The widespread adoption of electric vehicles has made lithium-ion batteries the dominant energy storage solution, prized for their high energy density and low self-discharge rate. However, these batteries inevitably degrade with prolonged charge-discharge cycling, characterized by a reduction in maximum discharge capacity and an increase in internal resistance. Typically, a lithium-ion battery is considered retired from automotive use when its capacity degrades to 70-80% of its initial value. By 2030, it is projected that over 5 million metric tons of these batteries will be retired annually. Despite being unsuitable for vehicles, retired batteries often retain significant residual capacity, making them ideal candidates for secondary applications in less demanding sectors like energy storage for renewable sources or backup power systems—a practice known as echelon utilization.
The economic and environmental potential of this second-life market is substantial. Yet, a critical bottleneck impedes its large-scale implementation: the time-consuming and often inaccurate process of assessing the State of Health (SOH) of retired lithium-ion battery packs. SOH, a key metric defining a battery’s remaining useful life and value, cannot be measured directly. Conventional estimation methods require lengthy full-cycle tests to extract health indicators (HIs), such as features from incremental capacity (IC) or differential voltage (DV) curves. This process is prohibitively slow for high-throughput screening needed in recycling or repurposing facilities. Therefore, developing a fast, accurate, and non-destructive SOH estimation technique is paramount for unlocking the circular economy potential of retired lithium-ion battery systems.
To address this challenge, this article introduces a novel, rapid SOH estimation framework for retired lithium-ion battery cells. The core innovation lies in the fusion of ultrasonic sensing technology with a sophisticated sequence learning model. Ultrasound provides a highly sensitive, millisecond-scale probe into the internal electrochemical state of a lithium-ion battery. By strategically extracting ultrasonic feature differentials within an extremely short voltage window during charging, we construct a powerful set of “voltage-ultrasonic differential” health indicators. These HIs are then fed into a hybrid deep learning model named Informer-GRU, which expertly maps the temporal evolution of these indicators to an accurate SOH value. This approach drastically reduces the testing time from hours to minutes while maintaining high estimation fidelity, offering a practical solution for the efficient grading of retired lithium-ion battery cells.
Ultrasonic Probing and Health Indicator Construction
Ultrasonic testing has emerged as a powerful non-destructive evaluation (NDE) tool for lithium-ion battery diagnostics. Its principle is based on the interaction of high-frequency sound waves with the battery’s internal multi-layer structure, which includes the anode, separator, cathode, and electrolyte.
Principles of Ultrasound-Battery Interaction
A lithium-ion battery can be modeled as a composite material. When an ultrasonic wave propagates through it, its behavior is governed by the acoustic properties of the constituent materials. The longitudinal wave speed \( v \) in a material is given by:
$$ v = \sqrt{\frac{K + \frac{4}{3}G}{\rho}} $$
where \( K \) is the bulk modulus, \( G \) is the shear modulus, and \( \rho \) is the density. The acoustic impedance \( Z \), a critical property determining wave transmission and reflection at interfaces, is defined as:
$$ Z = \rho v $$
At an interface between two materials with impedances \( Z_1 \) and \( Z_2 \), the transmission coefficient \( T \) for a wave normally incident from material 1 to material 2 is:
$$ T = \frac{2Z_2}{Z_1 + Z_2} $$
As a lithium-ion battery ages, irreversible changes occur: the solid electrolyte interphase (SEI) layer thickens, active materials are consumed, and electrode particles may crack. These degradation mechanisms alter the mechanical properties (moduli \( K \), \( G \)) and density (\( \rho \)) of the battery components. Consequently, the local acoustic impedance and the overall ultrasonic wave transmission characteristics change. Typically, this results in increased signal attenuation, meaning the amplitude of the ultrasonic wave received on the opposite side of the battery decreases as SOH declines. This sensitive physical relationship forms the foundation for using ultrasound as a health probe.
