# A Review of Early Fault Diagnosis Approaches and Their Applications in Rotating Machinery
## 3 Applications of FFD in Early Fault Diagnosis of Rotating Machinery
### Other Fault Frequency Based Methods
[139] proposed a tachometer-less synchronously averaged envelope feature extraction technique for rolling element bearing health assessment. [PERSON] et al. [140] proposed the minimum variance cepstrum for early fault detection of bearings by filtering a logarithmic power spectrum. [PERSON] et al. [141] put statistic features into adaptive fuzzy-means clustering to recognize different fault types of rolling bearings. [PERSON] et al. [142] proposed a fuzzy technique to select the informative frequency band for weak fault detection. [PERSON] et al. [143] proposed adaptive SR to detect bearing faults based on the quantum particle swarm algorithm. [PERSON] et al. [144] present an automatic filtering method based on improved genetic algorithm to extract fault signals and reduce the noise for fault type identification of rolling bearings. [PERSON] et al. [145] proposed the covariance and spectral characteristics of periodically correlated random processes to describe the state of rotary mechanical systems. [PERSON] et al. [146] used RMS and peak values of vibration signals for condition monitoring of wind turbine gearboxes. [PERSON] et al. [147] defined a new concept of RMS value calculation using angle domain signals within small angular ranges. Using the time pulses of an encoder, this new RMS could be used to diagnose helical gears fault at low rotational speeds. [PERSON] et al. [148] proposed modified time synchronous averaging to increase SNR, and statistical features were used to detect gear crack at different fluctuating speed. [PERSON] et al. [149] developed Mahalanobis distance to indicate the health condition of cooling fan and induction motor. All the abovementioned methods are summarized in Table 9. \begin{table}
\begin{tabular}{c c} \hline \hline
**Authors** & **Methodologies** \\ \hline [PERSON] et al. [121] & Morphological operators \\ [PERSON] et al. [122] & Morphological operators + fuzzy system \\ [PERSON] et al. [123] & Minimum entropy deconvolution + K-singular value decomposition \\ [PERSON]. [126] & Short-time Fourier-transform-based estimator of the spectral kurtosis \\ [PERSON]. [127] & Fast computation of the kurtogram \\ [PERSON] et al. [132] & Particle Filter + Kurtogram \\ [PERSON] et al. [125] & Minimum entropy de-convolution + Fast Kurtogram \\ [PERSON] et al. [129] & Spectral kurtosis + autoregressive model \\ [PERSON] et al. [130] & Spectral kurtosis \\ [PERSON] et al. [133] & Mean envelope Kurtosis + envelope analysis \\ [PERSON] et al. [131] & Maximum correlated kurtosis deconvolution \\ [PERSON] et al. [134] & Time synchronous averaging \\ [PERSON] et al. [135] & Frequency-shifted bispectrum \\ [PERSON] et al. [136] & Cyclic bispectrum \\ [PERSON] et al. [137] & Wigner-Ville spectrum \\ [PERSON] et al. [138] & Multi-fractal analysis \\ [PERSON] et al. [139] & Tachometer-less synchronously averaged envelope \\ [PERSON] et al. [140] & Minimum variance cepstrum \\ [PERSON] et al. [141] & Adaptive fuzzy-means clustering \\ [PERSON] et al. [142] & Informative frequency band \\ [PERSON] et al. [143] & Adaptive SR + quantum particle swarm \\ [PERSON] et al. [144] & Improved genetic algorithm \\ [PERSON] et al. [124] & Approximate entropy + sample entropy + Lempel-Ziv Complexity. \\ [PERSON] et al. [145] & Periodically correlated random processes \\ [PERSON] et al. [146] & Root mean square (RMS) + peak values \\ [PERSON] et al. [147] & RMS in angle domain \\ [PERSON] et al. [148] & Modified time synchronous averaging \\ [PERSON] et al. [149] & Mahalanobis distance \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Applications of other fault frequency based method in early fault diagnosis of rotating machinery.