## 1 Introduction  
Fuel cells currently have many applications in vehicles, spaceflight, ship, and building due to the advantages of generating electricity continuously, zero-emission, and high efficiency [1]. However, the commercialization of fuel cells still needs to overcome many obstacles, including the problems of high cost and durability. The durability of fuel cells benefits from a good design of Balance of Plant (BOP) which affects the performance of fuel cells [2, 3]. Issues of water management are relevant to guarantee electrical conductivity in the membrane and prevent redundant water from obstructing the reactant delivery [4, 5]. Therefore, better water management requires a comprehensive understanding of the water activity in the interior of the fuel cell, especially the water transportation in the membrane-electrode assembly (MEA). The redox reaction of hydrogen and oxygen occurs in MEA to produce electricity, heat, and water. Water is the only emission from fuel cells. And water management is considered a critical issue in the commercialization of PEM fuel cells [6]. Researchers working on fuel cells have described the transport model of water in various components of fuel cells [7]. Only a small part of water passes through the membrane and the electrode, and the rest is transmitted through the gas channels. This small amount of water is transported through porous media, but this complicates the overall water transport mechanism. Normally, water transport in the membrane is governed by the following basic modes: back diffusion, electro-osmotic drag, hydraulic permeation, and thermo osmosis flux [2]. Back diffusion is the transfer of molecules from a region of high concentration to a region of low concentration until a uniform distribution is achieved. The rate of diffusion is proportional to the concentration gradient of the substance. In fuel cells, the diffusion of water molecules from the cathode to the anode side is usually observed [8]. Electro-osmotic drag in membranes refers to the movement of water through a membrane as a result of the movement of ions caused by the electric field [9]. Hydraulic permeation can be described as water transported through the membrane as a result of gas or capillary pressure gradient between the anode and cathode side. Thermo-osmosis water flux is caused by the temperature gradient [10]. Compared with the transport mechanisms of thermo-osmosis flux and hydraulic permeation, electro-osmotic drag and back diffusion have a more profound effect on water transport processes [11]. In the gas diffusion layer (GDL), water exists in the forms of vapor and liquid in the pore region under normal working conditions. Meanwhile, water molecules in the gas phase are free to condense back into the liquid, and vice versa. Liquid water transmitted in GDL is very complicated [12]. [PERSON] et al. [13] illustrates that the water transport in GDL mainly consists of two transport mechanisms, namely, liquid percolation and vapor diffusion, and the liquid water configuration in high-current density in GDLs is highly affected by the relative humidity of the cathode. [PERSON] et al. [14] believed that the required data for electro-osmotic flow and back diffusion can be calculated by changing the humidity on both sides of the fuel cell. Experiments about the effect of water balance variation on electro-osmotic flow were implemented, and the optimum values for the humidity of the anode side and cathode side were determined [15; 16]. [PERSON] et al. [17] studied the influence of temperature and gas humidity on the performance stability of PEM fuel cells. They believed that the performance stability of a fuel cell possesses a relatively stable behavior when the relative humidity of the cathode side was in the range between 20% and 50%. Water transport is strongly determined by current density but also depends on stoichiometry and humidity level [18].