In recent years, with the widespread application of lithium-ion batteries, safety incidents such as fires have become increasingly frequent. Thermal runaway is a primary cause of these accidents, often triggered by various abusive operations like mechanical damage, electrical overload, or overheating. These abuses can lead to irreversible damage and eventual failure of li-ion batteries, posing significant risks. To prevent such failures and mitigate thermal runaway, it is crucial to trace the historical abuse conditions of li-ion batteries. This allows for early detection of damage and proactive maintenance. However, accurately identifying the type and intensity of past abuses remains challenging due to the subtle and complex nature of battery degradation signals. In this article, we propose a novel method for historical abuse backtrace in li-ion batteries, leveraging recurrence plot (RCP) transformation and deep learning via the GoogLeNet model. Our approach aims to enhance the reliability and accuracy of abuse diagnosis, contributing to safer battery management systems.
The diagnosis of abuse in li-ion batteries can be analogized to fault analysis, which typically involves detection, isolation, and assessment. Existing methods fall into three categories: model-based approaches, signal processing techniques, and data-driven methods. Model-based methods rely on physical or electrochemical models to simulate battery behavior. For instance, pseudo-two-dimensional (P2D) models have been used to study internal short circuits, and coupled mechanical-electrochemical-thermal models have analyzed failure mechanisms under mechanical abuse. While accurate, these models require precise parameterization and are often computationally intensive, limiting their practicality. Signal processing methods, such as wavelet transform and principal component analysis, extract features from voltage or current signals to identify anomalies. Though effective, they can be complex and may struggle with real-time implementation. Data-driven methods, particularly those using machine learning, have gained popularity due to their ability to handle large datasets without explicit physical models. For example, deep learning models have been applied to classify battery states based on spatial-temporal images converted from electrical behaviors. However, tracing historical abuse specifically for li-ion batteries—considering both type and intensity—remains underexplored. Our work addresses this gap by integrating an improved correlation analysis, recurrence plots, and a convolutional neural network to achieve robust backtrace capabilities.
Our proposed method consists of three key steps. First, we compute an improved Pearson correlation coefficient (IPCC) to assess voltage consistency among battery cells. This metric enhances sensitivity to abuse-induced variations while mitigating noise and load fluctuations. Second, we transform the one-dimensional IPCC sequence into a two-dimensional recurrence plot (RCP), which visualizes temporal patterns and amplifies discriminative features. Third, we employ the GoogLeNet model, a deep convolutional neural network, to classify the RCP images and infer the type and intensity of historical abuse. We validate our approach using real experimental data from li-ion battery packs subjected to various abusive conditions. The results demonstrate high accuracy in backtracing abuse, highlighting the effectiveness of our method. This article is structured as follows: we detail the methodology, describe the experimental setup, present validation results, and conclude with insights and future directions.
The core of our method lies in extracting abuse-sensitive features from voltage data. In a li-ion battery pack, individual cells may degrade differently under abuse, leading to voltage inconsistencies. However, direct voltage signals are often noisy and influenced by operational conditions, making them unsuitable for direct analysis. To address this, we introduce an improved Pearson correlation coefficient (IPCC) that incorporates recursion and forgetting mechanisms. For two voltage sequences \( X \) and \( Y \) from different cells, the IPCC at time \( i \) is defined as:
$$ R_c(X,Y)_i = \frac{P_i – Q_i R_i}{\sqrt{(S_i – Q_i^2)(T_i – R_i^2)}} $$
where \( X_i = v_{x,i} + \phi_i \) and \( Y_i = v_{y,i} + \phi_i \), with \( v_{x,i} \) and \( v_{y,i} \) being voltage measurements, and \( \phi_i \) an auxiliary alternating square wave to counteract measurement errors and noise. The terms \( P_i \), \( Q_i \), \( R_i \), \( S_i \), and \( T_i \) are updated recursively with a forgetting window of length \( w \), ensuring sensitivity to short-term features. The recursive updates are:
$$ \begin{aligned}
P_i &= P_{i-1} + x_i y_i – x_{i-w} y_{i-w} \\
Q_i &= Q_{i-1} + x_i – x_{i-w} \\
R_i &= R_{i-1} + y_i – y_{i-w} \\
S_i &= S_{i-1} + x_i^2 – x_{i-w}^2 \\
T_i &= T_{i-1} + y_i^2 – y_{i-w}^2
\end{aligned} $$
Here, \( w \) is set to match the dimensions of subsequent images, and the sampling period is adjusted to six intervals. The IPCC effectively captures voltage consistency while reducing the impact of load variations, providing a robust signal for abuse detection in li-ion batteries.
