## 1 Introduction  
Multi-axle heavy vehicles (MHVs) are usually used as land transport platforms for large-scale equipment. Compared with ordinary vehicles, MHVs have large inertia and a long wheelbase, and they usually work in complicated and changeable driving conditions. Hence, good braking performance is an important guarantee for fast maneuvering and safe driving. At present, the pneumatic braking system (PBS) is widely employed in MHVs with the advantages of large braking force, good reliability and easy maintenance [1]. Due to compressibility of gas, PBS will inevitably perform a hysteresis effect, which may easily lead to serious traffic accident in an emergency braking condition [2]. For example, when a vehicle runs at a normal speed of 20 m/s (approximately 70 km/h), if the braking time is delayed 0.5 s, the brakingdistance will increase by nearly 10 m. This delay could lead to heavy longitudinal loads along the vehicle instantaneously [3]. The consequences will be more serious for the MHV owing to its large inertia. Currently, electronic brake systems (EBSs), electronic brake force distribution (EBD) and other advanced control technologies have been successfully applied to the majority of passenger cars, while the applications on MHV are still relatively narrow and immature [4]. In this case, scholars have undertaken a large amount of related research recently, and various technologies have been proposed and successfully implemented for better pneumatic braking performance of MHVs, including sliding mode controllers [5; 6; 7], nonlinear model predictive controllers [8], indirect adaptive robust controllers (IARC) [9], and novel braking actuators [10]. Nevertheless, the braking performance of MHV is still much poorer than that of the passenger car [7]. The reason may be the following. Most of these studies have paid much attention only to the optimization and improvement of braking control strategies [11]. Actually, the response time of valves as well as the long pipeline length tremendously limit the performance of the pneumatic brake system, making it harder to control [9; 12]. Therefore, the properties of PBS itself is the basis for studying braking control strategies. Hysteresis is an inherent property of the PBS, which with no doubt has a significant impact on braking performance. Research on hysteresis characteristics can be divided into the system level and component level. Most literature has focused on the latter, such as treadle valves [13], brake pipelines [14], relay valves [15], proportional valves [16], and other subassemblies. However, subassemblies in a loop are connected to each other and affect each other; analysis of individual subassembly seems to be insufficient. In terms of the system level, [PERSON] [17] and He [18] established simulation models of the PBS on two-axle vehicles using AMEsim (Advanced Modeling Environment for performing Simulation of engineering systems) and MWorks, respectively. [PERSON] and his team [3; 19] have conducted in-depth research on the pneumatic braking plant of a railway vehicle and established a complete parametric simulation library using Matlab-Simulink, which makes customizable design possible. As for MHVs, existing literature concerned with the hysteresis effect is rare, and the few accessible studies mainly concentrate on road tests [20]. However, road tests imply high risk, have high costs, and involve a limited range of working conditions. In addition, sensors are not easily placed or replaced on subassemblies after the vehicle is completely assembled. Hence, a test bench for studying hysteresis characteristics of PBS for MHV is necessary. A PBS on an MHV is usually composed of a service brake circuit, a parking brake circuit and an auxiliary braking circuit. When a driver encounters an emergency braking condition, pushing the brake pedal is probably the most common behavior.