Fault Diagnosis Using Adaptive Multifractal Detrended Fluctuation Analysis

Multifractal detrended fluctuation analysis (MF-DFA) has been used for vibration-based fault diagnosis because it is able to uncover multifractality buried in nonlinear and nonstationary vibration signals and thus offers an opportunity to explore a new set of multifractal features for fault diagnosis. However, the choice of detrending polynomial orders is one of the major concerns in MF-DFA because improper polynomials can cause the underfitted or overfitted scale-dependent trend of the signals. To address this issue, adaptive MF-DFA (AMF-DFA) is developed in this paper. More specifically, the developed AMF-DFA uncovers multifractality of the signals by adaptively extracting a variable number of scale-dependent fluctuations present in the signals and automatically eliminating irrelevant trend components to the fundamental structure of the signals based on correlation analysis. Accordingly, the developed AMF-DFA does not require a priori knowledge (i.e., detrending polynomial order). The effectiveness of the developed AMF-DFA was verified for fault diagnosis applications.