Singularity analysis of the vibration signals by means of wavelet modulus maximal method

Machine fault diagnosis is vital for safe services and non-interrupted production. The key issue in fault diagnosis is the pattern recognition. A set of valid features will simplify the classifying operations and enhance the accuracy in diagnosis. In this paper, a novel singularity based fault features is presented. Vibration signals collected under different machine health conditions will show different patterns of singularities that can be measured quantitatively by the Lipschitz exponents. The wavelet transforms modulus maximal (WTMM) method provides a simple but accurate method in calculating the Lipschitz exponents. Therefore, the WTMM based Lipschitz exponent calculation as well as the method to select the appropriate wavelet function for WTMM and its range of scale are introduced. Three parameters about the singularity analysis are recommended. They are the number of Lipschitz exponents per rotation over(N, -), the mean value μ_α and the relative standard deviation over(s, -)_α of the Lipschitz exponents that are obtained from the extracted features. To verify the usefulness of the proposed methods, simulated signals and vibration signals generated by four types of faults commonly occurred in a rotating machine, including the imbalance, the oil whirl, the coupling misalignment and the rub-impact, had been used for testing purpose. The results show that the signal from the rub-impact possesses the highest singular value and the widest range of singularity. The signal of the coupling misalignment ranked the second. Whilst, the signal of imbalance is more regular or having the smallest singular value and the narrowest range of singularity. The results also prove that the three parameters are excellent fault features for pattern recognition as they can well separate the four fault patterns. © 2006 Elsevier Ltd. All rights reserved.