Predicting the remaining useful life (RUL) of energy storage lithium batteries is crucial for ensuring the reliability and safety of battery systems in applications such as electric vehicles and renewable energy storage. However, the degradation process of lithium batteries is complex and influenced by multiple factors, including temperature, charge-discharge rates, and chemical aging. Traditional prediction methods often treat all degradation data points equally, failing to account for their varying contributions to the prediction outcome, which leads to reduced accuracy. In this study, I propose a novel approach based on the Box-Cox algorithm to enhance the prediction of RUL for energy storage lithium batteries. This method involves linearizing battery capacity data using the Box-Cox transformation, calculating capacity degradation metrics, and incorporating an attention mechanism to weight data points based on their importance. The goal is to improve prediction accuracy and generalization in real-world scenarios.
The Box-Cox algorithm is a statistical technique designed to address non-normality, heteroscedasticity, and non-additivity in data. For energy storage lithium batteries, capacity data often exhibit nonlinear trends due to internal chemical processes and external operating conditions. By applying the Box-Cox transformation, I linearize the historical capacity data to make it more amenable to linear modeling. The transformation is defined as follows:
$$ y_i^{(\lambda)} = \begin{cases} \frac{y_i^\lambda – 1}{\lambda} & \text{if } \lambda \neq 0 \\ \ln y_i & \text{if } \lambda = 0 \end{cases} $$
where \( y_i^{(\lambda)} \) represents the transformed capacity observation, \( y_i \) is the original capacity value, and \( \lambda \) is the transformation parameter. To determine the optimal \( \lambda \), I maximize the log-likelihood function:
$$ \ln L(\lambda) = -\frac{n}{2} \ln \left[ \frac{1}{n} \sum_{i=1}^n (y_i^{(\lambda)} – \bar{y}^{(\lambda)})^2 \right] + (\lambda – 1) \sum_{i=1}^n \ln y_i $$
Here, \( n \) is the sample size, and \( \bar{y}^{(\lambda)} \) is the mean of the transformed data. This process enhances the stability and predictability of energy storage lithium battery data, facilitating subsequent analysis.
After linearizing the capacity data, I proceed to calculate the capacity degradation capability, which serves as a key indicator of battery health. This metric reflects the rate at which the battery’s energy storage capacity declines over charge-discharge cycles. To model this, I consider parameters such as energy utilization efficiency \( \eta \), charge degradation characteristics \( \hat{E} \), energy storage demand parameter \( k \), power supply coefficient \( \epsilon \), and initial energy storage \( y_i \). The capacity degradation capability \( C \) is expressed as:
$$ C = \frac{\hat{E} \cdot k \cdot \epsilon}{\eta \cdot y_i} $$
This equation quantifies how the energy storage lithium battery’s performance degrades over time, considering factors like efficiency and demand. For instance, a higher degradation capability indicates faster aging, which is critical for predicting RUL. In practical terms, monitoring this metric helps in timely battery replacement to maintain system stability.
To further refine the RUL prediction, I introduce an attention mechanism that assigns weights to different time points in the degradation data. This approach addresses the limitation of treating all data points equally by emphasizing those with higher predictive value. Given a time series of capacity degradation data \( (C_1, C_2, \ldots, C_t) \), where \( C_t \) is the degradation at time \( t \), the attention mechanism computes weights \( \alpha_t \) using a scoring function \( s(C_t, q) \), where \( q \) is a query vector representing contextual information. The normalized weights are obtained via the softmax function:
$$ \alpha_t = \frac{\exp(s(C_t, q))}{\sum_{j=1}^t \exp(s(C_j, q))} $$
The final prediction for the remaining life of the energy storage lithium battery is then given by:
$$ \text{RUL} = \sum_{t=1}^T \alpha_t \cdot f(C_t) $$
where \( f(C_t) \) is a function mapping degradation to life estimates. This mechanism enhances accuracy by focusing on critical periods in the battery’s lifespan.
In the experimental phase, I prepared the necessary software and hardware to validate the proposed method. The setup included high-performance computing resources to handle the data-intensive nature of energy storage lithium battery analysis. The following table summarizes the software and equipment used:
| Item | Specification |
|---|---|
| CPU | Intel Core i7-11700K |
| Memory | 32GB DDR4 RAM |
| Operating System | Windows 10 Pro |
| Data Processing Software | MATLAB |
| Box-Cox Algorithm Module | Custom scripts integrated with MATLAB |
This configuration ensured efficient processing of battery data, enabling accurate modeling of energy storage lithium battery degradation.
For the experimental data, I selected multiple energy storage lithium battery samples with varying specifications to assess the method’s robustness. The dataset included parameters such as temperature, charge and discharge currents, cutoff voltage, and capacity, as shown in the table below:
| Model | Temperature (°C) | Charge Current (A) | Discharge Current (A) | Cutoff Voltage (V) | Capacity (Ah) |
|---|---|---|---|---|---|
| B5 | 25 | 1.5 | 2.0 | 3.0 | 2.5 |
| B6 | 30 | 1.8 | 2.2 | 2.8 | 2.8 |
| B7 | 28 | 1.6 | 1.9 | 3.2 | 2.6 |
| B18 | 22 | 1.4 | 2.1 | 3.1 | 2.7 |
These parameters were recorded during charge-discharge cycles under controlled conditions, with the test terminating when the battery capacity dropped to 70% of its rated value. The data capture the linear degradation trends typical of energy storage lithium batteries, which are essential for RUL prediction.
In the results analysis, I compared the proposed Box-Cox-based method with two existing approaches: one based on integrated empirical mode decomposition and ensemble machine learning (Method 1), and another using CS-optimized deep belief networks (Method 2). For the B6 battery group, the Box-Cox method demonstrated superior accuracy in predicting RUL, with lower error rates and better alignment with actual degradation trajectories. The attention mechanism effectively highlighted significant degradation phases, resulting in more reliable forecasts for energy storage lithium battery systems. The comparative analysis confirmed that the Box-Cox algorithm, combined with capacity degradation calculations and attention weighting, offers a robust solution for RUL prediction.
In conclusion, the Box-Cox algorithm-based approach significantly improves the prediction of remaining life in energy storage lithium batteries by addressing data nonlinearities and emphasizing critical degradation points. This method enhances the accuracy and practicality of battery management systems, supporting timely maintenance and replacement decisions. Future work will focus on incorporating additional factors, such as thermal effects and cycling conditions, to further refine the model. The continued advancement of this technology will contribute to the sustainability and efficiency of energy storage lithium battery applications across various industries.