The global imperative to address the dual challenges of the energy crisis and environmental pollution has catalyzed a decisive shift towards the electrification of transportation. At the heart of this revolution lies the lithium-ion battery, prized for its high energy density, long cycle life, and environmental friendliness. Ensuring the safety and reliability of these energy storage units is paramount. Among all failure modes, the internal short-circuit (ISC) is recognized as a primary precursor to thermal runaway, a catastrophic event characterized by a rapid, uncontrolled temperature rise that can lead to fire or explosion. Early and precise identification of ISC faults is therefore a critical challenge for battery management systems (BMS).
Traditional model-based diagnostic methods, which rely on equivalent circuit or electrochemical models, face significant challenges. They often struggle with complex parameter identification and require frequent updates when the operating environment or the lithium-ion battery‘s state of health changes. In contrast, data-driven methods, which learn diagnostic patterns directly from operational data, offer a promising alternative due to their simplicity and adaptability. We propose a novel, data-driven method for the accurate detection and localization of early-stage ISC faults in series-connected lithium-ion battery modules, based on the analysis of voltage time series similarity.
Diagnostic Principle and Methodology
The core physical phenomenon underpinning our method is the voltage divergence of a faulty cell within a series string. When an ISC occurs in a single lithium-ion battery cell, it creates an alternative current path. During charging, this causes the faulty cell to charge more slowly, leading to a lower terminal voltage compared to its healthy peers. Conversely, during discharge, it may discharge faster. This relative voltage offset, though subtle in the early stages, is a consistent and detectable signature.
Our approach quantifies this offset by measuring the similarity between the voltage-time profiles of different cells over defined diagnostic windows. A healthy module will exhibit highly similar voltage trajectories across all cells. The introduction of an ISC causes the voltage profile of the faulty cell to warp and diverge from the others. By continuously monitoring this similarity, we can detect the onset of a fault. The overall diagnostic algorithm is structured as follows: first, dynamically select a reference cell and define the diagnostic time interval; second, calculate the voltage time series similarity for all cells; third, extract key fault-indicative features from these similarity metrics; fourth, use a data-driven classifier to identify the faulty cell; and finally, employ a fault-tolerant voting mechanism to validate the diagnosis.
Voltage Window Segmentation and Reference Selection
To ensure sensitivity across the entire state-of-charge (SOC) range, we segment the charge/discharge cycle into multiple diagnostic windows. This segmentation is guided by Incremental Capacity (IC) analysis, which links external electrical characteristics to internal electrochemical states of the lithium-ion battery. The IC curve, derived from galvanostatic voltage data, is smoothed and its characteristic peaks and valleys are identified. We typically use the voltage boundaries corresponding to major peaks to define three primary diagnostic windows (e.g., [3.5V, 3.6V], [3.6V, 3.9V], [3.9V, 4.1V]). This allows for frequent, in-cycle diagnosis.
For each window during operation, a reference cell is dynamically selected. During charging, the first cell to reach the window’s lower voltage bound is chosen as the reference. The time period for that cell’s voltage to traverse the window becomes the active diagnostic interval for all cells. During discharge, the last cell to reach the window’s upper bound is selected. This dynamic selection minimizes the impact of initial cell-to-cell variations.
Quantifying Similarity: The Dynamic Time Warping Algorithm
Direct Euclidean distance between voltage sequences is sensitive to temporal misalignments. To robustly compare the shape of two voltage trajectories, we employ the Dynamic Time Warping (DTW) algorithm. DTW finds an optimal non-linear alignment between two sequences by warping the time axis, minimizing the cumulative distance between aligned points.
Given two voltage time series, \( Q = [q_1, q_2, …, q_n] \) (reference cell) and \( C = [c_1, c_2, …, c_m] \) (test cell), DTW constructs an \( n \times m \) cost matrix where each element \( (i, j) \) represents the local distance \( d(q_i, c_j) \), typically the squared Euclidean distance: \( d(q_i, c_j) = (q_i – c_j)^2 \). It then finds the warping path \( W = w_1, w_2, …, w_K \), where \( w_k = (i_k, j_k) \), that minimizes the total cumulative distance:
$$ DTW(Q, C) = \min_W \sqrt{\sum_{k=1}^{K} d(w_k)} $$
The optimal path is computed efficiently using dynamic programming with the following recurrence relation, where \( \gamma(i,j) \) is the cumulative distance up to point \( (i, j) \):
$$ \gamma(i,j) = d(q_i, c_j) + \min\{ \gamma(i-1,j-1), \gamma(i-1,j), \gamma(i,j-1) \} $$
The final DTW distance, or “warping loss,” serves as our primary similarity metric. A high warping loss indicates significant morphological difference between the test cell’s voltage curve and the reference curve, signaling a potential fault.
