The reliable and accurate assessment of the State of Health (SOH) for electrochemical energy storage batteries is a cornerstone for ensuring the safety, longevity, and economic viability of modern energy storage systems. SOH quantifies the current capacity of an energy storage battery relative to its nominal capacity, serving as a critical indicator of its aging and remaining useful life. With the rapid global deployment of grid-scale and residential energy storage solutions to support renewable energy integration and achieve decarbonization goals, developing precise, data-driven methods for SOH estimation has become an urgent technical priority.
Traditional model-based methods, such as electrochemical or equivalent circuit models, often struggle with the complexity of internal battery reactions, leading to challenges in model establishment and robustness. In contrast, data-driven approaches, fueled by advances in machine learning and the availability of operational data from Battery Management Systems (BMS), offer a powerful alternative. These methods learn the relationship between easily measurable parameters (like voltage, current, and temperature) and the battery’s underlying state. However, the accuracy of these data-driven models heavily depends on the selection of informative features, known as health indicators (HIs), and the architecture of the learning algorithm itself.
This article presents a novel, high-accuracy method for evaluating the SOH of energy storage batteries. The core innovation lies in the extraction of highly correlated health indicators from routine charging voltage data and the application of a Genetic Algorithm-optimized Long Short-Term Memory (GA-LSTM) neural network for modeling. We first identify specific voltage change intervals during the constant-current charging phase that exhibit strong correlation with capacity fade. These intervals are processed into concise health indicators. Subsequently, a specialized LSTM network, renowned for handling temporal sequences, is trained to map these indicators to the SOH. To overcome the challenge of manually tuning the LSTM’s hyperparameters, a Genetic Algorithm (GA) is employed for global optimization, significantly enhancing the model’s predictive performance and stability. The proposed methodology is validated using long-term cycling data from commercial lithium iron phosphate (LiFePO₄) energy storage batteries.
Methodology: From Data to Health Indicator
The proposed SOH evaluation framework consists of two main stages: 1) Health Indicator (HI) extraction from operational charging data, and 2) the construction and optimization of the GA-LSTM prediction model.
Health Indicator Extraction Based on Voltage Dynamics
The search for effective health indicators begins with an analysis of the charging voltage curve. For lithium-ion energy storage batteries, particularly LiFePO₄, the voltage plateau during constant-current charging is highly indicative of the electrochemical state of the electrode materials. As the energy storage battery ages, internal resistances increase, and active material degrades, causing subtle shifts in this voltage profile.
To quantitatively capture these aging signatures, we analyze the Incremental Capacity Analysis (ICA) curve, obtained by differentiating capacity (Q) with respect to voltage (V), i.e., dQ/dV. The peaks in the ICA curve correspond to major phase transition reactions within the electrode. For LiFePO₄ energy storage batteries, these characteristic peaks consistently reside within the voltage window of approximately 3.25 V to 3.40 V during charging. This observation confirms that voltage data within this range encapsulates the most relevant electrochemical information for health assessment.
Instead of using the entire voltage curve or complex ICA curve shapes, we propose a simple yet effective set of HIs: the change in terminal voltage over fixed time intervals anchored to specific voltage points. Initially, nine candidate HIs were defined:
1. Voltage change in the 10, 20, and 30 minutes after reaching 3.25 V.
2. Voltage change in the 10, 20, and 30 minutes before reaching 3.35 V.
3. Voltage change in the 10, 20, and 30 minutes before reaching 3.40 V.
The Pearson correlation coefficient is then used to rigorously select the most relevant HIs. This coefficient measures the linear correlation between two variables X (the voltage change) and Y (the measured SOH), with values closer to 1 or -1 indicating stronger positive or negative correlation, respectively. It is calculated as:
$$
r = \frac{\text{Cov}(X, Y)}{S_X S_Y}
$$
where Cov(X, Y) is the covariance, and S_X and S_Y are the standard deviations of X and Y. The correlation results for the candidate HIs are summarized in the table below.
