## 1 Introduction  
Accurate fault detection of planetary gearboxes is important to reduce unscheduled machine downtime and avoid catastrophic accidents [1]. As key components, planetary gearboxes have been widely used in automotive, aerospace and heavy industry applications such as helicopters, wind turbines and mining machines because they have the advantages of large transmission ratios, strong load-bearing capacity and high transmission efficiency [2]. However, planetary gearboxes inevitably generate various faults because of long term running under complex and severe conditions such as heavy load, fatigue, corrosion and elevated temperature. As shown in Figure 1, an elementary planetary gear set [3] is composed of a sun gear, an internal or ring gear and several identical planet gears located around the sun gear. The planet gears are held by a common rigid structure, called planet carrier through planet bearings. In Figure 1, the ring gear is fixed, the sun gear rotates around its own center, the planet gears rotate around their own centers and revolve around the center of the sun gear. With a special gear transmission structure, planetary gearboxes exhibit complicated dynamic responses which are more difficult to detect than fixed-axis gear trains [4]. It is because multiple planet gears produce similar vibrations and these similar vibrations with different meshing phases couple with each other [5,6]. Researchers have found that compound vibration transmission paths from the gear mesh points to the acceleration sensors may deteriorate or attenuate vibration responses of gear faults through dissipation, interference and resonance effects [7]. Besides, abundant work indicates that most of the vibration energy occurs at various sidebands of the gear meshing frequency and its harmonics [8] and nonlinear transmission path effects caused by the torques or loads would weaken the fault features  
Figure 1: Schematic of an elementary planetary gear set having three planet gears. hidden in vibration signals [5]. These complicated dynamic responses increase the difficulty of planetary gearbox fault detection and reduce the effectiveness of fault diagnosis methods for fixed-axis gearboxes when applied to planetary gearboxes. Up to now, researchers have proposed a few interesting methods based on advanced signal processing techniques for detecting planetary gearbox faults. [PERSON] and [PERSON] [5] developed the planet carrier method and planet separation method to detect a fatigue crack in a planet carrier of an epicyclic transmission, which was a component of the main transmission gears in the US Army's UH-60 A Black Hawk helicopters. [PERSON] and [PERSON] [9] applied the spectral kurtosis (SK) technique to detect a tooth crack in the planetary gear of a wind turbine. [PERSON] and [PERSON] [10, 11] introduced the load susceptibility concept for the condition monitoring of planetary gearboxes under time-variable operating conditions. It was stated that the acceleration signal envelopes showed deeper amplitude modulation for the gearbox in bad condition than that in good condition. [PERSON] and [PERSON] [12] profoundly reviewed different techniques, methods and algorithms developed to monitor the performances of wind turbines to keep them away from catastrophic conditions caused by sudden breakdowns. [PERSON] and [PERSON] [4] proposed two diagnostic parameters specially designed for fault detection and diagnosis of planetary gearboxes. The two parameters are the root mean square of the filtered signal (FRMS) and the normalized summation of positive amplitudes of the difference spectrum between the unknown signal and the healthy signal (NSDS). [PERSON] and [PERSON] [13] introduced a method based on multisensor information fusion to classify the pitting damages with different levels in a planetary gearbox. In summary, researches on planetary gearbox fault diagnosis have only focused on the condition monitoring and fault classifications.