Vibration Signal Fault Diagnosis Based on Generalized Fractal Dimension

Abstract

To process the vibration signal fault diagnosis automatically and effectively, a method to calculate the generalized fractal dimension (Dq) based on the traditional G-P correlation dimension algorithm is presented. First, the vibration signal, a kind of random fractal that meets the statistical self-similarity, is reconstructed according to the phase space reconstruction theory. Second, for various weight factor values (q), calculation of the qth-order correlation integral, followed by the Dq, is processed. Range of the weight factor is discussed. With the generalized fractal dimension, the dynamic characteristics of the system are then reproduced more entirely and accurately. The effectiveness of the proposed method is verified by calculating the generalized fractal dimension for various measured vibration signals. The generalized fractal dimension distinguishes the state of vibration signal unambiguously. The analysis also indicates that the fluctuation amplitude of Dq is related to the frequency distribution of vibration signal. This would be helpful for the vibration signal fault diagnosis.