Next, we convert the IPCC sequence into a recurrence plot (RCP) to leverage image-based classification. RCPs are graphical representations of time series that reveal periodic patterns and hidden structures. Given an IPCC sequence \( C = \{c_1, c_2, \dots, c_N\} \), we first construct a delayed embedding matrix with dimension \( d \) and delay \( \tau \). Each vector \( \mathbf{v}_k \) in this matrix is:
$$ \mathbf{v}_k = \{c_k, c_{k+\tau}, c_{k+2\tau}, \dots, c_{k+(d-1)\tau}\} $$
for \( k = 1, 2, \dots, K \), where \( K = N – (d-1)\tau \). We then compute the pairwise distances between vectors using a norm, such as the Euclidean norm:
$$ \|\mathbf{v}_i – \mathbf{v}_j\| = \sqrt{\sum_{m=0}^{d-1} (c_{i+m\tau} – c_{j+m\tau})^2} $$
Alternatively, the infinity norm can be used. A threshold \( \varepsilon \) is applied to binarize the distance matrix, resulting in a recurrence matrix \( \mathbf{T} \) with elements:
$$ T_{i,j} = \Theta(\varepsilon – \|\mathbf{v}_i – \mathbf{v}_j\|) $$
where \( \Theta(\cdot) \) is the Heaviside step function. This matrix is visualized as a black-and-white image, where white points indicate recurrence. For li-ion battery abuse analysis, RCPs transform the temporal IPCC patterns into rich texture features, enhancing separability between different abuse types and intensities.
To classify the RCP images, we adopt the GoogLeNet model, a deep convolutional neural network known for its efficiency and accuracy. GoogLeNet incorporates Inception modules that perform multi-scale feature extraction through parallel convolutional layers with varying kernel sizes. The network architecture includes 22 layers, with Inception modules reducing computational cost while maintaining high performance. Compared to other models like LeNet or VGG, GoogLeNet is better suited for our RCP dataset due to its ability to handle diverse textures without overfitting. The model processes input images of size \( 224 \times 224 \) pixels, applying convolutions, ReLU activations, pooling, and dropout layers. We use the Adam optimizer with a learning rate of 0.0001 and a decay factor of 0.1 for training. The output layer provides probabilities for each abuse class, enabling precise backtrace of historical abuse in li-ion batteries.
We conducted experiments to validate our method using a custom-built test platform. The setup included a li-ion battery pack composed of 10 NCM cells (3.7 V, 3 Ah each). Voltage data were collected at 10 Hz via an LTC6811-based acquisition unit. An electronic load and DC power supply controlled charge-discharge cycles, while a vibration platform and ceramic heaters simulated mechanical and thermal abuses, respectively. The battery pack was subjected to various abusive operations, categorized by type and intensity. The abuse types included overcharge (OC), overdischarge (OD), vibration (VB), and overheating (OH). Each type had two intensity levels: weak (Level I) and severe (Level II). Parameters for these abuses are summarized in Table 1.
