## 1 Introduction  
In recent years, hydrogen as a renewable clean energy is widely used in hydrogen internal combustion engines and proton exchange membrane fuel cell (PEMFC) vehicles, due to the excessive consumption of fossil fuels and the emissions of pollutants [1; 2; 3]. PEMFC vehicles are considered to be a feasible alternative to internal combustion engines resulting from their high power density, high efficiency (85%) and zero pollution [4]. As a future development object of automotive power source, PEMFC has received extensive attention [5; 6; 7; 8]. For the PEMFC stack, as the core component of fuel cell vehicles, its cost and life are the pivotal factors for fuel cell commercialization [9; 10; 11; 12]. The excellent humidity of the fuel cell has a direct positive effect on single cell power attenuation and the stack performance, so as to prolong the cell life. However, on the one hand, it can lead to the serious drying, even cracking, of the proton exchange membrane, when the fuel cell humidification is insufficient [13]. On the other hand, water flooding phenomenon can be caused by excessive humidification, which leads to local hot spots due to gas accumulation in the fuel cell, and shortening the fuel cell life. Thus, it is beneficial to set appropriate humidification of the gas to ensure good conductivity of the proton exchange membrane and to improve water management system of the fuel cell [14]. At present, the humidification methods applied in experiments include internal humidification [15], external humidification [16; 17] and self-humidification [18; 19]. For internal humidification, liquid water is transferred in the membrane according to the effect of concentration difference. This method is convenient to operate, but the problems of hysteresis and inaccuracy are obvious. For external humidification, one commonly used method is liquid water humidification, which is simple and efficient; however, this method has serious flooding problems, which leads to the deterioration of PEMFC performance. Another method is bubble humidification, the issue for which is controlling the temperature and humidity when the gas enters. In addition, self-humidification is affected by working conditions, and it is only useful for low-power applications. External humidification is superior to internal humidification and self-humidification, especially under high power and high temperature conditions [20]. To some extent, relative humidity as an inlet parameter can influence the water management, thus affecting the PEMFC performance. Many researchers have focused on the relative humidity effects on the PEMFC performance from experiment and calculation. As a customary research method, the experimental research is not only intuitive, but it also has a high reliability. [PERSON] et al. [21] designed an air humidifier for evaluating the humidification performance under different operation conditions. [PERSON] et al. [22] revealed the effects of different anode and cathode gas humidity levels to determine the cause of the flooding. [PERSON] et al. [23] proposed that the water content, temperature, and conductivity of the proton exchange membrane could be improved by increasing the relative humidity and temperature of the cell. [PERSON] et al. [24] revealed that gas humidification played a crucial role in the low power range for high operating temperatures. Also, they explained the physical and chemical mechanism applications by observing the experimental phenomenon of fuel cell in two kinds of extreme cases, dry and flooded. Compared to experimental studies, simulations have a wide range of applications. They can greatly reduce material and financial resources, but also effectively shorten the test time required. [PERSON] et al. [25] evaluated the PEMFC using the system efficiency calculation method at different working temperatures and inlet relative humidities, and stated that the system efficiency was improved more availably by changing the relative humidity rather than the operating temperature. [PERSON] et al.