A Hybrid Method for Performance Degradation Probability Prediction of Proton Exchange Membrane Fuel Cell
Abstract
:1. Introduction
- (1)
- With consideration of the uncertainties in the degradation process, a Wiener process model is established to describe the overall degradation trend of PEMFC and multiple kinds of variability sources are adequately considered in the model.
- (2)
- To overcome the disadvantage of LSTM in parallel processing, a degradation prediction model is established by transformer, which is used to predict the degradation trend and capture the local fluctuation information.
- (3)
- The MC-dropout is added in transformer network to quantify the uncertainty of the prediction results in order to provide more effective decision support for practical engineering applications.
2. Degradation Modeling of PEMFC
3. State of Health Estimation and Parameter Estimation
Algorithm 1 The procedures of the UKF algorithm |
1. Initialization (k = 0): , 2. Time update: , 3. Sigma points and weights calculation: (1) ; ; where , is the ith column of the square root of the matrix . (2) ; ; , where is the scaling parameter, and the other parameters are generally set to = 3 4. Measurement update |
4. Method of Degradation Prediction
4.1. Problem Description
4.2. The Transformer Structure
4.2.1. Data Input
4.2.2. Encoder
4.2.3. Decoder
4.2.4. Output
4.3. The Method of MC-Dropout
4.4. The Hybrid Prediction Method for Performance Degradation
5. Experimental Study
5.1. Experimental Dataset
5.2. State Estimation
5.3. Performance Degradation Prediction Results
5.4. Verification with LSTM
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
References
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Parameters Setting | Value |
---|---|
Window length | 10 |
Batch size | 50 |
Epochs | 50 |
Dropout | 0.1 |
Multi-Head | 10 |
Learning rate | 0.001 |
Training Set | MAPE (%) | RMSE (%) | MAE (%) |
---|---|---|---|
40% | 4.0261 | 1.0416 | 0.9380 |
50% | 1.5429 | 0.4826 | 0.3630 |
60% | 1.2410 | 0.3845 | 0.2923 |
Training Set | MAPE (%) | RMSE (%) | MAE (%) |
---|---|---|---|
40% | 2.9276 | 0.9675 | 0.7665 |
50% | 1.1153 | 0.4408 | 0.2851 |
60% | 0.9896 | 0.4117 | 0.2515 |
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Hu, Y.; Zhang, L.; Jiang, Y.; Peng, K.; Jin, Z. A Hybrid Method for Performance Degradation Probability Prediction of Proton Exchange Membrane Fuel Cell. Membranes 2023, 13, 426. https://doi.org/10.3390/membranes13040426
Hu Y, Zhang L, Jiang Y, Peng K, Jin Z. A Hybrid Method for Performance Degradation Probability Prediction of Proton Exchange Membrane Fuel Cell. Membranes. 2023; 13(4):426. https://doi.org/10.3390/membranes13040426
Chicago/Turabian StyleHu, Yanyan, Li Zhang, Yunpeng Jiang, Kaixiang Peng, and Zengwang Jin. 2023. "A Hybrid Method for Performance Degradation Probability Prediction of Proton Exchange Membrane Fuel Cell" Membranes 13, no. 4: 426. https://doi.org/10.3390/membranes13040426