A Compound Framework for Forecasting the Remaining Useful Life of PEMFC
Abstract
:1. Introduction
1.1. Motivations
1.2. Literature Review
1.3. Research Gaps and Contributions
- (1)
- In view of the problem that the meta-model of stacking has a limited ability to capture significant information output of the base models, ASGM integrating the single model ELM, KRR, TCN, and LSTM is established, and an attention mechanism module is embedded into stacking to improve the prediction effect further.
- (2)
- IDBO is employed to optimize the hyperparameters of LSTM to achieve higher forecasting accuracy, where IDBO is attained by embedding the Levy flight strategy, adaptive variation, and polynomial variation into DBO to promote the global and local detection ability.
- (3)
- UIC is utilized in the selection of input variables to capture critical information, which is able to decrease the training complexity and enhance the overall efficiency of the proposed model.
2. Related Methodologies
2.1. Locally Weighted Scatterplot Smoothing (LOESS)
2.2. Uniform Information Coefficient (UIC)
2.3. Attention-Based Stacked Generalization Model (ASGM)
2.3.1. Extreme Learning Machine (ELM)
2.3.2. Kernel Ridge Regression (KRR)
2.3.3. Temporal Convolutional Network (TCN)
2.3.4. Long Short-Term Memory Network (LSTM)
2.3.5. Attention Mechanism
2.3.6. The Proposed Attention-Based Stacked Generalization Model (ASGM)
2.4. The Proposed IDBO for Optimization
- (1)
- obtain the position information of the optimal dung beetle X*;
- (2)
- perform the mutation operation on X* to obtain the new position according to Equation (44);
- (3)
- compare the fitness values of the two positions to update them optimally. Thus, the optimal position of dung beetles can be formulated as follows:
Optimization Process of IDBO-ASGM
3. PEMFC FDT and RUL Forecasting Framework Based on LOESS, UIC, ASGM, and IDBO
4. Experiment
4.1. Data Preprocessing
4.2. Model Hyperparameter Setting
5. Results and Discussion
- (1)
- Compute the predicted RUL (PRUL) and observe RUL (ORUL) with various FTS:
- (2)
- Compute the error (Er) between PRUL and ORUL:
- (3)
- Compute the accuracy score (Ascore) of RUL prediction:
- (4)
- Average the Ascore under all FTS to obtain the FAscore:
5.1. Results
5.1.1. Future Degradation Trend Forecasting Results
5.1.2. Remaining Useful Life Forecasting Results
5.2. Discussion
5.2.1. Discussion on the Effectiveness of UIC
5.2.2. Discussion on the Effectiveness of the Proposed IDBO
5.2.3. Discussion on the Effectiveness of the Proposed ASGM
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
ASGM | Attention-based Stacked Generalization Model |
ARIMA | Autoregressive Integral Moving Average |
Ave. | Average |
DBO | Dung Beetle Optimization |
ELM | Extreme Learning Machine |
ESN | Echo State Network |
FDT | Future Degradation Trend |
FAscore | Final Score Accuracy |
FTS | Failure Thresholds |
GRU | Gated Recurrent Unit |
IDBO | Improved Dung Beetle Optimization |
KRR | Kernel Ridge Regression |
LOESS | Locally Weighted Scatter Plot Smoothing |