| Time Interval (minutes) | After 3.25 V | Before 3.35 V | Before 3.40 V |
|---|---|---|---|
| 10 | 0.6406 | 0.1855 | 0.4912 |
| 20 | 0.2267 | 0.6358 | 0.0333 |
| 30 | 0.3857 | 0.3615 | 0.9028 |
Based on the high Pearson correlation coefficients, three HIs were selected as the final input features for the model:
1. HI₁: Voltage change in the 10 minutes after reaching 3.25 V (r = 0.6406).
2. HI₂: Voltage change in the 20 minutes before reaching 3.35 V (r = 0.6358).
3. HI₃: Voltage change in the 30 minutes before reaching 3.40 V (r = 0.9028).
These three indicators provide a compact and highly informative representation of the energy storage battery’s aging state, derived directly from simple operational data.
The GA-LSTM Prediction Model
The SOH of an energy storage battery is a parameter that degrades sequentially over time. Therefore, a model that can effectively learn from time-series data is essential. The Long Short-Term Memory (LSTM) network is a specialized type of Recurrent Neural Network (RNN) designed to overcome the vanishing gradient problem of standard RNNs, making it exceptionally well-suited for learning long-term dependencies in sequential data.
An LSTM unit incorporates a memory cell and three regulatory gates: the forget gate, input gate, and output gate. The operations at timestep t are described by the following equations:
Forget Gate: Determines what information to discard from the cell state.
$$ f_t = \sigma[W_f \cdot (h_{t-1}, x_t) + b_f] $$
Input Gate: Decides what new information to store in the cell state. It has two parts:
$$ i_t = \sigma[W_i \cdot (h_{t-1}, x_t) + b_i] $$
$$ \tilde{C}_t = \tanh[W_C \cdot (h_{t-1}, x_t) + b_C] $$
Cell State Update: The old cell state \(C_{t-1}\) is updated to the new cell state \(C_t\).
$$ C_t = f_t * C_{t-1} + i_t * \tilde{C}_t $$
Output Gate: Controls what part of the cell state is output as the hidden state.
$$ o_t = \sigma[W_o \cdot (h_{t-1}, x_t) + b_o] $$
$$ h_t = o_t * \tanh(C_t) $$
Here, \(x_t\) is the input vector (our health indicators at cycle t), \(h_t\) is the hidden state, \(C_t\) is the cell state, \(\sigma\) is the sigmoid activation function, and \(W\) and \(b\) terms are weights and biases learned during training.
The performance of an LSTM network is highly sensitive to the configuration of its hyperparameters, such as the number of hidden units, learning rate, and number of training epochs. Manually tuning these parameters is inefficient and often suboptimal. To address this, we employ a Genetic Algorithm (GA) for automatic hyperparameter optimization. The GA is a metaheuristic inspired by natural selection. It starts with a population of random hyperparameter sets (individuals). Each set is used to train an LSTM model, and its performance (fitness) is evaluated on a validation set. The fittest individuals are selected, and through operations like crossover and mutation, a new generation of hyperparameter sets is created. This process iterates, evolving towards an optimal configuration. The workflow of the GA-LSTM model is as follows:
- Initialize a GA population of LSTM hyperparameter sets.
- For each individual (hyperparameter set):
- Construct and train an LSTM model on the training data (sequences of HIs and SOH).
- Evaluate the model’s fitness (e.g., using validation Mean Squared Error).
- Apply GA selection, crossover, and mutation to create a new population.
- Repeat steps 2-3 until a termination criterion (e.g., max generations) is met.
- Train the final LSTM model using the best-found hyperparameters on the combined training and validation data.
Experimental Validation
To validate the proposed method, a cycling aging experiment was conducted on five commercial 20 Ah soft-pack LiFePO₄ energy storage batteries. The batteries were cycled in a temperature-controlled chamber at 25°C using a battery tester. The cycling protocol consisted of a constant-current constant-voltage (CC-CV) charge at 0.5C (10 A) to 3.65 V, followed by a constant-current discharge at 0.5C to 2.5 V. This represents a typical duty cycle for an energy storage battery in application.