| Abuse Type | Mode | Intensity Level | Parameters |
|---|---|---|---|
| Electrical | Overcharge (OC) | I (Weak) | 5% extra charge |
| Overcharge (OC) | II (Severe) | 15% extra charge | |
| Electrical | Overdischarge (OD) | I (Weak) | 5% extra discharge |
| Overdischarge (OD) | II (Severe) | 15% extra discharge | |
| Thermal | Overheating (OH) | I (Weak) | 100°C for 0.5 hours |
| Overheating (OH) | II (Severe) | 100°C for 1.5 hours | |
| Mechanical | Vibration (VB) | I (Weak) | 20 Hz for 2 hours |
| Vibration (VB) | II (Severe) | 20 Hz for 4 hours |
For each abuse condition, we recorded voltage data during standard charge-discharge cycles to simulate real-world operation. The dataset comprised 7,920 RCP images generated from IPCC sequences, covering healthy states and eight abused states (two intensities per abuse type). The images were split into training (80%) and testing (20%) sets. We trained the GoogLeNet model to classify abuse types and intensities, evaluating performance through accuracy metrics.
The IPCC signals demonstrated high sensitivity to abuse in li-ion batteries. Healthy cells showed IPCC values consistently above 0.999 with minimal fluctuations, while abused cells exhibited significant deviations. For instance, weak vibration abuse resulted in IPCC curves similar to healthy states, indicating minor damage, whereas severe electrical abuses caused pronounced drops. Figure 1 illustrates example IPCC curves for different abuses, though actual figures are not included per instructions. These curves highlight the discriminative power of IPCC, but overlapping values necessitated further processing via RCPs.
Recurrence plots effectively enhanced feature separation. As shown in Table 2, RCPs generated from IPCC sequences exhibited distinct textures for each abuse condition. Healthy and weak overheating states shared similar periodic patterns, but with finer textures in the latter. Overcharge abuses produced large uniform regions due to high IPCC volatility, while vibration abuses showed mixed features. The RCP transformation thus provided a robust visual representation for deep learning classification.
| Abuse Condition | RCP Texture Description | Key Features |
|---|---|---|
| Healthy | Regular periodic patterns with fine details | High consistency, minimal noise |
| Weak OC | Moderate uniform areas with some texture | Visible fluctuations, periodic breaks |
| Severe OC | Large uniform black/white regions | Strong volatility, sparse recurrence |
| Weak OD | Irregular patterns with scattered points | Moderate inconsistency, varied periods |
| Severe OD | Prominent uniform blocks | High degradation, reduced recurrence |
| Weak VB | Fine textures similar to healthy but coarser | Slight periodicity shifts |
| Severe VB | Mixed textures with distinct patches | Combined features of OC and OD |
| Weak OH | Fine periodic patterns with gradual fading | Slow decline in consistency |
| Severe OH | Coarser textures with pronounced fading | Steeper decline, reduced detail |
The GoogLeNet model achieved high accuracy in backtracing abuse for li-ion batteries. We evaluated two classification tasks: coarse-grained (5 classes: healthy, OC, OD, VB, OH) and fine-grained (9 classes including intensity levels). Results are presented in Table 3 and Table 4. For coarse-grained classification, the overall accuracy was 77.34%, with OC, OD, and OH achieving above 80% accuracy, while healthy states had lower accuracy due to confusion with weak abuses. Fine-grained classification yielded an overall accuracy of 75.37%, with severe abuses generally more recognizable than weak ones. These results underscore the efficacy of our RCP-GoogLeNet framework in diagnosing historical abuse in li-ion batteries.
