Improved singular value decomposition technique for detecting and extracting periodic impulse component in a vibration signal

Selection of effective singular values using difference spectrum and its application to fault diagnosis of headstock

“…Choosing the equal sign in formula (12) and substituting it into formula (11), thus we obtain s t ðA þ BÞ rs t ðAÞþs t ðBÞ…”

“…For example, Ahmed et al utilize SVD to compress the electrocardiogram (ECG) signal, their main idea is to transform the ECG signals to a rectangular matrix, compute its SVD, then discard the signals represented by the small singular values and only those signals represented by some big singular values are reserved so that ECG signal can be greatly compressed [1]. SVD also performs very well for extracting the faint signal, such as by the processing of SVD, the faint fetal ECG can be extracted from the complicated maternal abdominal ECG [11], and the periodic impulse information of bearing can also be isolated from a vibration signal contaminated by the strong noise [12]. SVD can even be used to estimate the number of hidden neurons in neural network for its performance of orthogonality and compression [14].…”

“…where U and V are the orthogonal matrix, UAR m  m , VAR n  n , D is the diagonal matrix, D=[diag (s 1 , s 2 , y, s q ), O] or its transposition, and this is decided by m on or m Zn, DAR m  n , O is the zero matrix, q=min(m, n), s 1 Zs 2 ZyZ s q 40. s i (i=1, 2, y, q) are called the singular values of matrix A. SVD method has been widely applied to many fields in recent years, such as data compression [1,2], system recognition [3], adaptive filter [4,5], principal component analysis (PCA) [6,7], noise reduction [8][9][10], faint signal extraction [11,12], machine condition monitoring [13] and so on. For example, Ahmed et al utilize SVD to compress the electrocardiogram (ECG) signal, their main idea is to transform the ECG signals to a rectangular matrix, compute its SVD, then discard the signals represented by the small singular values and only those signals represented by some big singular values are reserved so that ECG signal can be greatly compressed [1].…”

Application of MMI-SVP theory in spindle fault feature extraction

“…However, the noise suppression ability of SVD is highly associated with the decomposition matrix construction and the reconstruction component selection. In terms of matrix construction, such as the cyclic sub-matrices [10], Toeplitz matrix [11], covariance matrix [12], Cut-off the matrix [13], Hankel matrix [14], all of these were applied in SVD. Specifically, literature [15] stated that the Hankel matrix usually decomposes the original signal into a series of linear sub-signals.…”