## 1 Introduction  
Reciprocating compressors are key equipment most commonly used in oil extraction, gas production, oil refining, chemical industries, refrigeration, and gas transmission. The rated capacity of the reciprocating compressor is fixed, which was determined at the time of design. However, the actual demand is lower than the rated capacity of the compressor due to a change in the production process or an insufficient air source; therefore, the capacity of compressor needs to be adjusted. However, the capacity of the compressor is usually regulated by means of bypass backflow which results in a large amount of wasted energy. In order to solve the problem of the reciprocating compressor's high energy waste, many capacity regulation methods for reciprocating compressors have been developed, including intermittent operation of the compressor, a suction-gas throttling scheme, a compressed-gas by-pass scheme, and a cylinder unloading scheme [1]. These technologies have their own disadvantagesand suitable application conditions. With the advantages of a wide, adjustable range and high energy savings, the method of controlling the suction valve has become the most popular method to solve the reciprocating compressor's high energy consumption. In his invention which relates to a system for the infinitely variable capacity control of compressors, [PERSON] first proposed the compressor capacity control method based on controlling the suction valve in 1966 [2]. In the literature [3; 4], a mathematical model was established to theoretically deduce the principle and the method of capacity regulation for reciprocating compressors. In addition, a stepless capacity regulation system (SCRS) for reciprocating compressors was designed based on the regulation method of suction valve unloading. The movement rule of the inlet valve plate, the cylinder's thermodynamic characteristics, and the system dynamic characteristics were essentially analyzed under variable load conditions based on the system [5; 6; 7; 8]. [PERSON] et al. took the influence of variable load conditions on the compressor's mechanical characteristics into account. The variation rules of some important parameters of compressor were analyzed and compared under different load conditions, such as piston rod stress and reversal angle [9]. Other researchers also focused on the joint modeling of a reciprocating compressor equipped with the SCRS and on the optimization of operating parameters. [PERSON] et al. presented a modified reciprocating compressor model to analyze the suction valve plate movement rule under variable load. Some important parameters of SCRS, such as unloader speed, unloader displacement, and oil pressure, were optimized [10]. The influence of key design parameters of the SCRS, such as oil pressure, stiffness of the unloader reset spring, hydraulic cylinder diameter, and flow diameter of the solenoid valve, on the motion characteristics of the inlet valve were analyzed with the help of the proposed model coupling a hydraulic actuator and a compressor [11]. The optimized operating parameters made the system have higher security, economy, and reliability at the beginning of the system's operation. However, the influence of the parameter changes due to the degradation of system components in long-term operation on the system regulation performance had not been considered. Nevertheless, investigating the field application of SCRS, the regulation failure and (or) performance degradation often occurred in long-term operation. The failure of capacity regulation extremely affected the safe and stable operation of the reciprocating compressor. According to statistics, there are many factors that affect the regulation performance of the system. The main factors and their effects are listed in Table 1. Among these factors, the most commonly encountered factors include valve leakage, deviation of the solenoid valve's characteristics, and degradation of the unloader reset spring.