Signal Acquisition, Denoising, and Feature Extraction
We employ a through-transmission ultrasonic setup. A transmitter probe excited by a pulsed signal generates ultrasonic waves that travel through the lithium-ion battery pouch cell. A receiver probe on the opposite side captures the transmitted signal, which carries information about the battery’s internal state. The raw signal often contains noise from electronic equipment and environmental vibrations. To ensure robust feature extraction, we apply Empirical Mode Decomposition (EMD) for denoising. EMD adaptively decomposes the signal \( s(t) \) into a series of Intrinsic Mode Functions (IMFs) and a residue:
$$ s(t) = \sum_{i=1}^{n} IMF_i(t) + r_n(t) $$
The high-frequency noise components (typically the first few IMFs) are discarded, and the remaining IMFs are reconstructed to obtain a clean ultrasonic signal \( u(t) \). From this clean signal, we extract four distinct features in both time and frequency domains that are sensitive to changes in wave attenuation and dispersion caused by battery aging. These features are summarized in the table below:
| Feature Domain | Feature Name | Symbol | Description & Formula |
|---|---|---|---|
| Time Domain | Signal Amplitude | \( A_{SA} \) | The peak voltage of the received ultrasonic waveform: \( A_{SA} = \max(u(t)) \) |
| Energy Integral | \( E \) | The total energy of the received signal over time window \( \Delta t \): \( E = \int_{t_0}^{t_0+\Delta t} u(t)^2 dt \) | |
| Frequency Domain | Spectrum Peak Amplitude | \( A_{Pf} \) | The maximum amplitude in the signal’s frequency spectrum (in dB): \( A_{Pf} = \max(20 \cdot \log_{10}|U(f)|) \), where \( U(f) \) is the Fourier Transform of \( u(t) \). |
| Power Spectral Density Peak | \( A_{PSD} \) | The peak value of the signal’s Power Spectral Density: \( A_{PSD} = \max( \lim_{T\to\infty} \frac{|U(f)|^2}{T} ) \) |
Constructing the “Voltage-Ultrasonic Differential” Health Indicator
The key to rapid estimation is to avoid needing data from the entire charge cycle. We hypothesize that even within a very small change in battery voltage (and thus state of charge, SoC), the sensitive ultrasonic features will exhibit a measurable differential that correlates strongly with the global SOH. Therefore, we define our HI as the change in an ultrasonic feature across a short, fixed voltage window \( \Delta V \) during the constant-current (CC) charging phase.
Let \( F^j(V) \) represent the value of a specific ultrasonic feature (e.g., \( A_{SA} \)) measured at voltage \( V \) during the \( j \)-th charge cycle. We select a reference voltage window from \( V_{start} \) to \( V_{end} \), where \( \Delta V = V_{end} – V_{start} \) is small (e.g., 40 mV). The “voltage-ultrasonic differential” health indicator \( \Delta F^j \) for cycle \( j \) is:
$$ \Delta F^j = F^j(V_{end}) – F^j(V_{start}) $$
This calculation is performed for all four ultrasonic features, creating a multi-dimensional HI vector \( \mathbf{HI}^j \) for each cycle \( j \):
$$ \mathbf{HI}^j = [\Delta A_{SA}^j, \Delta E^j, \Delta A_{Pf}^j, \Delta A_{PSD}^j]^T $$
The selection of the optimal voltage window \( (V_{start}, V_{end}) \) is data-driven. We search the CC charging phase (e.g., 3.6V to 4.2V) by sliding windows of different sizes and computing the average Pearson Correlation Coefficient (PCC) between each \( \Delta F \) sequence and the true SOH sequence. The window with the smallest size that maintains a PCC very close to the maximum achievable is chosen to maximize speed without sacrificing indicator strength. Our experiments found a 40 mV window to be optimal, providing near-maximal correlation with minimal testing requirement.
| Voltage Window Size (mV) | Optimal Window (V) | Average PCC with SOH |
|---|---|---|
| 20 | 3.69 – 3.71 | 0.9385 |
| 30 | 3.66 – 3.69 | 0.9566 |
| 40 | 3.64 – 3.68 | 0.9822 |
| 50 | 3.66 – 3.71 | 0.9839 |
The Informer-GRU Hybrid Estimation Model
Estimating SOH from a temporal sequence of HIs is a sequential regression problem. The model must capture both long-term degradation trends and short-term fluctuations in the HI data. We propose a hybrid architecture combining the Informer model, excelling at long-sequence modeling, and the Gated Recurrent Unit (GRU), effective at capturing short-term temporal dependencies.
