## 4 Conclusions  
In this study, we developed a semi-physical and semi-empirical degradation model for onboard proton exchange membrane fuel cells (PEMFCs) and investigated the impact of fuel cell rated power and dynamic limitations on fuel cell hybrid electric vehicles (FCHEVs). Subsequently, the proposed degradation model was applied to an FCHEV. We conducted simulations on the China Heavy-duty Commercial Vehicle Test Cycle (CHTC) using fuel cells with different rated powers while controlling the dynamic responsiveness of the fuel cell via energy management strategies. The simulation results demonstrate the following findings:  
Increasing the fuel cell's rated power can improve the overall vehicle efficiency, resulting in an average reduction of around 6% in hydrogen consumption.  
Increasing the dynamic response limitations of the fuel cell leads to an approximately 3% increase in hydrogen consumption. However, it effectively enhances the durability of the fuel cell, and the projected lifespan is expected to increase by approximately 27% compared to a current density change rate of 0.001 A/cm\({}^{2}\cdot\)s.  
From the analysis of fuel cell degradation under different operating conditions, it is observed that when the dynamic variation rate is low, the proportion of degradation caused by load changes increases, accounting for approximately 48% of all degradation factors.  
In the design of the powertrain system for fuel cell hybrid electric vehicles, it is important to consider the degradation of fuel cells as part of the evaluation. Simply increasing the fuel cell power to improve efficiency does not significantly enhance durability or reduce hydrogen consumption. When comparing a 200 kW fuel cell to a 100 kW fuel cell, the hydrogen consumption increases by 1%, and the projected lifespan decreases by 8%.  
Conceptualization, W.S. and K.S.; Data curation, W.S.; Formal analysis, W.S. and M.L.; Funding acquisition, G.L. and S.B.; Investigation, W.S. and M.L.; Methodology, W.S. and M.L.; Project administration, K.S.; Resources, G.L., K.S. and S.B.; Supervision, G.L., K.S. and S.B.; Validation, G.S., M.L. and H.C.; Visualization, M.L. and H.C.; Writing--original draft, W.S. and H.C.; Writing--review and editing, G.S., H.C. and S.B. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key R&D Program of China [grant number 2022 YFB4004401], the Key Research and Development Program of Shandong Province [grant number 2020 CXGC010406], Asset & Laboratory Management Department of Shandong University, China [grant number sy20232305], and the Undergraduate School of Shandong University, China [grant number 2022Y155].  
Not applicable.  
All data and models used in the study appear in the submitted article.  
Mrs. [PERSON] was employed by Automotive Research Institute, China National Heavy Duty Truck Group Co., Ltd., Jinan, 250061, China and Mr. [PERSON] was employed by Welchai Power Emission Solutions Technology Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.