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

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Vibration data of faulty rolling bearings are usually nonstationary and nonlinear, and contain fairly weak fault features. As a result, feature extraction of rolling bearing fault data is always an intractable problem and has attracted considerable attention for a long time. This paper introduces multifractal detrended fluctuation analysis (MF-DFA) to analyze bearing vibration data and proposes a novel method for fault diagnosis of rolling bearings based on MF-DFA and Mahalanobis distance criterion (MDC). MF-DFA, an extension of monofractal DFA, is a powerful tool for uncovering the nonlinear dynamical characteristics buried in nonstationary time series and can capture minor changes of complex system conditions. To begin with, by MF-DFA, multifractality of bearing fault data was quantified with the generalized Hurst exponent, the scaling exponent and the multifractal spectrum. Consequently, controlled by essentially different dynamical mechanisms, the multifractality of four heterogeneous bearing fault data is significantly different; by contrast, controlled by slightly different dynamical mechanisms, the multifractality of homogeneous bearing fault data with different fault diameters is significantly or slightly different depending on different types of bearing faults. Therefore, the multifractal spectrum, as a set of parameters describing multifractality of time series, can be employed to characterize different types and severity of bearing faults. Subsequently, five characteristic parameters sensitive to changes of bearing fault conditions were extracted from the multifractal spectrum and utilized to construct fault features of bearing fault data. Moreover, Hilbert transform based envelope analysis, empirical mode decomposition (EMD) and wavelet transform (WT) were utilized to study the same bearing fault data. Also, the kurtosis and the peak levels of the EMD or the WT component corresponding to the bearing tones in the frequency domain were carefully checked and used as the bearing fault features. Next, MDC was used to classify the bearing fault features extracted by EMD, WT and MF-DFA in the time domain and assess the abilities of the three methods to extract fault features from bearing fault data. The results show that MF-DFA seems to outperform each of envelope analysis, statistical parameters, EMD and WT in feature extraction of bearing fault data and then the proposed method in this paper delivers satisfactory performances in distinguishing different types and severity of bearing faults. Furthermore, to further ascertain the nature causing the multifractality of bearing vibration data, the generalized Hurst exponents of the original bearing vibration data were compared with those of the shuffled and the surrogated data. Consequently, the long-range correlations for small and large fluctuations of data seem to be chiefly responsible for the multifractality of bearing vibration data.