## 1 Introduction
[PERSON] et al. [15] considered more influencing factors, such as a series of nonlinear factors: component manufacturing error, comprehensive transmission error, wear error and tooth side clearance, to establish a spur planetary transmission dynamics model, and studied the natural vibration characteristics of a multistage planetary gear system based on the established model. [PERSON] et al. [16] used simulation technology to undertake a detailed analysis of gear production and processing processes and studied the influence of gear meshing acoustics during gear processing. [PERSON] et al. [17] established a six-degree-of-freedom nonlinear semidefinite model with time-varying mesh stiffness, which was developed for the dynamic analysis of spur gears. In the nonlinear model developed, several factors such as time-varying mesh stiffness and damping, separation of teeth, backlash, single- and double-sided impacts, various gear errors and profile modifications were considered. Numerical examples are given in order to demonstrate the effect of the shaft and bearing dynamics on the gear dynamics. [PERSON] et al. [18] proposed a new dynamic model considering the influence of time-varying mesh stiffness (TVMS), and the new model was applicable to the gear system. The result demonstrated that the amplitudes of vibration and the dynamic mesh force of the proposed model are greater than that of the traditional model. In the experimental aspect of aero-engine gear resonance, [PERSON] et al. [19] conducted TWR monitoring tests and fatigue performance tests on bevel gears and analyzed the dangerous speed range and sound-pressure energy of the vibration. These tests found that the harmonic frequency, forward-traveling wave (FTW) frequency, backward-traveling wave (BTW) frequency and their combination frequency appeared alternately in the noise spectrum before the gears experienced fatigue fractures. [PERSON] et al. [20] designed active noise-cancellation technology using the least mean square (LMS) adaptive filter based on finite impulse response (FIR). They verified that acoustic signal analysis could be used as a suitable non-contact method for the precise identification of gear defects and gear health monitoring. [PERSON] et al. [21] studied the influence of tooth-root cracks on the dynamic response of TWR. They found that the amplitude of the dynamic response in both the frequency domain and the time domain increased with crack expansion, which provided a possibility for them to be used as indicators of state monitoring and fault diagnosis in planetary gear systems. [PERSON] et al. [22] studied the influence of the crack propagation path on time-varying meshing stiffness and vibration response. They found that at the same crack level, the influence of a rim crack on the vibration response was greater than that of a tooth surface crack. The vibration level increases with increasing crack depth. [PERSON] et al. [23] conducted TWV tests on a large hollow shaft of a gas turbine and obtained the fourth meridian FTW frequency of the shaft through strain gauge signal analysis and inductive distance detector confidence analysis. [PERSON] et al. [24] carried out two types of correlation analysis on the TWV of the stationary and rotating cylinder shells of a gas turbine. For stator shells surrounding rotating blades, the minimum wall-thickness criterion was proposed, and for rotor shells, the relationship between FTW and BTW was compared with the corresponding known relationship of the disk. [PERSON] et al. [25] proposed two test methods, a noise test and a strain gauge test, to obtain the vibration characteristics of level gears, and the feasibility of these methods was verified. [PERSON] et al. [26] used the derived acoustic measurement method to measure the TWV frequency and speed of the central level gear and verified the accuracy of the acoustic measurement method.