### State of the Art of Gearbox Fault Diagnosis  
#### 1.2.1 Feature Signal Adaptive Processing Aspect  
For non-stationary vibration signals, their spectrum changes over time. Therefore, single frequency- or time-domain representations fail to reflect all the characteristics of the signals. In this case, Time-Frequency Analysis (TFA) becomes a very effective method for processing the gearbox vibration signals for fault feature extraction [3], and many TFA techniques, such as short-time Fourier transform (STFT), Wigner-Ville distribution (WVD), Discrete Wavelet Transform (DWT), empirical mode decomposition (EMD), VMD, etc. have been proposed and applied.  
For example, [PERSON] et al. [4] adopted STFT to decompose the vibration signal from the time domain to the time-frequency domain for bearing fault diagnosis with changing rotational speed and load. [PERSON] et al. [5] used discrete STFT with long- and short-time windows to obtain time-frequency spectra with different resolutions. A new signal representation approach was put forward by [PERSON] et al. [6]; this method represented the vibration signals with a union of redundant dictionary and applied WVD to express the obtained atoms to get their time-frequency distribution. [PERSON] et al. [7] utilized DWT to decompose the measured vibration, acoustic, and torque signals to obtain fault features. [PERSON] et al. [8] proposed a Deep Residual Network (DRN) based on multiple wavelet coefficient fusion to obtain fault features. A new signal processing method combining EMD with adaptive multiscale morphological analysis was proposed by [PERSON] et al. [9]. [PERSON] et al. [10] presented an improved EMD to decompose gearbox vibration signals, and the IMFs were selected according to their energies for feature extraction. [PERSON] et al. [11] used VMD to decompose the vibration signals, and Particle Swarm Optimization (PSO) was applied to optimize the parameters of VMD. [PERSON] et al. [12] also adopted VMD to decompose the bearing vibration signals; the multi-scale permutation entropy and cuckoo search algorithm were further applied for VMD parameter optimization.  
The application of the above-mentioned TFA techniques in the literature has achieved very interesting experimental results. However, the following deficiencies may occur when these methods are applied. (1) STFT uses fixed-size window functions, and this makes temporal and frequency resolution constant; (2) when WVD is used to analyze multi-component signals, it has a cross interference problem; (3) the predefined and invariant wavelet basis function results in DWT's lack of adaptation, and its decomposition layer number needs to be manually set; (4) for EMD, there are problems of mode mixing, and over- and under-envelopes exist; and (5) for VMD, the decomposition effect relies on its parameter setting [13].  
Among the common adaptive signal processing methods, VMD is very attractive because this approach can alleviate the mode mixing problem of EMD and its varieties, such as local mean decomposition and Ensemble Empirical Mode Decomposition (EEMD), and this method also has high decomposition efficiency [13; 14]. Accordingly, the VMD method was selected in this paper for gearbox vibration signal decomposition.