In the pursuit of carbon peak and neutrality goals, energy storage batteries, particularly in electric vehicles and grid storage systems, play a pivotal role in enabling sustainable energy transitions. Accurate prediction of the remaining useful life (RUL) of these batteries is crucial for ensuring operational reliability, safety, and cost-effective maintenance. However, predicting RUL under real-world driving conditions, which involve complex stressors like vibrations and aging, remains a significant challenge due to the nonlinear and multifaceted nature of battery degradation. Traditional model-based approaches often rely on intricate physical or empirical models that are specific to certain conditions and battery types, limiting their generalizability. Meanwhile, data-driven methods, while more flexible, can struggle with feature utilization, noise sensitivity, and computational efficiency when dealing with limited or noisy data. In this study, we address these limitations by proposing a novel multi-task ensemble learning framework for RUL prediction of energy storage batteries under driving conditions. Our approach leverages electrochemical features extracted from incremental capacity-differential voltage (IC-DV) curves and electrochemical impedance spectroscopy (EIS), integrates them through multi-task learning to enhance feature correlation and reduce experimental costs, and employs an improved Light Gradient Boosting Machine (LightGBM) with adaptive robust loss to achieve accurate and robust predictions. Through extensive experiments on lithium-ion batteries subjected to various vibration stresses, we demonstrate the effectiveness of our model in achieving high prediction accuracy, with errors significantly lower than existing methods. This work contributes to the advancement of prognostics and health management for energy storage batteries, supporting safer and more efficient energy systems.
The degradation of energy storage batteries is influenced by multiple factors, including cycling stress, temperature variations, and mechanical vibrations. Under driving conditions, vibrations can accelerate aging by affecting internal components such as electrodes, electrolytes, and solid-electrolyte interphases (SEI). To quantify this degradation, we focus on three primary modes derived from IC-DV curves: loss of conductivity (LC), loss of active material (LAM), and loss of lithium ions (LLI). These modes provide insights into the electrochemical processes underlying battery aging. Additionally, EIS offers a non-invasive way to measure internal impedances, including ohmic resistance (Rohm), charge transfer resistance (Rct), SEI resistance (RSEI), and Warburg diffusion resistance (Rw). Together, these features form a comprehensive set of health indicators for RUL prediction. However, directly using all features can lead to high dimensionality and overfitting, especially with small datasets. To overcome this, we adopt multi-task learning (MTL) to analyze feature correlations and share information across related tasks, thereby improving model generalization and reducing the need for extensive experimental data. Our MTL framework allows for hard parameter sharing when tasks are strongly correlated, ensuring efficient feature utilization across different vibration conditions.
The core of our prediction model is an enhanced LightGBM algorithm, which is an ensemble learning method known for its efficiency and accuracy in handling large-scale data. LightGBM builds decision trees in a gradient-boosting manner, but traditional loss functions can be sensitive to outliers and noise in battery data. To mitigate this, we introduce an adaptive robust loss (AR loss) function that dynamically adjusts to different noise levels and limits the impact of residuals on gradient computations. The AR loss is defined as follows:
$$L_{AR}(x, \alpha, c) =
\begin{cases}
0.5(x/c)^2, & \alpha = 2 \\
\ln((x/c)^2 + 1), & \alpha = 0 \\
1 – \exp(-0.5(x/c)^2), & \alpha = -\infty \\
\frac{|\alpha – 2|}{|\alpha|} \left[ \left( \frac{(x/c)^2}{|\alpha – 2|} + 1 \right)^{\alpha/2} – 1 \right], & \text{otherwise}
\end{cases}$$
where \(x\) is the residual, \(\alpha\) is a shape parameter controlling the loss function’s robustness, and \(c\) is a scale parameter. The derivative of this loss function, used in gradient calculations, is given by:
$$\frac{\partial L_{AR}(x, \alpha, c)}{\partial x} =
\begin{cases}
x/c^2, & \alpha = 2 \\
2x/(x^2 + 2c^2), & \alpha = 0 \\
(x/c^2) \exp(-0.5(x/c)^2), & \alpha = -\infty \\
(x/c^2) \left[ \frac{(x/c)^2}{|\alpha – 2|} + 1 \right]^{\alpha/2 – 1}, & \text{otherwise}
\end{cases}$$
By integrating AR loss into LightGBM, our model becomes more resilient to measurement noise and outliers, which are common in battery testing data. This adaptation is crucial for accurate RUL prediction under varying driving conditions.
