## 1 Introduction  
Hydraulic power, as a type of renewable, clean, and efficient energy, has been well developed worldwide [1; 2; 3]. Pumped storage power plants (PSPPs) have become an important part of the energy infrastructure [4; 5; 6]. As the capacity and water head of the unit increase, the vibration of the unit becomes hazardous to the safety and reliable operation of the factory building structure [7]. The complex high-frequency pressure water pulsation generated by the turbine resonates with the high frequency of the plant structure, which can lead to abnormal vibration. For PSPPs, the rotating speed of the head and pump turbine will increase significantly, further intensifying the vibration response [8; 9]. In recent years, the operation of many large hydropower units has resulted in costly downtime due to vibration problems, such as cracking of key components [10; 11]. In order for a pumped storage plant to be cost-effective, the plant must have good reliability. Reliability is particularly crucial for PSPPs, because maintenance is expensive and often impossible to keep up for prolonged periods of time when regional power is available. Therefore, it is of great significance to study and overcome the vibration problem of PSPP structure for the safe operation of the unit. It is well known that the loading from water pressure can eventually cause fatigue or failure in structures, and researchers have used numerical simulation and analysis to study the load characteristics and have suggested various vibration reduction strategies. By establishing a substructure model of the Yantan hydropower plant, [PERSON] conducted a dynamic response analysis of the structure of the hydraulic vibration of the unit and proposed decreasing the vibrational response to the structural floor by adding cross beams, additional steel plates, and reinforced rib beams [12]. [PERSON] et al. proposed improving the integrity of the plant by strengthening the rigid connection between the upstream and downstream columns and implementing other measures to improve the plant strength and decrease the structural vibration in the initial stage of hydropower station structural design [13]. Scholars have proposed decreasing the pulsating pressure by supplementing the runner chamber or the draft tube with air to decrease the structural vibration [14]. Although progress was made on the vibration control of hydropower station structures in the above research, theoretical research has various limitations. First, if local strengthening of reinforced concrete structures is used as a strategy for vibration risk mitigation at the regional scale, the local vibration characteristics of the structure can be changed. However, for vibration of the plant structure that is caused by the complicated high-frequency pressure pulsation in the unit, the effect of local structural reinforcement is highly limited, and unnecessary economic losses due to the long construction period affect the normal operation of the hydropower station. Second, design optimization at the beginning of the design process is only applicable to new plant structures and not to existing plants. An optimized design can avoid the low-order mode of the structure in the resonance region; however, it cannot guarantee that the structural components will avoid the high-frequency resonance region. Finally, although the air admission method reduces the vibration of the unit, shortcomings such as high noise, high power consumption, difficult layout, and unfavorable economics remain, and the method does not fundamentally prevent the structure from resonating, hence the objective of suppressing the vibration of the superstructure is not realized. The above theoretical research is highly meaningful; however, the vibration problem of the plant structure remains and cannot be well solved for existing plants. An alternative approach to reduce the loads is structural control, which affects the response of the structure itself, and is the focus of this paper.