## 1 Introduction  
Currently, due to the increasing use of fossil fuels, global energy consumption and environmental pollution are intensifying. Researchers worldwide are exploring renewable and environmentally friendly energy solutions. Hydrogen, based on renewable energy sources, is widely regarded as a promising green energy solution for the future [1, 2]. In the realm of transportation, hydrogen fuel cell hybrid vehicles serve as a pivotal means to attain low-carbon and low-pollution mobility. Particularly, when hydrogen gas is generated via renewable energy sources, the overall greenhouse gas emissions associated with the entire life cycle of the vehicle, from production to operation, approach negligible levels [3]. However, hydrogen fuel cells face significant economic disadvantages compared to internal combustion engines, even though they meet emission requirements. Currently, the global infrastructure for hydrogen refueling stations is relatively limited, resulting in higher costs associated with the production and distribution of hydrogen gas [4]. Additionally,the application of proton exchange membrane fuel cells (PEMFCs) in vehicles suffers from the drawback of poor dynamic response. To overcome this limitation, a hybrid power system combining PEMFCs with a battery pack is required [5]. Therefore, the parameter matching and energy allocation strategies for dual power sources have been a longstanding research focus [6]. Currently, the most commonly used architecture is the parallel configuration of PEMFCs and batteries. During vehicle operation, the fuel cells serve as the primary power source, while the batteries compensate for the power demands that the fuel cells cannot meet [7]. [PERSON] et al. performed parameter matching for heavy-duty fuel cell commercial vehicles, considering fuel economy and the cost of the propulsion system. Their findings suggested that a power source system consisting of a 70 kW fuel cell and 696 battery cells demonstrated the best overall economic performance throughout the vehicle's lifecycle [8]. [PERSON] et al. employed a multi-objective optimization approach to match parameters for fuel cell buses, considering both the economic and durability aspects of the fuel cell. The results indicated that a 100 kW fuel cell exhibited the best performance for fuel cell buses [9]. [PERSON] et al. optimized the topology of a bus system incorporating fuel cells, batteries, and supercapacitors. Using the Interactive Adaptive-Weight Genetic Algorithm, they determined that a 90 kW fuel cell exhibited the best economic performance over the vehicle's entire lifecycle [10]. Literature research indicates that parameter matching for fuel cell vehicles has primarily focused on buses, with limited calculations for heavy-duty commercial vehicles or trucks. Additionally, the calculation of economic performance does not precisely account for fuel cell lifespan. Despite fuel cells being an important means to reduce greenhouse gas emissions as a substitute for internal combustion engines, their durability is relatively low [11]. As early as 2020, the U.S. Department of Energy set a target for fuel cell lifespan in stationary applications at over 40,000 h and 5000 h under actual driving conditions. When fuel cells are in operation, their voltage is not fixed due to the influence of activation, ohmic, and concentration losses. Therefore, quantifying the impact of losses on voltage is crucial. The degradation mechanisms of fuel cells differ between vehicle applications and laboratory testing due to the influence of load variations. When fuel cells and batteries jointly supply power to a vehicle, energy management strategies need to correctly identify the degradation state of the fuel cell to provide accurate energy consumption. As fuel cells operate, electrochemical losses increase, which can lead to changes in their output performance. Hence, the development of fuel cell degradation models is of paramount importance [12]. The membrane electrode assembly (MEA) is a crucial component of a fuel cell.