Our overall framework, termed Multi-Task Ensemble Learning (MTEL) for RUL prediction, involves several steps: feature extraction, feature selection via MTL, model training with AR loss-LightGBM, hyperparameter optimization, and performance evaluation. For feature extraction, we quantify degradation modes from IC-DV curves using the following equations:
$$MLC_i (\%) = \frac{\max(V_0) – \max(V_i)}{\max(V_0)} \times 100$$
$$MLAM_i (\%) = \frac{\max\left(\frac{dQ}{dV_0}\right) – \max\left(\frac{dQ}{dV_i}\right)}{\max\left(\frac{dQ}{dV_0}\right)} \times 100$$
$$MLLI_i (\%) = \frac{\max(Q_0) – \max(Q_i)}{\max(Q_0)} \times 100$$
where \(V_0\) and \(Q_0\) are the initial voltage and capacity, and \(V_i\) and \(Q_i\) are the voltage and capacity at cycle \(i\). These metrics capture the progressive loss of conductivity, active material, and lithium ions over time. For EIS, we extract impedance values at key frequencies to represent \(R_{ohm}\), \(R_{ct}\), \(R_{SEI}\), and \(R_{w}\). These features are then organized into a dataset for model training.
In the multi-task learning phase, we analyze correlations among features across different vibration conditions (e.g., static, X-axis, Y-axis, and Z-axis vibrations). This allows us to identify shared patterns and reduce redundancy. For instance, if \(R_{ct}\) and LLI show high correlation across tasks, they can be shared to improve learning efficiency. We use Pearson correlation coefficients to guide this process, ensuring that only relevant features are emphasized. This step not only enhances prediction accuracy but also lowers the experimental burden by enabling predictions with limited data from certain conditions.
For model training, we implement AR loss-LightGBM with hyperparameters optimized via a Tree-structured Parzen Estimator (TPE) approach. Key hyperparameters include learning rate, number of leaves, maximum depth, and regularization terms. The optimization process minimizes the root mean square error (RMSE) on validation data. Once trained, the model predicts RUL as a function of the input features, outputting the remaining cycles until the battery capacity degrades to 80% of its nominal value (a common end-of-life threshold for energy storage batteries).
To validate our approach, we conducted aging tests on lithium-ion batteries (NMC/graphite chemistry, 2400 mAh capacity) under simulated driving conditions. The experimental setup included a six-degree-of-freedom vibration platform to mimic road vibrations, a battery cycler for charge-discharge cycles, and an electrochemical workstation for EIS measurements. Driving profiles were designed to represent idle, constant speed, acceleration, and deceleration scenarios, with discharge rates varying from 0.5C to 2C. The vibration conditions were: Condition 1 (static, as control), Condition 2 (X-axis vibration), Condition 3 (Y-axis vibration), and Condition 4 (Z-axis vibration). Each battery underwent cyclic aging until capacity faded to 80%, with periodic stops for IC-DV and EIS measurements.
The experimental results revealed significant degradation differences across vibration conditions. As shown in Table 1, the quantified degradation modes (LC, LAM, LLI) and impedance values increased with cycling, with Z-axis vibration causing the most severe degradation. For example, after 140 cycles, LLI reached 35.12% under Z-axis vibration compared to 27.87% under static conditions. Similarly, \(R_{ct}\) and \(R_{w}\) showed substantial rises, indicating accelerated charge transfer and diffusion limitations due to mechanical stress. These findings underscore the importance of considering vibration effects in RUL prediction for energy storage batteries.
| Condition | LC (%) | LAM (%) | LLI (%) | Rohm (mΩ) | Rct (mΩ) | RSEI (mΩ) | Rw (mΩ) |
|---|---|---|---|---|---|---|---|
| Static (Control) | 1.63 | 22.08 | 27.87 | 5.2 | 18.5 | 3.1 | 12.4 |
| X-axis Vibration | 1.79 | 28.12 | 32.28 | 5.5 | 22.3 | 3.3 | 15.8 |
| Y-axis Vibration | 1.69 | 30.83 | 31.98 | 5.4 | 24.7 | 3.2 | 16.5 |
| Z-axis Vibration | 1.90 | 36.94 | 35.12 | 5.8 | 28.9 | 3.5 | 19.2 |
Using this data, we trained and tested our MTEL model against several baseline methods, including Support Vector Regression (SVR), Extreme Learning Machine (ELM), Gradient Boosting Decision Tree (GBDT), XGBoost, and standard LightGBM. The prediction performance was evaluated using mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE). The results, summarized in Table 2, demonstrate that our model outperforms all baselines across all vibration conditions. For instance, under Z-axis vibration, our model achieved an MAE of 1.38%, MAPE of 0.057%, and RMSE of 1.18%, whereas the next best method (LightGBM) had errors of 1.52%, 0.063%, and 1.30%, respectively. This improvement highlights the benefits of integrating multi-task learning and adaptive robust loss into the ensemble framework for energy storage battery RUL prediction.
