A Lithium-ion Battery RUL Prediction Method Considering the Capacity Regeneration Phenomenon
Abstract
:1. Introduction
2. Related Algorithms
2.1. Wavelet Decomposition
2.2. NAR Neural Network
3. WDT–NARNN Prediction Method
3.1. Experiment Data Analysis
3.2. WDT- NARNN Modeling Process
Algorithm 1. The integrated method with WDT and NARNN |
(1) Initialization: |
Select the wavelet function and the decomposition levels ; |
(2) Decomposition: |
Decompose the capacity series for the levels to obtain the low and high-frequency signals at different scales by Equations (4) and (5); |
(3) Initialize the NAR neural network: |
Initialize the parameters of NAR neural network, the numbers of input layer, hidden layer, and output layer are set to , , and respectively, the delay of the network is set to d, and the training function is set to ‘trainbr’; |
(4) Output the prediction results: |
Input the decomposed signals into the NAR models to predict the following changes after time T, then prediction results are obtained; |
(5) Wavelet reconstruction: |
The signals are reconstructed from 1 to levels by Equation (6) to obtain the fusing predicted series corresponding to capacity series, and then RUL value can be calculated by Equation (8); |
(6) Evaluate the prediction results: |
The evaluation is given with original testing data and prediction results through some criteria to evaluate the performance of the integrated method WDT–NARNN. |
3.3. Performance Analysis
- (1)
- Root Mean Square Error (RMSE) to evaluate the prediction accuracy. The smaller the RMSE is, the better the prediction performance:
- (2)
- R2 to evaluate the prediction performance. If the fitting degree between the prediction curve and real curve is high, R2 will be close to 1:
- (3)
- Absolute Error (AE) to evaluate the RUL accuracy of the prediction model:
- (4)
- Prediction Accuracy Improvement Ratio () to evaluate the RUL prediction accuracy improvement ratio of two different methods. If , the first method is more accurate, on the contrary, the second method has higher prediction accuracy:
4. Results and Discussion
4.1. RUL Prediction of Lithium-Ion Battery
4.2. Different Starting Point Predictions and Comparison
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Model | Model Description |
---|---|
M1 | WDT combine with NARNN |
M2 | NARNN without using WDT |
M3 | WDT combine with BPNN |
Evaluate Criteria | Model | #5 | #6 | #7 | #18 |
---|---|---|---|---|---|
RMSE | M1 | 0.0270 | 0.0087 | 0.0175 | 0.0064 |
M2 | 0.0949 | 0.0436 | 0.0678 | 0.0260 | |
M3 | 0.0500 | 0.0616 | 0.0234 | 0.0253 | |
R2 | M1 | 0.9226 | 0.9933 | 0.9460 | 0.9751 |
M2 | 0.4151 | 0.8457 | 0.4611 | 0.6494 | |
M3 | 0.7745 | 0.7298 | 0.9035 | 0.6091 |
Battery | Prediction starting point | Predicted RUL | RUL AE |
---|---|---|---|
#5 | 60 | 96 | 28 |
70 | 70 | 12 | |
80 | 48 | 0 | |
90 | 37 | 1 | |
#6 | 60 | 57 | 5 |
70 | 42 | 0 | |
80 | 33 | 1 | |
90 | 22 | 0 | |
#18 | 60 | 42 | 2 |
70 | 30 | 0 | |
80 | 20 | 0 | |
90 | 10 | 0 |
Battery | Method | Average RUL AE | Average |
---|---|---|---|
#5 | M1 | 10.3 | - |
M2 | 14 | 34.2% | |
M3 | 12 | 21.1% | |
M-LG | 16.3 | 14.3% | |
#6 | M1 | 1.5 | - |
M2 | 17.8 | 37.8% | |
M3 | 12 | 34.6% | |
M-LG | 22.3 | 54.9% | |
#18 | M1 | 0.5 | - |
M2 | 6.5 | 35.6% | |
M3 | 14.8 | 50% | |
M-LG | 6 | 25.8% |
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Share and Cite
Pang, X.; Huang, R.; Wen, J.; Shi, Y.; Jia, J.; Zeng, J. A Lithium-ion Battery RUL Prediction Method Considering the Capacity Regeneration Phenomenon. Energies 2019, 12, 2247. https://doi.org/10.3390/en12122247
Pang X, Huang R, Wen J, Shi Y, Jia J, Zeng J. A Lithium-ion Battery RUL Prediction Method Considering the Capacity Regeneration Phenomenon. Energies. 2019; 12(12):2247. https://doi.org/10.3390/en12122247
Chicago/Turabian StylePang, Xiaoqiong, Rui Huang, Jie Wen, Yuanhao Shi, Jianfang Jia, and Jianchao Zeng. 2019. "A Lithium-ion Battery RUL Prediction Method Considering the Capacity Regeneration Phenomenon" Energies 12, no. 12: 2247. https://doi.org/10.3390/en12122247