Fault diagnosis of rolling bearings using multifractal detrended fluctuation analysis and Mahalanobis distance criterion

Vibrations of a defective rolling bearing often exhibit nonstationary and nonlinear characteristics which are submerged in strong noise and interference components. Thus, diagnostic feature extraction is always a challenge and has aroused wide concerns for a long time. In this paper, the multifractal detrended fluctuation analysis (MF-DFA) is applied to uncover the multifractality buried in nonstationary time series for exploring rolling bearing fault data. Subsequently, a new approach for fault diagnosis is proposed based on MF-DFA and Mahalanobis distance criterion. The multifractality of bearing data is estimated with the generalized the Hurst exponent and the multifractal spectrum. Five characteristic parameters which are sensitive to changes of bearing fault conditions are extracted from the spectrum for diagnosis of fault sizes. For benchmarking this new method, the empirical mode decomposition (EMD) method is also employed to analyze the same dataset. The results show that MF-DFA outperforms EMD in revealing the nature of rolling bearing fault data.