Every 100 cycles, the actual capacity of the energy storage battery was calibrated using a low-rate discharge test to determine the ground-truth SOH value according to the formula:
$$
\text{SOH} = \frac{Q_{\text{current}}}{Q_{\text{nominal}}} \times 100\%
$$
where \(Q_{\text{current}}\) is the measured discharge capacity at the check-up cycle and \(Q_{\text{nominal}}\) is 20 Ah. Concurrently, the detailed voltage and current profiles from the preceding regular cycle were recorded to extract the defined health indicators (HI₁, HI₂, HI₃).
The experiment resulted in over 4,000 cycles of data per battery, showing a near-linear capacity fade. From an initial capacity of approximately 19.65 Ah (~98.25% SOH), the energy storage batteries degraded to about 17.80 Ah (~89.0% SOH) after 4,000 cycles, demonstrating a typical aging trajectory for this chemistry.
Results and Analysis
The dataset from three energy storage batteries was used for model development. The data was structured into sequences and split into a training set (80% of the data) and a testing set (20%). The model was trained to predict the SOH at cycle t based on the sequence of health indicators up to that cycle. To demonstrate the effectiveness of our approach, we compared the proposed GA-LSTM model against two benchmarks:
1. A standard LSTM model with manually chosen hyperparameters.
2. A Genetic Algorithm-optimized Backpropagation Neural Network (GA-BP), a common feedforward architecture.
The performance was quantitatively evaluated using two common metrics: Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE). Lower values indicate better accuracy.
$$
\text{MSE} = \frac{1}{n} \sum_{i=1}^{n} (y_i – \hat{y}_i)^2
$$
$$
\text{MAPE} = \frac{1}{n} \sum_{i=1}^{n} \left| \frac{y_i – \hat{y}_i}{y_i} \right| \times 100\%
$$
where \(y_i\) is the actual SOH, \(\hat{y}_i\) is the predicted SOH, and \(n\) is the number of samples.
The SOH prediction results on the independent test set (data from a fourth energy storage battery not used in training) are graphically shown in the conceptual plot below and quantified in the subsequent table. The proposed GA-LSTM model’s predictions closely track the actual SOH degradation curve, significantly outperforming the unoptimized LSTM. The GA-BP model also benefits from optimization but fails to capture the temporal dynamics as effectively as the LSTM-based model.
| Model | Mean Absolute Percentage Error (MAPE, %) | Mean Squared Error (MSE) |
|---|---|---|
| Unoptimized LSTM | 2.11 | 0.000548 |
| GA-BP Neural Network | 1.33 | 0.000282 |
| Proposed GA-LSTM | 1.09 | 0.000142 |
The performance comparison reveals the clear advantage of the proposed method. The GA-LSTM model achieved an MAPE of 1.09% and an MSE of 0.000142. Compared to the unoptimized LSTM, this represents a reduction of approximately 48.3% in MAPE and 74.1% in MSE. This dramatic improvement underscores the critical importance of proper hyperparameter tuning for deep learning models applied to energy storage battery diagnostics. Furthermore, while the GA-BP model showed decent performance due to GA optimization, the GA-LSTM’s superior accuracy highlights the inherent strength of LSTM architectures in modeling the sequential degradation of an energy storage battery, leading to a 18% lower MAPE than GA-BP.
Conclusion
This article has presented a highly accurate data-driven method for evaluating the State of Health of electrochemical energy storage batteries. The method’s efficacy stems from a two-pronged approach: First, the intelligent extraction of health indicators from readily available charging voltage data, focusing on specific time-voltage windows that exhibit strong correlation with capacity fade. Second, the deployment of a sophisticated GA-LSTM neural network that leverages the sequential nature of battery aging and is optimized for peak performance.
The experimental validation on LiFePO₄ energy storage batteries confirmed the model’s accuracy and robustness, with prediction errors significantly lower than those from unoptimized or simpler network architectures. The GA optimization proved essential for unlocking the full potential of the LSTM model. The proposed method relies solely on data that is easily accessible from the battery management system during normal operation, making it practical for real-world implementation. This work provides a reliable tool for the precise assessment of energy storage battery health, which is vital for optimizing system performance, planning maintenance, and ensuring the safe and economic operation of modern energy storage installations.