forget gate: This gate determines which information from the previous memory cell state should be discarded.
$$
f_t = \sigma \left( W_f [h_{t-1}, x_t] + b_f \right)
$$
Input gate: This gate controls how much new information should be stored in the memory cell. It consists of two parts: a sigmoid layer that decides which values to update, and a tanh layer that creates a candidate vector.
$$
i_t = \sigma \left( W_i [h_{t-1}, x_t] + b_i \right)
$$
$$
\tilde{C}_t = \tanh \left( W_C [h_{t-1}, x_t] + b_C \right)
$$
Memory cell update: The old memory cell state Ct-1 is updated to the new state Ct by combining the forget and input gates.
$$
C_t = f_t * C_{t-1} + i_t * \tilde{C}_t
$$
Output gate: This gate decides what information from the memory cell will be passed to the hidden state.
$$
o_t = \sigma \left( W_o [h_{t-1}, x_t] + b_o \right)
$$
$$
h_t = o_t * \tanh(C_t)
$$
In these equations, σ denotes the sigmoid activation function, W and b represent the weight matrices and bias vectors for each gate, xt is the input at time step t, ht-1 is the hidden state from the previous time step, and Ct is the memory cell state at time t.
Despite the powerful capability of LSTM networks, their performance is highly sensitive to hyperparameter selection, such as the number of hidden layer neurons, the learning rate, the batch size, and the maximum number of training epochs. Manually tuning these parameters is often inefficient and may lead to suboptimal results. To overcome this limitation, I integrated a genetic algorithm (GA) to automatically search for the optimal hyperparameter configuration.
The GA is a global optimization technique inspired by the principles of natural selection and evolution. In my implementation, I defined a population of candidate hyperparameter sets, each represented as a chromosome. The fitness of each chromosome was evaluated by training the LSTM model with the corresponding hyperparameters and computing the mean squared error on the validation set. Through successive generations of selection, crossover, and mutation, the GA converges toward the optimal hyperparameter combination that minimizes the estimation error.
The overall workflow of the GA-LSTM model is as follows:
- Initialize the GA parameters, including population size, crossover probability, mutation probability, and maximum number of generations.
- Generate an initial population of hyperparameter sets randomly.
- For each individual in the population, assign the hyperparameters to the LSTM model and train the model on the training set.
- Evaluate the fitness of each individual based on the SOH estimation error on the validation set.
- Apply selection, crossover, and mutation operations to create a new generation of individuals.
- Repeat steps 3 to 5 until the maximum number of generations is reached or the convergence criterion is satisfied.
- Use the optimal hyperparameters obtained from the GA to train the final LSTM model and perform SOH estimation on the test set.
The key hyperparameters that I optimized using the GA are summarized in Table 3.
Table 3: Hyperparameter optimization range for the LSTM model
| Hyperparameter | Search Range | Optimal Value Found by GA |
|---|---|---|
| Number of Hidden Neurons | [8, 128] | 64 |
| Learning Rate | [0.0001, 0.01] | 0.003 |
| Batch Size | [16, 128] | 32 |
| Maximum Epochs | [50, 500] | 200 |
| Dropout Rate | [0.0, 0.5] | 0.2 |
The GA optimization process significantly stabilized the model training and improved the generalization capability of the LSTM network. The optimal hyperparameters were then used to construct the final SOH estimation model.
Model Training and Validation Protocol
I divided the experimental data from three energy storage cells into a training set and a test set using an 80 / 20 ratio. The training set comprised 3200 aging data points (from 3200 cycles across three cells), while the test set contained 800 data points. Additionally, I reserved the data from a fourth energy storage cell as an independent validation set to assess the model’s performance on entirely unseen data.
Each data sample consisted of three input features (the three voltage variation values described in the previous section) and one target output (the actual SOH value measured during calibration). I normalized all input features to the range [0, 1] to accelerate the convergence of the neural network training.
To demonstrate the superiority of the GA-LSTM model, I compared its performance against two benchmark models:
- A standard LSTM model without GA optimization (using manually selected hyperparameters)
- A back-propagation neural network (BPNN) optimized with the same GA procedure (GA-BP)
All models were implemented using the TensorFlow framework and trained on a workstation equipped with an Intel Core i9 processor and 64 GB of RAM. The training time for the GA-LSTM model was approximately 12 minutes, including the GA optimization process.
Results and Comparative Analysis
The SOH estimation results from the three models are compared against the actual measured SOH values. The evaluation was conducted on the independent test set from the fourth energy storage cell, which was not used during the training phase. The SOH range in the test set spanned from 91.3% to 98.4%, covering a moderate aging range representative of practical energy storage applications.
To quantify the accuracy of each model, I employed two widely used error metrics: the mean square error (MSE) and the mean absolute percentage error (MAPE). These are defined as:
$$
MSE = \frac{1}{n} \sum_{i=1}^{n} \left( \hat{y}_i – y_i \right)^2
$$
$$
MAPE = \frac{1}{n} \sum_{i=1}^{n} \left| \frac{y_i – \hat{y}_i}{y_i} \right| \times 100\%
$$
where ŷi is the estimated SOH value, yi is the actual SOH value, and n is the number of test samples. Lower values of MSE and MAPE indicate higher estimation accuracy.
Table 4 presents the error metrics for all three models.
Table 4: Comparison of SOH estimation errors across different models
| Model | MAPE (%) | MSE |
|---|---|---|
| Standard LSTM (without optimization) | 2.11 | 0.000548 |
| GA-BP | 1.33 | 0.002820 |
| GA-LSTM (proposed method) | 1.09 | 0.000142 |
The results clearly demonstrate the effectiveness of the proposed GA-LSTM model. Compared to the standard LSTM model without optimization, the GA-LSTM reduced the MAPE by 48.3% (from 2.11% to 1.09%) and the MSE by 74.1% (from 0.000548 to 0.000142). This substantial improvement is attributed to the optimal hyperparameter configuration discovered by the genetic algorithm, which enabled the LSTM network to capture the complex aging dynamics more accurately.
