Health condition monitoring of bearings based on multifractal spectrum feature with modified empirical mode decomposition-multifractal detrended fluctuation analysis

Multifractal detrended fluctuation analysis (MFDFA) is proved to be a powerful tool for fault diagnosis of rotating machinery due to its ability to reveal multifractal structures hidden in nonstationary and nonlinear vibration signals. To overcome the discontinuity of the fitting scale-dependent trend and the poor adaptability of this algorithm, Empirical Mode Decomposition-Multifractal Detrended Fluctuation Analysis (EMD-MFDFA) is introduced. However, EMD-MFDFA runs into difficulties in reverse segmentation and the selection of the expected Intrinsic Mode Functions (IMFs). Aiming at solving these deficiencies, a Modified EMD-MFDFA (MEMD-MFDFA) approach with IMF selection strategy and Step-Moving Window (SMW) segmentation method is proposed in this paper. In MEMD-MFDFA, a metric for distinguishing deterministic and random components is established to select expected IMF components by scaling exponent. Meanwhile, SMW segmentation method is exploited to reduce the estimated errors caused by reverse segmentation. The robustness of the proposed method is investigated through comparing MEMD-MFDFA, MFDFA, and EMD-MFDFA by multifractality of simulated signals with different Signal-to-Noise Ratio (SNR). Furthermore, the proposed approach is applied to three bearing run-to-failure datasets containing three types of faults, and the results show that the multifeatures of the multifractal spectrum obtained by MEMD-MFDFA have the ability to simultaneously identify early fault and assess performance degradation of bearings.