An eigen decomposition and denoising algorithm based on information entropy

Abstract

Rub-impact is one of typical secondary failures for large-sized machines like aero-engine. As the feature information of rubbing failure is weak and complicated and vulnerable to the interference of ambient noise, it is often hard to precisely recognize. To reduce the noise and further highlight the information of weak fault included in signals, and precisely recognize a rub-impact fault, the study has proposed a denoising method based on eigen decomposition (ED) of Hankel matrix and information entropy (IE). Firstly, Hankel matrix is built from signal with 1 as step-size and then Hankel matrix is decomposed. Meanwhile, corresponding eigenvalues and eigenvectors can be obtained and hidden feature information in matrix is descripted by eigenvalues. Secondly, in concerning that the larger information entropy of signal is, the more chaotic system will be and the harder it is to extract the hidden fault feature information, minimum information entropy is taken as standard to choose the eigenvalues and eigenvectors for signal reconstruction. Finally, feature of rub-impact fault is extracted according to the frequency spectrum of reconstructed signal. To verify the effectiveness and feasibility of proposed method, single spot rub-impact fault data collected in case of different rub-impact positions, extents and rotating speeds has been verified and analyzed according to proposed method. Comparison is made between proposed method and classical singular value difference spectrum denoising and feature mode decomposition. The result indicates that proposed method can more effectively suppress the interference of noise components to an ideal effect and highlight the feature information of rub-impact fault.