Feature Engineering for Fault Classification
Raw DTW distances are processed to extract robust features for classification. For each diagnostic window \( j \) and cell \( i \), we compute the following feature vector \( F_{i,j} \):
| Feature Symbol | Name | Mathematical Definition | Physical Interpretation |
|---|---|---|---|
| \( P_{i,j} \) | Distribution Index | $$ P_{i,j} = \frac{D_{i,j} – D_{min,j}}{D_{max,j} – D_{min,j}} $$ | Relative position of the cell’s warping loss within the module. A faulty cell tends toward 1. |
| \( \Delta_{i,j} \) | Increment Index | $$ \Delta_{i,j} = D_{i,j} – D_{i,j-1} $$ | Change in warping loss between consecutive cycles. A sharp positive jump is indicative of fault onset. |
| \( F_j \) | Reference Change Flag | $$ F_j = \begin{cases} 1 & \text{if } S_j \neq S_{j-1} \\ 0 & \text{otherwise} \end{cases} $$ | Flags cycles where the dynamically selected reference cell changes. |
| \( \text{Var}_j \) | Variance | $$ \text{Var}_j = \frac{1}{m}\sum_{i=1}^{m} (D_{i,j} – \mu_j)^2 $$ | Spread of warping losses across the module. Increases when a fault appears. |
| \( \text{Ske}_j \) | Skewness | $$ \text{Ske}_j = \frac{\frac{1}{m}\sum_{i=1}^{m}(D_{i,j} – \mu_j)^3}{\text{Var}_j^{3/2}} $$ | Asymmetry of the loss distribution. Becomes positive with a fault (outlier). |
| \( \text{Kur}_j \) | Excess Kurtosis | $$ \text{Kur}_j = \frac{\frac{1}{m}\sum_{i=1}^{m}(D_{i,j} – \mu_j)^4}{\text{Var}_j^{2}} – 3 $$ | Tailedness of the loss distribution. Increases due to the faulty cell outlier. |
Where \( D_{i,j} \) is the DTW loss for cell \( i \) in window \( j \), \( D_{max,j} \) and \( D_{min,j} \) are the maximum and minimum losses in the module for that window, \( S_j \) is the index of the reference cell, \( m \) is the number of cells, and \( \mu_j \) is the mean loss. These features collectively describe both the absolute anomaly of a single lithium-ion battery and the statistical shape of the module’s state.
Classification Model: Boosting Tree
We frame the fault detection as a binary classification problem (faulty vs. normal) for each cell in each diagnostic window. A Boosting Tree model, specifically using the AdaBoost framework with decision trees as weak learners, is chosen for its high accuracy and robustness. The model \( G(x) \) is an ensemble of \( M \) weak tree classifiers \( G_m(x) \):
$$ G(x) = \text{sign}\left(\sum_{m=1}^{M} \alpha_m G_m(x)\right) $$
The AdaBoost algorithm iteratively trains the weak learners. Initially, all training samples \( (x_i, y_i) \) have equal weight. In each iteration \( m \):
- A weak classifier \( G_m(x) \) is trained on the weighted dataset.
- Its weighted error rate \( \epsilon_m \) is calculated.
- Its contribution weight \( \alpha_m \) is computed: \( \alpha_m = \frac{1}{2} \ln \left( \frac{1-\epsilon_m}{\epsilon_m} \right) \).
- Sample weights are updated: incorrectly classified samples have their weights increased, focusing subsequent learners on harder cases.
This process produces a strong classifier that performs significantly better than any individual weak learner, making it highly effective for identifying the subtle patterns of early ISC in a lithium-ion battery.
Fault-Tolerant Voting Mechanism
To enhance reliability and prevent false alarms from sporadic model errors, we introduce a multi-level queue-based voting mechanism. Instead of triggering an alarm after a fixed number of consecutive fault diagnoses—which is sensitive to single false-negative errors—we maintain a dynamic fault-grade counter for each cell.
- Initialization: Each cell starts with a counter of zero (“Normal” grade).
