Multistage Early Warning of Sodium-Ion Battery Thermal Runaway Using Multidimensional Signal Analysis and Redundancy Optimization
Abstract
:1. Introduction
- A hierarchical early warning method based on multidimensional signals is proposed, utilizing redundancy analysis and an LSTM neural network to achieve accurate early detection of different stages of thermal runaway in sodium-ion batteries.
- The proposed method is validated through electrical abuse experiments under different charging rates, demonstrating superior performance in reducing data redundancy, enhancing early warning accuracy, and improving stage classification capability, with a prediction accuracy exceeding 95%.
2. Methodology
2.1. PCA-Based Feature Extraction
- (1)
- To mitigate the effects of differing parameter dimensions, the original data matrix X is standardized to matrix K. The standardization is expressed by Equation (1).
- (2)
- Following data standardization, the covariance matrix for these features is calculated, which indicates the relationship of changes between each feature. The covariance matrix is calculated by Equation (4).
- (3)
- The eigenvalues and eigenvectors are extracted from the covariance matrix. Each eigenvalue represents the magnitude of the variance explained by its corresponding eigenvector, while each eigenvector explains the direction of a principal component. These values help identify the most important directions, or components, in the data for dimensionality reduction. Eigenvectors and eigenvalues are calculated in Equation (5).
- (4)
- Project the original data onto the principal component eigenvectors to achieve dimensionality reduction. The projection of the sample onto the eigenvector is calculated in Equation (6).
- (5)
- Calculate the contribution rate of each eigenvalue, which is expressed in Equation (7). Then, the eigenvectors of each principal component are weighted by the ratio of their corresponding eigenvalues as shown in Equation (8). Furthermore, the coefficients of each parameter within the eigenvector are utilized to characterize the contribution of each parameter to the evaluation of thermal runaway stages. This approach allows for a quantifiable and systematic assessment of how each parameter influences the progression of thermal runaway.
2.2. Long Short-Term Memory Neural Network-Based SIBs Warning
- (1)
- Identify and specify input features (selected parameters) and corresponding output labels (thermal runaway stages) required for the modeling task.
- (2)
- Normalize input data using a standard normalization method to ensure all features are on a similar scale. Divide the normalized data into two subsets, including a training set for model learning and a testing set for performance evaluation.
- (3)
- Construct an LSTM network and randomly initialize its hyperparameters, including learning rate, weights, and biases. Train the LSTM model using a training dataset, iteratively updating parameters until termination criteria are met.
- (4)
- After training the LSTM model, evaluate the network’s classification performance using a confusion matrix. The confusion matrix provides a quantitative comparison of actual class labels () and predicted class labels () for the test dataset. It is structured in Equation (10).
3. Experiment
3.1. Experimental Settings
3.2. Error Analysis
3.3. Repeatability Analysis
4. Thermal Runaway Multi-Parameter Hierarchical Warning
4.1. Division of Thermal Runaway Stages
4.2. Parameter Contribution Degree Analysis
4.3. Predictive Performance of the LSTM Model
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameters | Value |
---|---|
Nominal capacity | 3.29 Ah |
