To address the insufficient reliability of conventional proton exchange membrane fuel cell(PEMFC) degradation prediction methods under complex operating conditions

this study proposes a deep learning-based hybrid prediction approach. The method employs a Butterworth band-pass filter combined with mutual information (MI) feature selection for data preprocessing

and constructs a hybrid model integrating temporal convolutional network and generalized regularized extreme learning machine (TCN- GRELM) to achieve deterministic prediction. Furthermore

this paper introduces an adaptive bandwidth kernel density estimation (ABKDE) algorithm to perform probabilistic interval prediction

while the Newton-Raphson-based optimizer (NRBO) is enhanced by incorporating an elite set strategy

chaotic local search

and a fitness-distance balance (FDB) mechanism to improve optimization performance. Experimental results on the FC1 and FC2 datasets show that

at 90% and 95% confidence levels

the proposed method reduces the MC metric by 45.89% and 47.02%(FC1)

and by 48.68% and 59.26%(FC2)

compared with benchmark models

thereby significantly improving the reliability of prediction intervals. This study provides valuable insights for PEMFC lifetime prediction and health management.