## 1 Introduction
[15] designed Y-shaped folded sandwich plates based on the isostatic stiffness method with a 33.19% weight reduction and a 68.4% reduction in response amplitude than the conventional reinforced plates, which have a better noise reduction performance. [PERSON] et al. [16] made a significant shift in the mass-air resonance frequency of the double wall by adjusting the Helmholtz resonator to increase the energy transfer loss of the double wall using the induced resonance. [PERSON] [17] proposed a double-layer plate structure with rubber grids for low-frequency sound insulation, and although the effect is better than that of the traditional light barrier sheet, the structure still belongs to the passive sound insulation category and cannot take into account the sound insulation effect in the resonance and high-frequency regions. [PERSON] [18] modeled and simulated the vibration and sound radiation of a double-layer cylindrical shell system based on the impedance analysis method, and found that the solid ribbed plate has a certain effect on the sound insulation of the double-layer cylindrical shell in the medium- and high-frequency regions, and no significant effect in the frequency area below 100 Hz. [PERSON] et al. [19] proposed an acoustic isolation metamaterial for distributed piezoelectric resonators, derived an acoustic prediction model, and verified its correctness by the STL simulation results of the corresponding acoustic-structural fully coupled finite element model. In recent years, many control strategies have been proposed one after another for solving low-frequency sound insulation problems in practical engineering, such as canopy damping control, active feedback control, passive control, discrete control, optimal control, and other methods [20; 21; 22]. [PERSON] et al. [23] developed an investigation on the mechanism analysis of the active control of sound transmission through an orthogonal rib-stiffened double-panel structure, and used numerical analysis to verify the accuracy of the model. [PERSON] et al. [24] used the impedance analysis method to model a vibration isolation system, and introduced a feedback control link to analyze the vibration isolation performance of the active control system under different conditions. Although active control technology is used in noise reduction in areas such as high-speed trains and automobiles [25; 26; 27], it is still not widely used. In particular, there are fewer applications in underwater sound insulation systems. As can be seen from the above literature review, passive sound insulation structures are still mainly used with various damping sandwich layers for double-layer panel systems to solve low-frequency problems. In recent years, there has been little research on active control techniques in sound insulation applications, especially in underwater sound insulation. In this paper, the active actuator is combined with the double-layer plate structure, and the active feedback control link is added, forming an active sound insulation structure with a double-layer plate. It is applied to underwater sound insulation systems and its control strategy is analyzed. Different from the average sound pressure level commonly used in related studies, the average power flow is used as an evaluation index to analyze the sound insulation performance of the system from the perspective of energy transfer, which is more comprehensive. In this paper, based on the theoretical model for a coupled system of elastic plate structure and water-filled acoustic cavity, the theoretical model of a sound insulation system with the double-layer plate structure and active feedback control strategy is established for the water-filled acoustic cavity. The average energy transfer of the system is derived and used as the evaluation index of the active sound insulation effect. Then, MATLAB numerical simulations are used to analyze the average energy transfer characteristics of the system under continuous variation of each feedback parameter. Finally, some important conclusions are drawn.