Singular value decomposition packet and its application to extraction of weak fault feature

• The concept of singular value decomposition packet (SVDP) is put forward.
• The decomposition and reconstruction algorithm of SVDP is proposed.
• SVDP can extract weak feature hidden in original signal without waveform distortion and phase shift.
• SVDP shows a better performance than wavelet packet in weak feature extraction.

The concept of singular value decomposition packet (SVDP) is put forward, and the purpose of SVDP is to use singular value decomposition (SVD) to implement the signal decomposition way of wavelet packet. SVDP can decompose an original signal into a series of component signals of the different layers, in which the first one reflects the approximation information of the original signal, while the others reflect the detail information. When the decomposition layer increases one layer, the number of component signals will be doubled, and this decomposition structure is as same as the one of wavelet packet. SVDP is especially suited to extract the weak fault feature, and signal processing examples show that SVDP has better performance at the extraction of weak fault feature than wavelet packet. Finally, the reason why there is no phase lag and waveform distortion in the feature extraction results of SVDP is explained.