Lithium-Ion Battery Prognostics with Hybrid Gaussian Process Function Regression
Abstract
:1. Introduction
- (1)
- The domain transformation method is fused with the time series prognostic model to predict the RUL of lithium-ion battery.
- (2)
- The wavelet denoising method is selected by the experimental and theoretical analysis.
2. Methodologies
2.1. Wavelet De-Noising
2.2. GPR Model
2.3. HGFPR Model
3. Fusion Framework with WD Method and HGPFR Model
Algorithm 1. The hybrid method with WD method and HGPFR algorithm |
(1) Initialization: |
Select the wavelet function , the value of soft threshold , and the decomposition levels ; |
(2) Decomposition: |
Decompose the for the levels and calculate the detail coefficient form 1 to levels with Equation (6); |
(3) Wavelet reconstruction: |
The signals are reconstructed with the value of soft threshold and detail coefficient form 1 to levels by the Equations (6) and (8); |
(4) Initialize the hype-parameter and times of optimization: |
Initializing value of hype-parameter is set to , and the times of optimization are set to ; |
(5) Optimized the hype-parameter |
FOR I = 1, … |
Calculate the hype-parameter using Equation (9) with the reconstruct signal |
Update the value of hype-parameter with |
END FOR; |
(6) Output the prediction result: |
Input the reconstruct signal to the prognostic model, and then capacity degradation trajectory with the 95% confidence bounds is obtained; |
(7) Prognostic result evaluation: |
The evaluation is given with testing data set and prediction results through some criteria to evaluate the performance of hybrid method. |
4. Experiments and Discussion
4.1. Raw Data from Lithium-Ion Battery and Evaluation Criteria
4.1.1. DES Lithium-Ion Battery Data Set
- The thermal chamber is set to 40 °C.
- The lithium-ion battery is charged under the constant current of 0.74 A condition until the voltage attained 4.2 V.
- The battery is discharged under the constant current of 0.74 A condition until the voltage fell to 2.7 V.
- The capacity data are recorded every 100 cycles of drive cycles.
4.1.2. CALCE Lithium-Ion Battery Data Set
- The thermal chamber was set to 20 °C–25 °C.
- The lithium-ion battery was charged under the constant current of 0.55 A condition until the voltage attained 4.2 V.
- The battery was discharged under the constant current of 1.1 A condition until the voltage fell to 2.7 V.
4.1.3. Evaluation Criteria
- SNR. It evaluates the performance of de-noising. The detailed information is shown as follows:
- Err: relative error of RUL prediction. The detailed information is shown as follows:
- RMES reflects the root mean squared error. The detailed information is shown as follows:
- MAPE means absolute percentage error. The detailed information is shown as follows:
4.2. The Selection of Wavelet De-Noising Method
4.2.1. The Selection of Threshold Value
4.2.2. The Selection of Wavelet Basis and Decomposition Levels
4.3. Battery RUL Prognostics with Hybrid Method
4.3.1. DES Lithium-Ion Battery RUL Prediction Result
4.3.2. CALCE Lithium-Ion Battery RUL Prediction Result
5. Conclusions
Author Contributions
