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The vibration signals of rotating machinery in fault conditions are non-stationary and nonlinear. For the non-stationary and nonlinear characteristics of fault vibration signals, a novel multifractal manifold (MFM) method based on detrended fluctuation analysis (DFA) is proposed. The proposed method consists of three steps. Firstly, calculate the multifractal fluctuation functions of signal series with an appropriate polynomial order, according to multifractal DFA method. Secondly, construct multifractal feature vector for each signal sample to reveal the nonlinear characteristics in different scales. Finally, implement manifold learning to reduce the dimension of multifractal feature vectors. The obtained low-dimensional MFM features can reveal the differences of signal samples from different fault patterns effectively, which are benefit for automatic pattern recognition and multiple fault diagnosis. The recognition performance of the proposed MFM method is verified by fault experiments of gearbox and rolling element bearing, which demonstrates the superiority of MFM method in rotating machinery fault diagnosis compared to other DFA-based methods.

Multifractal manifold for rotating machinery fault diagnosis based on detrended fluctuation analysis