## 1 Introduction  
Gearboxes are an essential part of a mechanical transmission system. The diagnosis of gear pitting faults has always been an important problem in the industry. In recent years, the development of sensing technology and the improvement of computing power have provided more tools for gear fault diagnosis. Analysis of vibrational signals is the most common means of monitoring gear conditions. Vibrational signals have been used as a popular input in the diagnosis of gear pitting faults. [PERSON] et al. [1] presented an automatic vibration-based program that utilizes health and usage monitoring system data for the early diagnosis of mechanical properties of drivetrain components. There is no general indication of the minimum training collection times required to accurately describe a set of condition indicators, which largely depend on the characteristics of the distribution. [PERSON] et al. [2] found that the vibration acceleration descriptor of the peak signal was related to the pitting of the gear contact. Traditional vibrational signals are significantly affected by the external environment. For example, the statistical vibration acceleration descriptor which indicates the random peak value in the vibration signal is more suitable to indicate the tooth wear than the spectral method. So other sensors are gradually applied to the diagnosis of gear pitting faults. [PERSON] et al. [3] presented the use of optic fiber sensors to detect the initial gear pitting fault. The results show that the optic fiber Bragg grating signal can effectively detect pitting faults under heavy load conditions. However, when the transmission has high structural stiffness, fiber Bragg gratings (FBGs) performance may be limited by relatively weak strain signals. Acoustic emission (AE) is a non-destructive diagnostic technique. [PERSON] et al. [4] took advantage of the Hertz contact method to establish a relationship between the fault/defect size and the AE energy generated during the gear meshing process. The results of the study indicated that if the defect size increases, the AE level also increases. [PERSON] et al. [5] compared the AE data with traditional vibration data. The results showed that the AE signals were more sensitive to defect excitation and the background noise was reduced in AE signals. The results of [PERSON] et al. [6] showed that AE recognizes defects earlier than vibration analysis, regardless of the tortuous transmission path. The effect of AE could be limited by how close the AE sensor to the defect. Many methods have been developed for pitting diagnosis of gears. The most representative research is the hidden semi-Markov model [7]. In general, a hidden semi-Markov model is difficult to train. Therefore, other learning models such as support vector machine (SVM) [8] and principal components (PCA) [9] were used. [PERSON] et al. [10] presented a method for detecting 11 kinds of rotating machinery faults by feature sorting method and SVM. Thirty features were calculated from the analysis of the vibration signal and the electromyography. Classification accuracy was 98.7% achieved using SVM. [PERSON] et al. [11] studied gear tooth surface damage diagnosis based on analyzing the vibration signal of an individual gear tooth. The characteristics of damaged and normal teeth were studied by analyzing their waveforms. The results showed that almost all the damaged teeth were correctly detected by the proposed method, even if there were some misdiagnoses in the identification of the extent of the damage. However, the paper does not explore the exact classification of damage degree. [PERSON] et al. [12] presented a method for diagnosing the absolute deviation of gear faults. The method used single fault gear broken teeth, pitting corrosion and composite fault gear tooth damage setting dynamics model. The results of different broken teeth were obtained through simulation analysis. This method was to investigate the case of broken teeth, but the authors did not verify the early pitting corrosion of gear.