Furthermore, the GA-LSTM outperformed the GA-BP model by a significant margin. Although both models were optimized using the same GA procedure, the GA-LSTM achieved a lower MAPE (1.09% vs. 1.33%) and a much lower MSE (0.000142 vs. 0.002820). This confirms that the LSTM architecture, with its ability to model long-term dependencies in sequential data, is inherently more suitable for SOH estimation of energy storage cells than the conventional BP neural network.
The SOH estimates produced by the GA-LSTM model closely tracked the actual degradation trajectory across the entire test set. The maximum absolute error did not exceed 1.8%, and the majority of the estimation errors were within ±1.2%. For practical energy storage management systems, such accuracy is considered highly acceptable and can support reliable decision-making for maintenance and replacement scheduling.
To further analyze the robustness of the proposed method, I evaluated the GA-LSTM model on data from a fifth energy storage cell, which had a slightly different aging path due to manufacturing variations. Even in this case, the model maintained an MAPE of 1.21%, demonstrating good generalization capability across different cells of the same chemistry and form factor.
Discussion on Practical Implications
The method I have developed offers several advantages that make it attractive for real-world energy storage applications. First, the health factors are derived from fragmentary charging data that are readily available during routine operations. Most battery management systems (BMS) already record voltage and current data at regular intervals, so no additional sensors or specialized test procedures are required. This significantly lowers the implementation barrier.
Second, the computational cost of the GA-LSTM model after training is relatively low. Once the model parameters are fixed, the SOH estimation for a new data sample can be completed in milliseconds on a standard BMS microcontroller. This makes the method suitable for real-time or near-real-time applications.
Third, the use of a genetic algorithm to automate hyperparameter tuning eliminates the need for manual trial-and-error, which is often time-consuming and domain-specific. The GA-LSTM framework is general and can be easily adapted to other types of energy storage cells, such as nickel-manganese-cobalt (NMC) or lithium-titanate (LTO) cells, by retraining the model with appropriate data.
Table 5 summarizes the key advantages of the proposed method in comparison with conventional approaches.
Table 5: Comparative advantages of the GA-LSTM based SOH estimation method
| Aspect | Conventional Methods | Proposed GA-LSTM Method |
|---|---|---|
| Data Requirement | Full charge-discharge cycles or extensive lab tests | Fragmentary charging data (voltage fragments) |
| Model Building Effort | Manual feature engineering and parameter tuning | Automated feature selection + GA-based optimization |
| Estimation Accuracy (MAPE) | Typically 2% ~ 5% | 1.09% (48.3% reduction) |
| Computational Speed | Moderate to slow for complex models | Fast (real-time capable) |
| Transferability | Low (model-specific to cell chemistry) | High (retrainable with new data) |
The combination of high accuracy, low data requirement, and computational efficiency makes the proposed method a practical solution for online SOH monitoring in large-scale energy storage systems. In particular, for stationary battery energy storage stations that contain thousands of energy storage cells, the ability to assess the health status of each individual cell using routine operational data can greatly improve system reliability and reduce maintenance costs.
Conclusion and Future Directions
In this work, I have presented a comprehensive study on the state of health (SOH) estimation of electrochemical energy storage cells based on operational data. The key contributions of my research are as follows.
First, I identified three highly correlated health factors from the charging voltage profile: the voltage variation in 10 minutes after reaching 3.25 V, the voltage variation in 20 minutes before reaching 3.35 V, and the voltage variation in 30 minutes before reaching 3.40 V. These features showed Pearson correlation coefficients of 0.6406, 0.6358, and 0.9028, respectively, with the actual SOH, confirming their strong predictive power.
Second, I developed a GA-LSTM model that integrates a genetic algorithm for automatic hyperparameter optimization with a long short-term memory neural network for sequential data modeling. The GA effectively searched for the optimal combination of hidden layer neurons, learning rate, batch size, and other critical parameters, resulting in a model that is both accurate and robust.
Third, through extensive experiments on five 20 Ah LiFePO4 pouch-type energy storage cells, I demonstrated that the GA-LSTM model achieves an MAPE of 1.09% and an MSE of 0.000142, representing reductions of 48.3% and 74.1%, respectively, compared to an unoptimized LSTM model. The proposed method also outperformed a GA-optimized back-propagation neural network, highlighting the advantage of the LSTM architecture for time-series based SOH estimation.
Fourth, the entire methodology is designed with practical deployment in mind. The health factors are extracted from routinely available charging data, and the trained model is computationally efficient enough to run on embedded BMS hardware. This makes the approach highly scalable for large-scale energy storage systems.
Looking ahead, I plan to extend this work in several directions. One promising avenue is to incorporate temperature variation and current rate effects into the health factor extraction process, as real-world operating conditions are rarely as controlled as laboratory environments. Another direction is to explore transfer learning techniques that would allow a model trained on one type of energy storage cell to be quickly adapted to another type with minimal retraining data. Finally, I am interested in combining the SOH estimation model with a remaining useful life (RUL) prediction framework to provide a complete health management solution for energy storage systems.
In conclusion, the GA-LSTM based SOH estimation method presented in this article offers a practical, accurate, and efficient solution for monitoring the degradation of energy storage cells. By leveraging fragmentary operational data and advanced machine learning techniques, this approach addresses the critical need for reliable health assessment in modern energy storage applications. I believe that this work will contribute to the wider adoption of data-driven battery management strategies and ultimately support the safe and economic operation of energy storage systems.