## 1 Introduction  
In recent years, environmental pollution has aroused the attention of various countries, and clean energy such as wind energy and solar energy has become the most important renewable energy in the world. With the expansion of the installation and operation scale of global wind turbines, the maintenance of wind turbines has become one of the most important research topics in the field of wind power. The wind turbine unit is in a complex environment with strong random wind load for a long time in operation, and the internal and external excitation is complex, which easily causes the failure of key parts of the transmission system, and then leads to the shutdown of the whole unit. Therefore, research on the structural health monitoring (SHM) of key components of wind turbines plays an important role in ensuring the safe and stable operation of the unit [1]. Structural health monitoring (SHM) can effectively avoid early failures of the wind turbine drive system and reduce maintenance and repair costs [2; 3]. The planetary gearbox is the core of the wind turbine drive system. It has the advantages of compact structure, high transmission ratio, and small volume. It is mainly composed of planetary gears, planet carriers, sun gears, ring gears, boxes, and bearings. The planetary gearbox has several groups of gears engaged at the same time during transmission. Compared with the fixed shaft gear transmission, the planetary gearbox has special structure and dynamic characteristics, which also leads to its complex dynamics response, thus increasing the spectral complexity of the vibration signal [4; 5; 6]. The frequency spectrum of vibration signals of a planetary gearbox has typical asymmetry and nonlinearity due to the rotation of planetary gears [7; 8; 9]. The literature [10; 11] summarizes the research methods of wind turbine fault detection proposed in recent years. The research shows that the traditional time-frequency analysis technology has some shortcomings in the condition monitoring and fault detection of wind turbines. In view of these shortcomings, in recent years, researchers in the field of rotating machinery fault detection have proposed many new methods, such as: [PERSON] et al. [4] proposed a joint amplitude frequency demodulation analysis method based on ensemble empirical mode decomposition (EEMD) and an energy separation algorithm. [PERSON] et al. [12] combined a blind deconvolution algorithm and a vibration model to detect seed faults in a helicopter planetary gearbox. [PERSON] et al. [13; 14] proposed four kinds of planetary gearbox fault detection parameters: root mean square of the filter signal, normalization of the positive amplitude of the difference spectrum between an unknown signal and a healthy signal, carrier series based on difference spectrum, and cumulative amplitude based on energy ratio. The key task of planetary gearbox fault detection is to determine the gear characteristic frequency [15]. [PERSON] et al. [16] used the adaptive optimal kernel method to extract the frequency components and time-varying characteristics of the non-stationary signals of the planetary gearbox. [PERSON] et al. [17] proposed a planetary gear fault detection method based on ensemble empirical mode decomposition entropy feature fusion. [PERSON] et al. [18] proposed a fault detection method for the planetary gearbox based on improved multi-scale symbolic dynamic entropy and minimum-redundancy maximum-relevancy. Most of the above methods are for the case of measuring a single-stage planetary transmission system with a single sensor. However, planetary gear transmission systems generally consist of multi-stage planetary transmissions. At the same time, multiple sets of planetary gears and sun gears along with planetary gears and ring gears are meshed simultaneously.