| True Label | Predicted Labels (A: Healthy, B: OC, C: OD, D: VB, E: OH) | Accuracy |
|---|---|---|
| A (Healthy) | 112 as A, 10 as B, 3 as C, 34 as D, 17 as E | 63.6% |
| B (OC) | 11 as A, 291 as B, 14 as C, 21 as D, 15 as E | 82.7% |
| C (OD) | 6 as A, 17 as B, 291 as C, 6 as D, 32 as E | 82.7% |
| D (VB) | 48 as A, 13 as B, 10 as C, 269 as D, 12 as E | 76.4% |
| E (OH) | 6 as A, 9 as B, 32 as C, 19 as D, 286 as E | 81.3% |
| Overall Accuracy | 77.34% | |
| True Label | Predicted Labels (1: Healthy, 2: Weak OC, 3: Severe OC, 4: Weak OD, 5: Severe OD, 6: Weak VB, 7: Severe VB, 8: Weak OH, 9: Severe OH) | Accuracy |
|---|---|---|
| 1 (Healthy) | 104 as 1, 5 as 2, 1 as 3, 2 as 4, 1 as 5, 43 as 6, 6 as 7, 11 as 8, 3 as 9 | 59.1% |
| 2 (Weak OC) | 7 as 1, 135 as 2, 10 as 3, 3 as 4, 1 as 5, 9 as 6, 3 as 7, 6 as 8, 2 as 9 | 76.7% |
| 3 (Severe OC) | 1 as 1, 8 as 2, 137 as 3, 13 as 4, 2 as 5, 8 as 6, 3 as 7, 4 as 8, 0 as 9 | 77.8% |
| 4 (Weak OD) | 1 as 1, 7 as 2, 11 as 3, 130 as 4, 4 as 5, 7 as 6, 1 as 7, 7 as 8, 8 as 9 | 73.9% |
| 5 (Severe OD) | 0 as 1, 0 as 2, 5 as 3, 6 as 4, 141 as 5, 2 as 6, 0 as 7, 2 as 8, 20 as 9 | 80.1% |
| 6 (Weak VB) | 38 as 1, 5 as 2, 1 as 3, 3 as 4, 2 as 5, 108 as 6, 10 as 7, 9 as 8, 0 as 9 | 61.4% |
| 7 (Severe VB) | 0 as 1, 4 as 2, 0 as 3, 1 as 4, 1 as 5, 12 as 6, 154 as 7, 4 as 8, 0 as 9 | 87.5% |
| 8 (Weak OH) | 4 as 1, 3 as 2, 2 as 3, 3 as 4, 2 as 5, 13 as 6, 6 as 7, 134 as 8, 9 as 9 | 76.1% |
| 9 (Severe OH) | 0 as 1, 1 as 2, 0 as 3, 6 as 4, 11 as 5, 0 as 6, 0 as 7, 7 as 8, 151 as 9 | 85.8% |
| Overall Accuracy | 75.37% | |
The performance analysis reveals several insights. First, the IPCC method successfully captured voltage inconsistencies induced by abuse in li-ion batteries, with electrical abuses showing the most significant effects. Second, RCPs provided enhanced visual features that facilitated deep learning classification. The texture differences between abuse types and intensities were effectively leveraged by GoogLeNet, as seen in the accuracy metrics. Third, the model struggled slightly with distinguishing healthy states from weak abuses, particularly vibration, due to subtle damage signatures. However, severe abuses were consistently identified with high accuracy, underscoring the method’s reliability for critical cases. Compared to prior work, our approach improved classification accuracy by leveraging recurrence plots and a sophisticated neural network, offering a practical solution for historical abuse backtrace in li-ion battery systems.
In conclusion, we have presented a novel method for tracing historical abuse in li-ion batteries using recurrence plots and the GoogLeNet model. Our approach integrates an improved Pearson correlation coefficient to measure voltage consistency, converts these signals into recurrence plot images for feature enhancement, and applies deep learning for accurate classification. Experimental results on real li-ion battery data demonstrate that our method can reliably identify both the type and intensity of past abuses, with accuracies of 77.34% for coarse-grained and 75.37% for fine-grained classification. This work contributes to battery safety by enabling proactive maintenance and risk assessment. Future directions include extending the method to online monitoring, incorporating additional sensor data like temperature, and exploring other deep learning architectures for improved performance. The continued advancement of such data-driven techniques will enhance the reliability and longevity of li-ion batteries in various applications.
The implications of this research are significant for industries relying on li-ion batteries, such as electric vehicles and renewable energy storage. By accurately backtracing abuse, operators can identify compromised cells early, prevent catastrophic failures, and optimize battery lifespan. Our method’s reliance on voltage data alone makes it cost-effective and easily integrable into existing battery management systems. Moreover, the use of recurrence plots and GoogLeNet showcases the potential of image-based deep learning for time-series analysis in engineering domains. As li-ion battery technology evolves, robust diagnostic tools like ours will be essential for ensuring safety and performance in an increasingly electrified world.