# A Two-Stage Framework for Time-Frequency Analysis and Fault Diagnosis of Planetary Gearboxes
## 1 Introduction  
Planetary gearboxes are widely used in many industrial categories such as wind power generation, mining, metal forming, etc., due to their compact structure, large transmission ratio, and stable operation [1; 2]. In these applications, planetary gearboxes are usually installed in the transmission chain transmitting large torque and are subject to harsh working environments such as dynamic load and extreme temperature. Hence, they are prone to various failures [3]. It is important to ensure the safe operation of equipment to detect faults as early as possible through the analysis of sensor data to avoid unplanned shutdowns or catastrophic failures [4; 5; 6]. As a well-established field, the vibration analysis-based fault diagnosis method has been widely used in planetary gearboxes. The representation methods of vibration signals can generally be summarized into three categories: time domain, frequency domain, and time-frequency (T-F) domain [7]. T-F domain analysis is a powerful tool for dealing with non-stationary signals. [PERSON] and [PERSON] [8] proposed an iterative generalized T-F reassignment method by exploiting the uniqueness of iterative generalized demodulation to decompose nonstationary, multi-component signals into mono-components of constant frequency, thus, meeting the requirement of mono-component with linear instantaneous frequency by T-F reassignment and improving the T-F readability in planetary gearbox fault diagnosis. With consideration of the time-varying characteristics of planetary gearboxes, [PERSON] and [PERSON] [9] used the local maximum mean discrepancy to evaluate the data distributions between relevant subclasses in source and target tasks and proposed a deep residual joint subclass alignment transfer network based on T-F features. [PERSON] et al. [10]extracted fault features from wavelet T-F images from the perspective of image texture analysis and proposed a novel fusion fault diagnosis framework of gray level co-occurrence matrix and label consistent K-SVD. [PERSON] et al. [11] developed a new method termed as generalized wavelet-based synchro squeezing transform to deal with a strong, modulated non-stationary signal, which has better performance as compared with traditional approaches in the energy concentration of T-F representations and accuracy of the mode reconstruction. In [12], [PERSON] and [PERSON] considered a more complex but real situation: compound gear-bearing fault and proposed a fault diagnosis method based on T-F statistical features of the discrete wavelet transform and continuous wavelet transform. T-F segmentation is one of the crucial means of analyzing T-F distribution. Limited by computer calculation levels, early investigations mainly focused on threshold segmentation methods represented by the Otsu method [13], edge detection [14], and gray level histogram [15]. With the development of computer technology and machine learning, researchers have put forward many new ideas and methods for T-F analysis. Medical Informatics is the field where early T-F analysis technologies have achieved fruitful results. For example, [PERSON] et al. [16] combined the Hilbert transform with the Wigner-Ville distribution to bring about hybrid T-F analysis and used ResNet to analyze cardiac arrhythmia via heartbeat classification. [PERSON] et al. [17] proposed a novel method based on T-F analysis and the CNN-LSTM cascade model to automatically detect atrial fibrillation, solving the problem of burst atrial fibrillation detection based on electrocardiograms. In the field pf mechanical fault diagnosis, [PERSON] et al. [18] proposed a fusion method based on multi-resolution T-F spectrum segmentation and sparse decomposition of vibration signals. Compared with traditional Gabor T-F atoms, the new method has a faster pursuit speed of the best atom and higher approximation precision. [PERSON] et al.