Acknowledgments
Conflicts of Interest
References
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Data Set | Start Point | WD-HGPFR | HGPFR | GPR | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Err | RMSE | MAPE | Err | RMSE | MAPE | Err | RMSE | MAPE | ||
C-1 | 20 | 25.0% | 0.0236 | 0.0253 | 32.2% | 0.0406 | 0.0444 | 37.7% | 0.1589 | 0.2319 |
30 | 8.9% | 0.0108 | 0.0103 | 23.2% | 0.0408 | 0.0438 | 17.0% | 0.0600 | 0.0720 | |
35 | 5.4% | 0.0072 | 0.0075 | 17.9% | 0.0181 | 0.0167 | 13.2% | 0.0525 | 0.0632 | |
40 | 3.6% | 0.0108 | 0.0099 | 7.3% | 0.0163 | 0.0181 | 9.4% | 0.0598 | 0.0767 | |
C-4 | 20 | 6.7% | 0.0079 | 0.0076 | 20.0% | 0.0600 | 0.0645 | 24.4% | 0.0984 | 0.1035 |
30 | 11.1% | 0.0509 | 0.0639 | 15.6% | 0.0772 | 0.0901 | 20.0% | 0.0893 | 0.0907 | |
35 | 4.4% | 0.0044 | 0.0046 | 15.6% | 0.0053 | 0.0055 | 17.8% | 0.0482 | 0.0578 | |
40 | 2.2% | 0.0026 | 0.0026 | 6.7% | 0.0028 | 0.0037 | 11.1% | 0.0364 | 0.0471 | |
C-7 | 20 | 10.9% | 0.0273 | 0.0289 | 16.0% | 0.0354 | 0.0433 | 21.0% | 0.1305 | 0.1437 |
30 | 6.7% | 0.0061 | 0.0126 | 12.0% | 0.0147 | 0.0141 | 17.1% | 0.1026 | 0.1147 | |
35 | 5.3% | 0.0056 | 0.0050 | 9.3% | 0.0444 | 0.0465 | 13.2% | 0.0833 | 0.0945 | |
40 | 2.7% | 0.0145 | 0.0169 | 5.3% | 0.0231 | 0.0248 | 10.5% | 0.0681 | 0.0842 |
Data Set | Start Point | WD-HGPFR | HGPFR | GPR | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Err | RMSE | MAPE | Err | RMSE | MAPE | Err | RMSE | MAPE | ||
C-8 | 150 | 11.9% | 0.0979 | 0.1036 | 14.2% | 0.3980 | 0.4746 | 17.9% | 0.4058 | 0.5318 |
180 | 9.1% | 0.0817 | 0.0952 | 9.9% | 0.1935 | 0.2579 | 11.5% | 0.3368 | 0.4238 | |
210 | 7.1% | 0.0774 | 0.0853 | 8.7% | 0.1309 | 0.1537 | 10.3% | 0.2088 | 0.2607 | |
230 | 4.7% | 0.0895 | 0.1299 | 6.3% | 0.1371 | 0.1625 | 7.5% | 0.1366 | 0.1452 | |
C-21 | 70 | 9.7% | 0.1363 | 0.1428 | 12.3% | 0.1784 | 0.1908 | 14.2% | 0.2355 | 0.3087 |
90 | 7.8% | 0.0933 | 0.1132 | 9.9% | 0.1012 | 0.1398 | 10.4% | 0.1177 | 0.1736 | |
110 | 6.4% | 0.0767 | 0.0973 | 7.8% | 0.0907 | 0.1124 | 11.0% | 0.1325 | 0.2038 | |
130 | 5.2% | 0.0663 | 0.0909 | 5.8% | 0.0832 | 0.0922 | 7.2% | 0.0912 | 0.1331 | |
C-33 | 40 | 8.6% | 0.0784 | 0.1637 | 15.1% | 0.0947 | 0.1340 | 20.4% | 0.1637 | 0.1921 |
60 | 7.5% | 0.0817 | 0.1053 | 12.9% | 0.0992 | 0.1340 | 11.8% | 0.1184 | 0.2191 | |
70 | 5.3% | 0.0245 | 0.0369 | 7.5% | 0.0463 | 0.0576 | 8.6% | 0.3391 | 0.4790 | |
80 | 3.2% | 0.0863 | 0.1989 | 4.3% | 0.0954 | 0.2129 | 10.7% | 0.2373 | 0.2717 |
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Peng, Y.; Hou, Y.; Song, Y.; Pang, J.; Liu, D. Lithium-Ion Battery Prognostics with Hybrid Gaussian Process Function Regression. Energies 2018, 11, 1420. https://doi.org/10.3390/en11061420
Peng Y, Hou Y, Song Y, Pang J, Liu D. Lithium-Ion Battery Prognostics with Hybrid Gaussian Process Function Regression. Energies. 2018; 11(6):1420. https://doi.org/10.3390/en11061420
Chicago/Turabian StylePeng, Yu, Yandong Hou, Yuchen Song, Jingyue Pang, and Datong Liu. 2018. "Lithium-Ion Battery Prognostics with Hybrid Gaussian Process Function Regression" Energies 11, no. 6: 1420. https://doi.org/10.3390/en11061420