Cathode material | Na4Fe3(PO4)2(P2O7) |
Cut-off voltage | 1.5–3.9 V |
Overall dimensions | 100’75’10 mm |
Experimental Apparatus | Instrument Model | Parameter | Value |
---|---|---|---|
Thermocouple | K-type | Maximum temperature/°C | 482 |
Carbon dioxide sensor | NDIR 6703 | Sample frequency/Hz | 1 |
Range/ppm | 5000 | ||
Sensitivity ratio | ±0.5% | ||
Carbon monoxide sensor | ZE03 | Sample frequency/Hz | 1 |
Range/ppm | 1000 | ||
Sensitivity ratio | ±0.5% | ||
Strain sensor | BSF120-3AA-T | Size of base (length’width)/mm | 6.6’3.2 |
Size of wire grating (length’width)/mm | 3.0’2.3 | ||
Resistance/Ω | 120 ± 0.1 | ||
Sensitivity ratio | 2.0 ± 1% |
Stage | I | II | III | IV |
---|---|---|---|---|
Voltage | 0.5017 | 0.0221 | 0.6244 | 0.6359 |
Temperature | 0.8478 | 0.1393 | 0.0960 | 0.2926 |
Strain | 0.1141 | 0.9758 | 0.0094 | 0.0202 |
Carbon dioxide | 0.0095 | 0.0195 | 0.1575 | 0.3533 |
Carbon monoxide | 0.0007 | 0.0432 | 0.0334 | 0.0898 |
Feature | Voltage | Temperature | Strain | CO2 | CO |
---|---|---|---|---|---|
Voltage | 1.00000 | 0.18274 | −0.00636 | 0.25351 | 0.49282 |
Temperature | 0.18274 | 1.00000 | 0.24005 | 0.94737 | 0.87906 |
Strain | −0.00636 | 0.24005 | 1.00000 | 0.04167 | 0.04826 |
CO2 | 0.25351 | 0.94737 | 0.04167 | 1.00000 | 0.93118 |
CO | 0.49282 | 0.87906 | 0.04826 | 0.93118 | 1.00000 |
Battery Number | Charging Rate | Type | Dataset | ||||
---|---|---|---|---|---|---|---|
Data Points | Stage 1 Data Points | Stage 2 Data Points | Stage 3 Data Points | Stage 4 Data Points | |||
#1 | 1C | Train | 2500 | 827 | 1047 | 551 | 75 |
#2 | Test | 2296 | 1500 | 374 | 347 | 75 | |
#3 | 0.5C | Test | 6248 | 2634 | 2124 | 855 | 634 |
#4 | 2C | Test | 1234 | 180 | 610 | 68 | 375 |
Charging Rate | 1C | 0.5C | 2C |
---|---|---|---|
Accuracy | 0.975 | 0.964 | 0.963 |
Precision (Stage Ⅰ) | 0.998 | 0.955 | 1 |
Precision (Stage Ⅱ) | 0.900 | 1 | 0.985 |
Precision (Stage Ⅲ) | 1 | 0.898 | 0.653 |
Precision (Stage Ⅳ) | 0.843 | 1 | 1 |
Recall (Stage Ⅰ) | 1 | 1 | 0.950 |
Recall (Stage Ⅱ) | 0.992 | 0.937 | 0.941 |
Recall (Stage Ⅲ) | 0.841 | 1 | 1 |
Recall (Stage Ⅳ) | 1 | 0.860 | 1 |
F1-Score (Stage Ⅰ) | 0.999 | 0.977 | 0.974 |
F1-Score (Stage Ⅱ) | 0.944 | 0.967 | 0.962 |
F1-Score (Stage Ⅲ) | 0.914 | 0.946 | 0.790 |
F1-Score (Stage Ⅳ) | 0.915 | 0.925 | 1 |
Charging Rate | Training Dataset | |||
---|---|---|---|---|
Voltage | Temperature | Voltage-Temperature | Multidimensional Parameter | |
0.5C | 0.722 | 0.717 | 0.775 | 0.964 |
1C | 0.951 | 0.932 | 0.955 | 0.975 |
2C | 0.552 | 0.593 | 0.601 | 0.963 |
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Li, J.; Xie, Y.; Xu, B.; Zhang, J.; Wang, X.; Mao, L. Multistage Early Warning of Sodium-Ion Battery Thermal Runaway Using Multidimensional Signal Analysis and Redundancy Optimization. Batteries 2025, 11, 108. https://doi.org/10.3390/batteries11030108
Li J, Xie Y, Xu B, Zhang J, Wang X, Mao L. Multistage Early Warning of Sodium-Ion Battery Thermal Runaway Using Multidimensional Signal Analysis and Redundancy Optimization. Batteries. 2025; 11(3):108. https://doi.org/10.3390/batteries11030108
Chicago/Turabian StyleLi, Jinzhong, Yuguang Xie, Bin Xu, Jiarui Zhang, Xinyu Wang, and Lei Mao. 2025. "Multistage Early Warning of Sodium-Ion Battery Thermal Runaway Using Multidimensional Signal Analysis and Redundancy Optimization" Batteries 11, no. 3: 108. https://doi.org/10.3390/batteries11030108
APA StyleLi, J., Xie, Y., Xu, B., Zhang, J., Wang, X., & Mao, L. (2025). Multistage Early Warning of Sodium-Ion Battery Thermal Runaway Using Multidimensional Signal Analysis and Redundancy Optimization. Batteries, 11(3), 108. https://doi.org/10.3390/batteries11030108