Model Architecture Overview
The Informer-GRU model takes a historical sequence of HI vectors as input and outputs the estimated SOH for the current cycle. The input sequence is partitioned into three sections for the encoder-decoder structure: a long past context window for the encoder, a short recent context for the decoder’s initial input, and a placeholder for the target (set to zero). The core components are:
- Informer Encoder: Processes the long historical HI sequence. Its key innovation is the Probabilistic Sparse Self-Attention mechanism, which reduces the quadratic complexity of standard attention by allowing each key to only attend to the top-u most dominant queries. This is coupled with a Distilling operation, which applies a 1D convolutional layer followed by an ELU activation and max-pooling to halve the sequence length between encoder layers, efficiently extracting hierarchical features and reducing redundancy.
$$ \text{Distill}( \mathbf{X}_l ) = \text{MaxPool}( \text{ELU}( \text{Conv1D}(\mathbf{X}_l) ) ) $$
where \( \mathbf{X}_l \) is the attention output of layer \( l \). - Informer Decoder: Takes the concatenation of a short, recent HI sequence and the target placeholder. It uses a masked multi-head attention mechanism to prevent information leakage from future steps and attends to the encoded historical context.
- GRU Enhancement Layer: The output from the Informer decoder’s final layer, which contains rich contextualized features, is then passed through a GRU layer. The GRU’s update and reset gates allow it to model fine-grained, short-term sequential patterns in the features that the Informer’s global attention may smooth over.
$$ \begin{aligned}
z_t &= \sigma(W_z \cdot [h_{t-1}, x_t]) \\
r_t &= \sigma(W_r \cdot [h_{t-1}, x_t]) \\
\tilde{h}_t &= \tanh(W \cdot [r_t * h_{t-1}, x_t]) \\
h_t &= (1 – z_t) * h_{t-1} + z_t * \tilde{h}_t
\end{aligned} $$
Here, \( x_t \) is the input from the Informer decoder at step \( t \), \( h_t \) is the hidden state, \( z_t \) is the update gate, \( r_t \) is the reset gate, and \( \tilde{h}_t \) is the candidate activation. - Fully Connected Output Layer: The final hidden state from the GRU is fed into a linear layer to produce the single SOH estimate.
Advantages of the Hybrid Approach
The degradation of a lithium-ion battery is a slow, nonlinear process with complex dynamics. The Informer component is ideal for modeling the long-range dependencies in the HI sequence, effectively learning the overarching degradation trajectory from hundreds of cycles. Simultaneously, local SOH variations or minor recovery effects can cause short-term fluctuations in the HI trend. The GRU layer excels at capturing these local temporal patterns, adding a layer of refinement to the Informer’s global prediction. This synergy allows the Informer-GRU model to achieve higher accuracy and robustness compared to using either model alone.
Experimental Validation and Analysis
The proposed method was validated using a commercial 2000 mAh soft-pouch lithium-ion battery (model 903450). The battery underwent aging cycles at room temperature, each consisting of a 0.5C constant-current constant-voltage (CCCV) charge to 4.2V, a 15-minute rest, a 1C constant-current discharge to 2.75V, and another 15-minute rest. Ultrasonic through-transmission data was collected concurrently during charging using 1 MHz transducers. The experiment continued for 80 full cycles.
SOH Calculation and Data Preparation
The true SOH for cycle \( j \) was calculated based on the measured maximum discharge capacity \( C_j \):
$$ SOH_j (\%) = \frac{C_j}{C_0} \times 100\% $$
where \( C_0 \) is the initial discharge capacity. The ultrasonic data from the CC charging phase was processed to extract the four features. The optimal 40 mV window (3.64V to 3.68V) was identified, and the differential HIs \( \mathbf{HI}^j \) were computed for each cycle. The dataset of HI sequences and corresponding SOH labels was expanded using spline interpolation to increase the amount of training data. The dataset was then split into training and testing sets with different ratios (6:4, 7:3, 8:2) to evaluate model generalization.
