A new method of noise reduction grounded on Hankel matrix and its application in rubbing fault diagnosis

Abstract In processing signals with singular value decomposition (SVD), one of the keys lies in building an appropriate Hankel matrix from signals. To address the difficulty in extracting the feature information of rubbing faults between rotor and stator, by taking advantage of the nature of rubbing fault information closely related to the rotation period of equipment, a new method of SVD is presented based on the Hankel matrix built from the periodicity of a rotation machine. First, with the periodicity of the rub-impact fault as the basis, the interval step size between Hankel vectors was determined to self-adaptively build a Hankel matrix of signals. Second, the newly-built Hankel matrix was denoised through the singular value differential spectrum. Third, to reduce the loss of data as much as possible, a strategy was proposed to rebuild signals according to the first and last rows of denoised signals. Fourth, features of rubbing faults were extracted according to the frequency spectrum of reconstructed signals, and faults were identified. To verify the applicability and effectiveness of the presented algorithm, various types of simulation signals and tester signals from different states were incorporated. Meanwhile, the presented algorithm was compared with a variety of classical methods. The results prove that the proposed method can not only effectively constrain noise interference, but also highlight fault feature information and correctly identify rub-impact faults.