Optimal Autoregressive Modelling of a Measured Noisy Deterministic Signal Using Singular-Value Decomposition

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

“…For a discrete signal X=[x(1), x(2), y, x(N)], a Hankel matrix can be created as follows: where 1on oN, let m =N À n+ 1, then AAR m  n , this matrix is also called trajectory matrix in some references [3,15]. The traditional noise reduction procedure of SVD can be summarized as follows [3,9,10,15]: first, matrix A is decomposed by SVD, so matrices U, D and V can be obtained. Second, in diagonal matrix D some significant singular values are reserved while the rest are set to zero, so a new diagonal matrix D 0 can be obtained.…”

“…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].…”

Damage detection in a benchmark structure using AR-ARX models and statistical pattern recognition

“…There are several criteria to determine this order. For example, Shin et al (2003) proposed a criterion based on the singular-value decomposition. The two most widely used methods are Akaike's information theoretic criterion (AIC) and Akaike's final prediction error (FPE), (Aguirre, 2004).…”

Face description based on adaptive local weighted Gabor comprehensive histogram feature

“…For example, the Singular Value Decomposition (SVD) methods are proposed by Shin et al [25,33,34]. Linear Discriminant Analysis (LDA) technology is adopted to represent face discriminant feature by J. Fabregas et al [2,4,17,18,23,24,26,27,35,39,45].…”