Abbreviations		ss	The ssth label of testing sample
AC	Accuracy	Mel	Mel frequency
EEMD	Ensemble empirical mode decomposition	f	Hertz frequency
EVCI	Exhaust valve closing impact	Y	Fast Fourier transform of mode component $u_k^l(\mathrm{s})$
FFT	Fast fourier transform	t	Time
FI	Fire impact	E	The linear spectrum energy of pth line of each frame signal
FINC	Fire impact adjacent cylinder	$u_k$	The kth decomposed mode components
IVCI	Intake valve closing impact	${\omega }_k$	Central frequency
IVMD-MFCC	Improved vibrational mode decomposition and Mel frequency cepstrum coefficient	${\stackrel{⌢}{u}}_k^{n+1}(\omega )$, ${\omega }_k^{n+1}$, ${\stackrel{⌢}{\lambda }}^{n+1}(\omega )$	The corresponding Fourier transformation
LBG	Linde -Buzo-Gray	x(t)	Original signal
LDA	Linear discriminative analysis	j	Imaginary unit
LFE	Large clearance fault of exhaust valve	p	The pth line in frequency-domain
LFI	Large clearance fault of intake valve	N	The data point number of $u_k^l(\mathrm{s})$
LFIE	Large clearance fault of intake and exhaust valve	s	The sth data of $u_k^l(\mathrm{s})$
LMD	Local mean decomposition	L	the integer cycle signal length
Ma Tec	Maintenance technicians	M	Number of sliding windows
MFC	Mel frequency cepstrum coefficient	IM	IVMD-MFCC feature
MFCC	Mel frequency cepstrum coefficient	l	the lth sub-frame signal
NVC	Normal valve clearance	Rrms	Mean square root of correlation coefficient
PCA	Principal component analysis	d	Euclidean distance between X and Yc
PR	Precision	n	Number of iterations
IMFs	Intrinsic mode functions	J	The number of feature vector subspaces
ISOMap	Isometric feature mapping	ρ	A constant
SE	Sensitivity	F	The total number of Mel filter banks
SHM	Structural health monitoring	fr	The frth Mel filter bank
SI	Signal improvement	X	Training set of vector quantization
SFE	Small clearance fault of exhaust valve	Yc	Codebook of cth subspace
SFI	Small clearance fault of intake valve	S	Mel-frequency spectrum energy of each frame signal
SFIE	Small clearance fault of intake and exhaust valve	SU	Number of training set subspaces
SMVK	The proposed method without VMD	Tts	Training sample of KNN
SVMK	The proposed method without vector quantization	Wls	Label set of Tn
SVMS	The proposed method replacing KNN with SVM	SSS	Testing sample of KNN
STFT	Short time Fourier transform spectrum	Nwl	Length of sliding window
VMD	Variational mode decomposition	Nss	Moving step size of sliding window
VMVK	The proposed method without signal improvement	m	The mth data point of the sliding window
VQ	Vector quantization	Convergence criteria of vector quantization	The mth data point of the sliding window
Symbols		$\Psi$	Total distortion of all subspaces
$\gamma$	Convergence criteria	Ra	Correlation coefficient between (a − 1)th and ath sliding window
$\alpha$	A castigatory quadratic	TS	Number of training sample
$\lambda$	Lagrangian multiplicator operator	SS	Number of testing sample
$ℒ$	extended Lagrangian function	ts	The tsth training sample
δ	Dirac distribution function	ls	The lsth label of training sample
τ	Noise tolerance parameter