LSTM | Long Short-term Memory Neural Network |
MAPE | Mean Absolute Percentage Error |
PEMFC | Proton Exchange Membrane Fuel Cell |
UIC | Uniform Information Coefficient |
RUL | Remaining Useful Life |
R2 | R Square |
RMSE | Root Mean Square Error |
SGM | Stacked Generalization Model |
Std. | Standard Deviation |
TCN | Temporal Convolutional Network |
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Parameters | Unit | Physical Meaning |
---|---|---|
US; U1~U5 | V | Stack voltage and 5 single-cell voltages. |
Cur; CurD | A; A/cm2 | Current and current density. |
Tin_H2; Tout_H2 | °C | The temperature of H2 at the inlet and outlet. |
Tout_Air; Tin_Air | °C | The temperature of air at the inlet and outlet. |
Tin_Wat; Tout_Wat | °C | The temperature of cooling water at the inlet and outlet. |
Pin_H2; Pout_H2 | mbara | The pressure of H2 at the inlet and outlet. |
Pin_Air; Pout_Air | mbara | The pressure of air at the inlet and outlet. |
Din_H2; Dout_H2 | L/mn | The flow rate of H2 at the inlet and outlet. |
Din_Air; Dout_Air | L/mn | The flow rate of air at the inlet and outlet. |
DWat | L/mn | The flow rate of cooling water. |
HAir | % | The hygrometry of air at the inlet. |
Models | Parameters | Determination Methods | Values/Research Range |
---|---|---|---|
ELM | Number of hidden neurons | Grid search | [50, 200] |
Kernel Ridge | Regularization parameter | Grid search | [0, 1] |
TCN | Convolution kernel size | Trial and error method | 3 |
Batch size | Trial and error method | 32 | |
The number of filters in the convolution layer | Trial and error method | 16 | |
Epochs of training | Trial and error method | 350 | |
LSTM | Number of hidden layer nodes | Trial and error method | 64 |
Batch size | Trial and error method | 16 | |
Epochs of training | IDBO | [300, 500] | |
Initial learning rate | IDBO | [0, 1] | |
IDBO | Population number | Present | 30 |
Maximum iterations | Present | 50 |
Models | Evaluation Indicators | ||
---|---|---|---|
RMSE (V) | MAPE (%) | R2 | |
LSTM | 0.00751 | 17.413 | 0.72915 |
SGM | 0.00415 | 10.487 | 0.91735 |
UIC-SGM | 0.00276 | 8.081 | 0.96323 |
UIC-IDBO-SGM | 0.00237 | 6.830 | 0.97297 |
UIC-ASGM | 0.00177 | 5.141 | 0.98496 |
UIC-IDBO-ASGM | 0.00147 | 4.296 | 0.98969 |
Models | Evaluation Indicators | ||
---|---|---|---|
RMSE (V) | MAPE (%) | R2 | |
LSTM | 0.00826 | 25.377 | 0.90247 |
SGM | 0.00598 | 17.337 | 0.94880 |
UIC-SGM | 0.00428 | 11.934 | 0.97382 |
UIC-IDBO-SGM | 0.00299 | 8.482 | 0.98719 |
UIC-ASGM | 0.00334 | 7.990 | 0.98401 |
UIC-IDBO-ASGM | 0.00212 | 4.572 | 0.99359 |
Models | Predicted RUL(h) | Final Score | ||
---|---|---|---|---|
3% | 3.5% | 4% | ||
LSTM | 46 | 230 | 236 | 0.6708 |
SGM | 47.5 | 228 | 231 | 0.7837 |
UIC-SGM | 57 | 226 | 230 | 0.8912 |
UIC-IDBO-SGM | 60 | 227.5 | 230 | 0.9293 |
UIC-ASGM | 60 | 227.5 | 230.5 | 0.9319 |
UIC-IDBO-ASGM | 62 | 227.5 | 231 | 0.9671 |
Models | Predicted RUL(h) | Final Score | ||
---|---|---|---|---|
4.5% | 5% | 5.5% | ||
LSTM | 260 | 414.5 | 428 | 0.4444 |
SGM | 249.5 | 262 | 425 | 0.9210 |
UIC-SGM | 247.5 | 262.5 | 425.5 | 0.9506 |
