Deep Echo State Network for Predicting Degradation and Remaining Useful Life in Proton Exchange Membrane Fuel Cells

introduction: The limited durability caused by the degradation of proton exchange membrane fuel cells(PEMFCs) hinder their large-scale application in various fields. Understanding the performance degradation trend and effectively predicting the remaining useful life(RUL) can effectively improve the durability of PEMFCs. Introduction: The limited durability caused by the degradation of proton exchange membrane fuel cells (PEMFCs) hinders their large-scale application in various fields. Understanding the degradation trends and effectively predicting the remaining useful life (RUL) can significantly improve the durability of PEMFCs. materials and methods: This paper proposes a long-term prediction method based on the deep echo state network. First, the input data is screened and smoothed by wavelet threshold denoising. Then, the Gaussian kernel function is introduced into the deep echo state network to establish a prediction model. Finally, the degradation performance and remaining useful life of PEMFCs are predicted under steady-state and dynamic operating conditions. Method: This paper proposes a long-term prediction method based on the Deep Echo State Network (DESN). First, the input data are screened and smoothed using wavelet threshold denoising. Next, the Gaussian kernel function is introduced into the deep echo state network to establish a prediction model. Finally, the degradation and remaining useful life of PEMFCs are predicted under steady-state and dynamic operating conditions. results: The results show that under steady-state conditions, when the training duration is 450h , the degradation prediction performance is the best, with RMSE and MAPE being 0.0156 and 0.0036 respectively. When the training length is 450h , the prediction error of the remaining useful life is the lowest, which is 19.31%. Under dynamic conditions, the degradation performance prediction is good, with RMSE and MAPE being 0.0281 and 0.0069 respectively, and the prediction error of the remaining useful life is 12.61%. Results: Under steady-state conditions, when the training duration is 450 h, degradation prediction is optimal, with RMSE and MAPE of 0.0156 and 0.0036, respectively. The prediction error of the RUL is the lowest at 19.31%. Under dynamic conditions, degradation prediction is also satisfactory, with RMSE and MAPE of 0.0281 and 0.0069, respectively, and the prediction error of RUL is 12.61%. discussion: The DESN model is used to predict the performance degradation and RUL of PEMFC under both steady and dynamic conditions. For the prediction under steady conditions, the data set FC1 is used, and the performance degradation and RUL prediction performance are compared when the training duration is 400h, 450h, 500h, 550h . For the prediction under dynamic conditions, the data set FC2 is used. First, all the data under steady-state conditions are used as the training set, and then the performance degradation and RUL prediction performance after the actual operation of PEMFC for are evaluated. Discussion: The DESN method can effectively predict degradation and RUL of PEMFCs. However, further validation with real-world data and automated hyperparameter tuning are required to ensure broader applicability beyond laboratory conditions. conclusion: The deep echo state network can effectively realize the performance degradation and RUL prediction of PEMFC. In the data preprocessing stage, performing wavelet threshold denoising and smoothing on the input data can effectively extract the main features of the data. Introducing the Gaussian kernel function into the deep echo state network can reduce the computational complexity and improve the prediction accuracy. Conclusion: The proposed method, combining wavelet threshold denoising and the Gaussian kernel function, effectively extracts data features, improving the prediction accuracy of degradation trends and remaining useful life for PEMFCs under various operating conditions. This demonstrates its potential to enhance durability and support practical applications in real-world energy systems.