# A Review of Early Fault Diagnosis Approaches and Their Applications in Rotating Machinery
## 3 Applications of FFD in Early Fault Diagnosis of Rotating Machinery
### Wavelet Transform Methods  
A WT employs wavelets as the basis to extract the transient signals from the measured vibration signals. [PERSON] et al. [95] proposed a wavelet-based statistical signal detection approach for monitoring and diagnosing the bearing compound faults at an early stage. [PERSON] et al. [96] introduced a fuzzy rule to maximize the amplitudes of bearing characteristic frequencies (BCFs), then the sum of the BCFs amplitude and their harmonics were used for early fault detection in bearings. [PERSON] et al. [97] utilized the wavelet transform, time-frequency analysis and blind source separation theory to determine the shared frequencies for early bearing fault diagnosis. [PERSON] et al. [98] used WT to de-noise the signals, and then extracted the fault characteristics in both the time domain and the time-frequency domain. Finally, the fault location was identified using the grey correlation method. [PERSON] et al. [99] proposed an adaptive wavelet stripping algorithm to extract fault information for early bearing fault detection. [PERSON] et al. [100] used the instantaneous wavelet bicoherence as fault features for local damage detection in gears. [PERSON] et al. [101] used wavelets multiresolution analysis and the high-frequency resonance technique to demodulate signals for gear or bearing defects detection. [PERSON] et al. [102] used the relative energy ratio to select the sensitive frequency bands of multiwavelet packet coefficients for compound faults detection of rotating machinery. [PERSON] et al. [103] proposed maximal-overlap adaptive multiwavelet to extract the fault symptom for mechanical fault detection at an early stage. [PERSON] et al. [104] applied intrinsic characteristic-scale decomposition (ICD) to decompose the measured vibration signals into a set of PC components. Then the tunable Q-factor wavelet transform is used to generate the high \begin{table}
\begin{tabular}{c c} \hline
**Authors** & **Methodologies** \\ \hline [PERSON] et al. [90] & Least mean squares (LMS)+fast block LMS \\ [PERSON] et al. [91] & Reweighted singular value decomposition \\ [PERSON] et al. [92] & Least mean squares algorithm \\ [PERSON] et al. [93] & Multi-order self-adaptive filter \\ [PERSON] et al. [94] & Machine learning + intrinsic characteristic-scale decomposition \\ \hline \end{tabular}
\end{table} 
Table 6: Applications of other adaptive method in early fault diagnosis of rotating machinery. \begin{table}
\begin{tabular}{c c} \hline
**Authors** & **Methodologies** \\ \hline [PERSON] et al. [84] & Adaptive scale space spectrum segmentation + VMD + Teager energy operator \\ [PERSON] et al. [85] & Improved autoregressive-Minimum entropy deconvolution + VMD \\ [PERSON] et al. [86] & Optimized VMD + simulated annealing \\ [PERSON] et al. [87] & VMD + parameter optimization \\ [PERSON] et al. [88] & Rescaling subsampling compression + analytical mode decomposition + VMD \\ [PERSON] et al. [89] & EMD + VMD \\ \hline \end{tabular}
\end{table} 
Table 5: Applications of variational mode decomposition (VMD) method in early fault diagnosis of rotating machinery. and low Q-factor components. Finally, the envelope analysis is implemented to obtain the low Q-factor component for the EFD. Discrete wavelet transform discretizes the scale and translation of basic wavelets. With other wavelet transforms, a key advantage over Fourier transform is temporal resolution: it captures both frequency and location information. [PERSON] et al. [105] used discrete wavelet transform to reduce the noise and decompose the signal into several decomposition levels, and then statistical parameters were applied for detecting the gear damage. [PERSON] et al. [106] used a discrete wavelet transform to extract fault information, and then envelope detection was used for online condition monitoring of unbalanced rotor induction motor. [PERSON] et al. [107] used a discrete wavelet transform to extract fault information for fault diagnosis of partially damaged rotor bars in induction motors under different load conditions.