UIC-IDBO-SGM | 247.5 | 263 | 422 | 0.9632 |
UIC-ASGM | 247 | 263 | 425 | 0.9667 |
UIC-IDBO-ASGM | 246.5 | 263 | 423 | 0.9831 |
Datasets | PIindex (%) | SGM vs. UIC-SGM | UIC-SGM vs. UIC-IDBO-SGM | UIC-IDBO-SGM vs. UIC-IDBO-ASGM |
---|---|---|---|---|
FC1 | 33.49 | 14.13 | 37.9 | |
22.94 | 15.48 | 37.1 | ||
5.00 | 1.01 | 1.718 | ||
FC2 | 28.4 | 30.14 | 29.10 | |
31.39 | 28.92 | 46.09 | ||
2.63 | 1.37 | 0.65 |
Function | Dimension | Range | |
---|---|---|---|
30 | [−30, 30] | 0 | |
30 | [−100, 100] | 0 | |
30 | [−1.28, 1.28] | 0 | |
30 | [−32, 32] | 0 | |
30 | [−50, 50] | 0 | |
30 | [−50, 50] | 0 | |
2 | [−65, 65] | 1 | |
4 | [−5, 5] | 0.1484 | |
2 | [−5, 5] | 0.3 |
ID | Metric | IDBO | DBO | ALO | WOA | SCA | GWO | MFO |
---|---|---|---|---|---|---|---|---|
F5 | AVG | 24.57 | 27.10 | 9.86 × 104 | 28.61 | 3.22 × 106 | 28.12 | 1.27 × 107 |
STD | 0.17 | 0.48 | 1.51 × 105 | 0.18 | 4.57 × 106 | 0.75 | 2.91 × 107 | |
F6 | AVG | 7.11 × 10−12 | 0.28 | 9.04 × 102 | 1.18 | 7.93 × 102 | 1.29 | 3.99 × 103 |
STD | 2.23 × 10−11 | 0.21 | 6.84 × 102 | 0.43 | 9.72 × 102 | 0.35 | 4.46 × 103 | |
F7 | AVG | 9.51 × 10−4 | 0.0028 | 0.98 | 0.0090 | 1.043 | 0.0062 | 6.01 |
STD | 7.39 × 10−4 | 0.0024 | 0.45 | 0.013 | 1.18 | 0.0027 | 9.47 | |
F10 | AVG | 8.88 × 10−16 | 1.42 × 10−15 | 12.29 | 2.33 × 10−14 | 13.69 | 1.98 × 10−5 | 16.93 |
STD | 0 | 1.30 × 10−15 | 2.05 | 1.57 × 10−14 | 7.19 | 7.98 × 10−6 | 4.78 | |
F12 | AVG | 1.88 × 10−13 | 0.0066 | 31.31 | 0.076 | 2.38 × 106 | 0.069 | 2.03 × 105 |
STD | 5.29 × 10−13 | 0.0075 | 20.10 | 0.052 | 3.90 × 106 | 0.034 | 2.40 × 105 | |
F13 | AVG | 0.15 | 1.04 | 2.88 × 103 | 0.84 | 1.00 × 107 | 1.07 | 2.28 × 107 |
STD | 0.18 | 0.59 | 8.51 × 103 | 0.28 | 1.20 × 107 | 0.24 | 9.12 × 107 | |
F14 | AVG | 0.19 | 0.44 | 3.05 | 2.64 | 1.31 | 4.50 | 0.44 |
STD | 0.61 | 1.176 | 3.25 | 4.05 | 2.21 | 4.56 | 0.99 | |
F15 | AVG | 4.91 × 10−4 | 9.37 × 10−4 | 3.66 × 10−3 | 9.64 × 10−4 | 9.99 × 10−4 | 4.66 × 10−3 | 1.23 × 10−3 |
STD | 3.85 × 10−4 | 4.20 × 10−4 | 6.47 × 10−3 | 6.87 × 10−4 | 3.39 × 10−4 | 8.27 × 10−3 | 4.83 × 10−4 | |
F17 | AVG | 0.098 | 0.098 | 0.098 | 0.098 | 0.10 | 0.098 | 0.098 |
STD | 2.85 × 10−17 | 2.85 × 10−17 | 2.44 × 10−13 | 7.91 × 10−5 | 0.0035 | 4.70 × 10−6 | 2.85 × 10−17 |
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Wu, C.; Fu, W.; Shan, Y.; Shao, M. A Compound Framework for Forecasting the Remaining Useful Life of PEMFC. Electronics 2024, 13, 2335. https://doi.org/10.3390/electronics13122335
Wu C, Fu W, Shan Y, Shao M. A Compound Framework for Forecasting the Remaining Useful Life of PEMFC. Electronics. 2024; 13(12):2335. https://doi.org/10.3390/electronics13122335
Chicago/Turabian StyleWu, Chuanfeng, Wenlong Fu, Yahui Shan, and Mengxin Shao. 2024. "A Compound Framework for Forecasting the Remaining Useful Life of PEMFC" Electronics 13, no. 12: 2335. https://doi.org/10.3390/electronics13122335
APA StyleWu, C., Fu, W., Shan, Y., & Shao, M. (2024). A Compound Framework for Forecasting the Remaining Useful Life of PEMFC. Electronics, 13(12), 2335. https://doi.org/10.3390/electronics13122335