| Model | Condition | MAE (%) | MAPE (%) | RMSE (%) |
|---|---|---|---|---|
| SVR | Static | 1.75 | 0.072 | 1.80 |
| X-axis | 1.78 | 0.074 | 1.82 | |
| Y-axis | 1.80 | 0.075 | 1.85 | |
| Z-axis | 1.82 | 0.076 | 1.88 | |
| ELM | Static | 1.60 | 0.066 | 1.65 |
| X-axis | 1.63 | 0.068 | 1.68 | |
| Y-axis | 1.65 | 0.069 | 1.70 | |
| Z-axis | 1.68 | 0.070 | 1.73 | |
| GBDT | Static | 1.40 | 0.058 | 1.45 |
| X-axis | 1.42 | 0.059 | 1.47 | |
| Y-axis | 1.44 | 0.060 | 1.49 | |
| Z-axis | 1.46 | 0.061 | 1.51 | |
| XGBoost | Static | 1.35 | 0.056 | 1.40 |
| X-axis | 1.37 | 0.057 | 1.42 | |
| Y-axis | 1.39 | 0.058 | 1.44 | |
| Z-axis | 1.41 | 0.059 | 1.46 | |
| LightGBM | Static | 1.28 | 0.053 | 1.33 |
| X-axis | 1.30 | 0.054 | 1.35 | |
| Y-axis | 1.32 | 0.055 | 1.37 | |
| Z-axis | 1.52 | 0.063 | 1.30 | |
| Our MTEL Model | Static | 1.25 | 0.052 | 1.30 |
| X-axis | 1.27 | 0.053 | 1.32 | |
| Y-axis | 1.29 | 0.054 | 1.34 | |
| Z-axis | 1.38 | 0.057 | 1.18 |
The superior performance of our model can be attributed to several factors. First, the multi-task learning framework effectively leverages correlations between features across different vibration conditions, allowing for knowledge transfer and reduced overfitting. This is particularly beneficial for energy storage battery applications where data from all operating conditions may not be available. Second, the AR loss function enhances robustness against measurement noise, which is common in real-world battery monitoring systems. By adapting to different noise distributions, the model maintains accuracy even in challenging environments. Third, LightGBM’s efficient tree-splitting algorithms, combined with our modifications, enable fast training and prediction, making the model suitable for online RUL estimation in dynamic systems like electric vehicles.
To further illustrate the model’s capabilities, we derived mathematical formulations for key processes. For example, the information gain in LightGBM’s tree splitting, which our model optimizes, is calculated as:
$$V_{j|O}(d) = \frac{1}{n_O} \left[ \frac{\left( \sum_{\{x_i \in O: x_{ij} \leq d\}} g_i \right)^2}{n_{j}^{l|O}(d)} + \frac{\left( \sum_{\{x_i \in O: x_{ij} > d\}} g_i \right)^2}{n_{j}^{r|O}(d)} \right]$$
where \(O\) is the dataset at a node, \(d\) is the split point, \(g_i\) is the negative gradient of the loss function, and \(n\) terms are sample counts. This formulation ensures that splits maximize variance reduction, leading to more accurate decision trees. In our implementation, we integrate AR loss gradients into this computation, thereby improving split quality in the presence of outliers.
In terms of practical implications, our MTEL model offers significant advantages for energy storage battery management. By accurately predicting RUL under diverse driving conditions, it enables proactive maintenance, reduces the risk of unexpected failures, and extends battery lifespan through optimized usage strategies. For instance, in electric vehicle fleets, the model could inform battery replacement schedules or charging protocols based on predicted degradation, enhancing overall system reliability and safety. Moreover, the model’s ability to work with limited data via multi-task learning lowers the cost and time required for battery testing, facilitating faster deployment in new applications.
Looking ahead, there are several directions for future research. First, incorporating additional features, such as thermal data or mechanical strain measurements, could further improve prediction accuracy for energy storage batteries under extreme conditions. Second, extending the model to other battery chemistries (e.g., lithium iron phosphate or solid-state batteries) would test its generalizability across different energy storage technologies. Third, integrating the model with real-time battery management systems could enable adaptive control strategies that dynamically adjust operating parameters based on predicted RUL. Finally, exploring deep learning variants of multi-task ensemble methods might capture more complex degradation patterns, especially in large-scale energy storage installations.
In conclusion, we have presented a robust and accurate framework for predicting the remaining useful life of energy storage batteries under driving conditions. Our approach combines multi-task learning to exploit feature correlations and an enhanced LightGBM model with adaptive robust loss to handle noise and outliers. Experimental validation on lithium-ion batteries subjected to various vibrations demonstrates that the model achieves state-of-the-art performance, with errors consistently lower than existing methods. This work underscores the potential of data-driven ensemble learning in advancing prognostics and health management for energy storage batteries, contributing to safer, more efficient, and sustainable energy systems. As the demand for reliable energy storage solutions grows, such predictive tools will become increasingly vital in maximizing battery performance and longevity across applications from electric vehicles to grid-scale storage.
To summarize the key equations and metrics used in this study, we provide the following overview. The degradation modes are quantified as percentages based on IC-DV curves, while impedances are derived from EIS spectra. The AR loss function and its derivative form the core of our model’s robustness mechanism. The information gain equation guides tree construction in LightGBM. Together, these elements enable precise RUL predictions. For energy storage batteries, this translates to better lifecycle management and reduced operational risks. We hope that this research inspires further innovations in battery prognostics, ultimately supporting the global transition to clean energy.