Estimation Performance and Comparative Study
The performance of the Informer-GRU model was evaluated using Mean Absolute Error (MAE) and Root Mean Square Error (RMSE):
$$ \text{MAE} = \frac{1}{N} \sum_{j=1}^{N} | \widehat{SOH}_j – SOH_j |, \quad \text{RMSE} = \sqrt{ \frac{1}{N} \sum_{j=1}^{N} ( \widehat{SOH}_j – SOH_j )^2 } $$
where \( \widehat{SOH}_j \) is the estimated value and \( SOH_j \) is the true value.
We compared our model against three established benchmarks: Support Vector Regression with Particle Filtering (SVR-PF), a standard Long Short-Term Memory network (LSTM), and the standalone Informer model. The results across different train-test splits are summarized below:
| Model | TEST1 (6:4 Split) | TEST2 (7:3 Split) | TEST3 (8:2 Split) | |||
|---|---|---|---|---|---|---|
| MAE (%) | RMSE (%) | MAE (%) | RMSE (%) | MAE (%) | RMSE (%) | |
| SVR-PF | 0.075 | 0.102 | 0.022 | 0.033 | 0.035 | 0.048 |
| LSTM | 0.128 | 0.180 | 0.126 | 0.173 | 0.141 | 0.180 |
| Informer | 0.096 | 0.115 | 0.034 | 0.045 | 0.073 | 0.098 |
| Informer-GRU (Proposed) | 0.058 | 0.074 | 0.016 | 0.021 | 0.025 | 0.036 |
The results demonstrate the clear superiority of the proposed Informer-GRU model. It consistently achieves the lowest MAE and RMSE across all dataset splits, showcasing its robustness and generalization capability. The 7:3 split (TEST2) yielded the best overall performance, with the model achieving an exceptional MAE of 0.016% and RMSE of 0.021%. This indicates that the “voltage-ultrasonic differential” HIs extracted from just a 40 mV window contain highly predictive information, and the hybrid model effectively decodes this information. The standalone Informer model performs reasonably well but is generally outperformed by the hybrid, confirming the value added by the GRU in capturing fine-grained temporal dynamics. The SVR-PF method shows variable performance, while the standard LSTM struggles with the complexity of the sequence learning task in this context.
Conclusion and Future Perspectives
This article has presented a comprehensive and efficient framework for the rapid estimation of State of Health in retired lithium-ion battery cells. The methodology successfully addresses the critical need for speed in echelon utilization screening by combining two key innovations. First, it introduces the concept of “voltage-ultrasonic differential” health indicators, which leverage the high sensitivity of ultrasonic waves to internal battery state changes. By extracting feature differentials within a strategically chosen, narrow voltage window of only 40 mV (3.64V–3.68V), the method eliminates the need for time-consuming full-cycle tests. Second, it proposes the Informer-GRU hybrid deep learning model, which is specifically designed to model the long-term degradation trends and short-term fluctuations present in the sequential HI data, leading to highly accurate SOH predictions.
Experimental validation on a commercial pouch lithium-ion battery confirmed the framework’s effectiveness. The extracted HIs showed a very strong correlation (PCC > 0.98) with the actual SOH. The Informer-GRU model utilizing these HIs achieved outstanding estimation accuracy, with mean errors below 0.02% under optimal conditions, significantly outperforming several benchmark models. This demonstrates that accurate SOH assessment for a retired lithium-ion battery is feasible within a dramatically shortened testing timeframe.
For future work, the focus will shift towards practical implementation and broader validation. The current method requires historical HI data from a few preceding cycles to estimate the current SOH. Further research is needed to develop single-cycle estimation techniques or very short sequential models suitable for the first assessment of a completely unknown retired lithium-ion battery. Furthermore, extensive testing must be conducted on a wide variety of battery form factors (cylindrical, prismatic), chemistries (NMC, LFP), and capacities to establish universal calibration guidelines and understand the impact of cell geometry and design on the ultrasonic signal characteristics. Finally, integrating this ultrasonic method with other fast non-destructive techniques like electrochemical impedance spectroscopy (EIS) could lead to a multi-modal, ultra-rapid, and highly reliable grading system for the sustainable management of the burgeoning stream of retired lithium-ion battery resources.