- Dynamic Update: After each diagnostic window result:
- If the model labels the cell as faulty, its counter is incremented.
- If labeled normal, its counter is decremented (with a floor of zero).
- Multi-Level Queues: Cells are categorized into grades (e.g., Low, Medium, High) based on their counter value.
- Alarm Trigger: An ISC fault alarm is only confirmed and issued when a cell’s counter exceeds a predefined high threshold. This mechanism introduces a short, predictable diagnostic delay (a few cycles) while effectively filtering out random classification errors, ensuring both timeliness and high accuracy for the lithium-ion battery management system.
Experimental Validation and Results
To validate the proposed method, we constructed experimental setups using series-connected modules of commercial 18650 NCM lithium-ion battery cells. Internal short circuits were simulated by connecting external resistors of varying values in parallel with a designated cell within the module, controlled by a switch. We conducted tests under multiple driving profiles to evaluate robustness across different operational conditions.
| Experiment ID | Operating Profile | Simulated ISC Resistance (Ω) | Purpose |
|---|---|---|---|
| 1 | Constant Current (CC-CV) | 100 | Training / Severe Fault |
| 2 | Constant Current (CC-CV) | 510 | Training / Moderate Fault |
| 3 | Constant Current (CC-CV) | 1000 | Testing / Early-Stage Fault |
| 4 | Dynamic Stress Test (DST) | 1000 | Testing / Dynamic Profile |
| 5 | New European Driving Cycle (NEDC) | 1000 | Testing / Dynamic Profile |
| 6 | Urban Dynamometer Driving Schedule (UDDS) | 1000 | Training / Dynamic Profile |
| 7 | Worldwide Harmonized Light Vehicles Test Cycle (WLTC) | 1000 | Training / Dynamic Profile |
The Boosting Tree model was trained on data from Experiments 1, 2, 6, and 7. Its performance was then evaluated on the unseen test data from Experiments 3, 4, and 5, which represent the challenging case of early-stage (1000Ω) ISC under both constant current and complex dynamic loads.
The DTW algorithm successfully amplified the subtle voltage divergence. The warping loss for the faulty cell exhibited a marked and sustained increase immediately after fault initiation, while losses for healthy cells remained low and stable. The extracted features clearly captured this transition.
The classification performance was exceptional. The Boosting Tree model achieved an overall accuracy of 99.34% on the combined test set. The confusion matrix for the test data reveals high precision and recall:
| Predicted Condition | ||
|---|---|---|
| Actual Condition | Faulty | Normal |
| Faulty | 118 (True Positives) | 6 (False Negatives) |
| Normal | 2 (False Positives) | 1080 (True Negatives) |
This translates to a sensitivity (True Positive Rate) of 95.16% and a specificity (True Negative Rate) of 99.82%. Comparative analysis with other common classifiers demonstrated the superiority of the Boosting Tree approach for this application.
The fault-tolerant mechanism effectively validated these results. In test scenarios, isolated false-negative classifications from the model only caused a minor delay of 2-3 diagnostic cycles before the cell’s counter progressed to the “High” fault grade and triggered a confirmed alarm. This proves the mechanism successfully enhances diagnostic reliability without significantly compromising timeliness for the lithium-ion battery pack.
Conclusion
In this work, we have presented a comprehensive, data-driven methodology for the early detection and precise localization of internal short-circuit faults in series-connected lithium-ion battery modules. The method’s strength is multi-faceted. By segmenting the voltage curve using IC analysis and applying the DTW algorithm, we transform a subtle voltage offset into a pronounced, quantifiable similarity metric that is sensitive to early-stage faults. The feature extraction process creates a robust signature for classification. The Boosting Tree model, trained on these features, demonstrates remarkably high accuracy (99.34%) across both steady-state and dynamic operational profiles, showing its independence from specific loading conditions or pre-defined thresholds. Finally, the innovative voting-based fault-tolerant mechanism adds a crucial layer of reliability, ensuring the system is robust against sporadic classification errors.
Experimental validation on a practical lithium-ion battery module under varied driving cycles and fault severities confirms the method’s efficacy and practicality for integration into a BMS. Future work will focus on extending this data-driven paradigm to not only detect and locate but also quantitatively estimate the severity (equivalent resistance) of an ISC. Furthermore, investigating methods to diagnose the progression of an ISC toward thermal runaway remains a vital direction for ensuring the ultimate safety of lithium-ion battery energy storage systems.