A rubbing fault identification method of combining the covariance of the Hankel matrix and 1D-LBP

1D local binary pattern (1D-LBP) is more capable of representing local features and is suitable for extracting weak information. However, the method is too sensitive to noise and inaccurate in signal quantization. Meanwhile, most studies on fault identification with 1D-LBP are based on original vibration signals. Due to the influence of noise and weakness of fault information, it is difficult to exactly extract fault features. As the representation forms of fault information are complex, variable, and somewhat uncertain, it is difficult to evaluate the state of equipment according to some kind of determinate indexes, which adds to the difficulty of fault identification. To effectively estimate rubbing faults, an approach that blends the covariance of the Hankel matrix and 1D-LBP was proposed. Firstly, the Hankel matrix of the original signals is constructed, and 1D time sequence is extended to a high-dimensional space to dig out hidden feature information of low-dimensional space. Secondly, the covariance matrix of the Hankel matrix is calculated to highlight periodic features while reducing the noise. Thirdly, to avoid randomness involved in screening effective components of the covariance matrix based on signal evaluation indexes, a method was proposed in which column vectors are replaced with the mean value of each column to create a new sequence of signals. Furthermore, local features of reconstructed signals (not the original signals) were extracted using the 1D-LBP algorithm. Finally, rubbing faults were determined using the spectrum of decimal signals regained after quantization. An analysis was conducted on signals under various states and a comparative validation was performed with conventional methods to verify the effectiveness of this proposed method. The result indicates that the proposed method not only effectively controls noise, but also correctly determines a rubbing fault, and there is an ideal application value in engineering.