## Nomenclature  
Acronyms or VariablesConnotations  
VMDVariational Mode Decomposition  
GWOWWOf Grey Optimizer  
KELMKernel Extreme Learning Machine  
DEDifferential Evolutionary  
IMFIntrinsic Mode Function  
TFATime-Frequency Analysis  
STFTShort-Time Fourier Transform  
WVDWigner-Ville Distribution  
DWTDiscrete Wavelet Transform  
EMDEmpirical Mode Decomposition  
PSOParticle Swarm Optimization  
EEMDEnsemble Empirical Mode Decomposition  
CNNConvolution Neural Network  
DRNDeep Residual Network  
ELMExtreme Learning Machine  
TLTransfer Learning  
\begin{tabular}{l l} SVM & Support Vector Machine \\ NN & Neural Network \\ DL & Deep Learning \\ SNR & Signal-Noise Ratio \\ PE & Permutation Entropy \\ GA & Genetic Algorithm \\ \(v(t)\) & Gearbox vibration signal \\ \(u_{k}(t)\) & The \(k^{th}\) IMF of \(v(t)\) \\ \(K\) & Number of imfs \\ \(\omega_{k}\) & Frequency centers of the \(k^{th}\) IMF (Hz) \\ \(\alpha\) & Penalty factor in VMD algorithm \\ \(\lambda\) & Lagrange multiplier in VMD \\ \(fn\) & Fitness function of GWO \\ \(kt\) & Kurtosis in GWO fitness function \\ \(Hp\) & Permutation entropy in GWO fitness function \\ \(\mu\) & Mean value for Kurtosis calculation \\ \(\sigma\) & Standard deviation for Kurtosis calculation \\ \(m_{1}\), \(q\) & Dimensional parameters of the reconstruction matrix for \(Hp\) calculation \\ \(p_{i}\) & Probability of each row of the reconstruction matrix \\ \(alpha\), beta, delta, omega & Grey wolf names in their social hierarchy \\ \(Corr\) & Correlation coefficient \\ \(Corr_{th}\) & Correlation coefficient threshold for signal reconstruction \\ \(v^{\prime}(t)\) & Reconstructed gearbox vibration signal \\ \(v_{max}\) & Maximum amplitude of \(v^{\prime}(t)\) \\ \(v_{min}\) & Minimum amplitude of \(v^{\prime}(t)\) \\ \(v_{p}\) & Peakedness of \(v^{\prime}(t)\) \\ \(v_{pp}\) & Peak-to-peak value of \(v^{\prime}(t)\) \\ \(v_{m}\) & Mean value of \(v^{\prime}(t)\) \\ \(v_{s}\) & Slant of \(v^{\prime}(t)\) \\ \(v_{rms}\) & Root mean square value of \(v^{\prime}(t)\) \\ \(v_{r}\) & Root square amplitude of \(v^{\prime}(t)\) \\ \(v_{m}\) & Mean of absolute value of \(v^{\prime}(t)\) \\ \(v_{r}\) & Variance of \(v^{\prime}(t)\) \\ \(v_{sf}\) & Shape factor of \(v^{\prime}(t)\) \\ \(v_{m}\) & Skewness of \(v^{\prime}(t)\) \\ \(v_{f}\) & Impulse factor of \(v^{\prime}(t)\) \\ \(v_{cf}\) & Crest factor of \(v^{\prime}(t)\) \\ \(v_{clf}\) & Clearance factor of \(v^{\prime}(t)\) \\ \(v_{bf}\) & Kurtosis factor of \(v^{\prime}(t)\) \\ \(v_{E}\) & Energy of \(v^{\prime}(t)\) \\ \(v_{pe}\) & Permutation entropy of \(v^{\prime}(t)\) \\ \(N_{v}\) & Length of \(v^{\prime}(t)\) \\ \(T\) & Fault feature vector \\ \(x(t)\) & Constructed experimental signal with noise \\ \(s(t)\) & Periodic impulsive signal for experiments \\ \(x_{m}(t)\) & Gauss white noise for experiments \\ \(n\) & KELM input node number \\ \(L\) & KELM hidden layer node number \\ \(m\) & KELM output node number \\ \(N\) & Number of KELM training sample pairs \\ \(x_{i}\) & Input vector of the \(i^{th}\) KELM sample \\ \(t_{i}\) & Target output of \(x_{i}\) \\ \(Y\) & \(N\times m\) output matrix of KELM \\ \(H\) & \(N\times L\) output matrix of KELM hidden layer \\ \(\omega\) & KELM input weight matrix \\ \(b\) & Bias vector of KELM hidden layer \\ \(x\) & KELM sample input matrix \\ \(\beta\) & \(L\times m\) output weight matrix of KELM \\ \(C\) & Regularization factor of KELM \\ \end{tabular}