## 1 Introduction  
New energy vehicles have been vigorously developed in recent years due to the problems of environmental pollution and oil shortages. Among them, fuel cell vehicles (FCVs) have a long-range, fast energy replenishment and high efficiency, which have more potential and are more attractive than lithium battery vehicles and traditional internal combustion engine vehicles. However, the high cost also limits their development. The fuel cell system (FCS) mainly consists of an electric stack, air supply system, hydrogen supply system, and water and thermal management systems. First, the electric motor drives a centrifugal impeller to pressurise the air. Then, the pressurised and humidified air is sent to the hydrogen fuel reactor for a chemical reaction. The final output of electricity provides energy for the electric motor and the whole vehicle. The compressor is the core component of the air supply system, accounting for 16.89% of the overall vehicle cost, second only to the fuel stack in the fuel cell (FC). Improving the aerodynamic performance and efficiency of the compressor can effectively save the overall cost. Common types of air compressors are screw, scroll, roots, and centrifugal. A large mass flow is easy to achieve for the screw, roots and centrifugal compressors, and high pressure can be easily realized for the screw and centrifugal compressors [1]. The scroll, screw, and slide compressors are all in a type of positive displacement, which can boost the pressure through the shrinkage of inner chambers. In contrast, centrifugal compressors take in the gas and elevate the kinetic energy through a rotating impeller at high speed to boost the pressure of air. Centrifugal compressors have high efficiency, a compact structure and a high-pressure ratio, as well as favourable noise, vibration and harshness (NVH) performance [2]. [PERSON] et al. [3] highlighted centrifugal compressors as a good choice for FCSs due to their relatively low weight and high pressure. Therefore, centrifugal compressors are considered to be more suitable for FCs. As the most important compressor component, the performance of the high-speed centrifugal impeller has a vital impact on the overall efficiency of an air compressor and fuel cell system which then affects the cost of the whole vehicle [4]. Although high-speed centrifugal impellers have been used extensively in internal combustion engines (ICE) and have similarities to FC centrifugal impellers, concerning size, weight, NVH behaviour and cost, centrifugal impellers for internal combustion engines are unfortunately not directly usable in FCS for several reasons. 1. The working environment is different. The FC reactor requires oil-free air, while the centrifugal impeller used in ICE is driven by oil-lubricated bearings, which can cause reactor contamination. 2. The rated rotational speed is different. The ICE can make the centrifugal impeller reach more than 200,000 revolutions per minute (rpm) using high-temperature exhaust gas. Meanwhile, the exhaust gas of the FC cannot drive the centrifugal impeller to the required speed. The centrifugal impeller can only be driven by oil-free electric bearings, and its maximum speed can only reach 140,000 rpm. Further, the rated speed of 80,000 rpm-110,000 rpm is considered reasonable. 3. It has a different working condition range. The specific speed of the centrifugal impeller in the FC is usually smaller than that of the ICE [5]. Further, their operating conditions are different. The operating range of the FC centrifugal impeller is narrow and usually runs along the surge boundary, while the operating range of the ICE centrifugal impeller is larger. If the ICE centrifugal impeller is applied to the FC system, there is a high risk of surge or blockage. In summary, FC centrifugal impellers need to be specifically designed and optimised for their own use. Since the total pressure ratio of the FC air compressor can reach 0.2-0.4 Mpa, the driving power consumption can reach 25% of the output power of FCS [1,6].