Multifractal detrended fluctuation analysis based on optimized empirical mode decomposition for complex signal analysis

Multifractal detrended fluctuation analysis (MFDFA) is a powerful tool to uncover nature of complex signals. However, MFDFA runs into difficulties in determining the type of the fitting polynomial trend and making the fitting polynomial trend continuous. To solve these problems, MFDFA based on empirical mode decomposition (MFDFAemd) is developed. Unfortunately, MFDFAemd suffers from negative frequency and difficulties in selecting fractal components. To overcome deficiencies of these traditional methods, this paper proposes a novel version of MFDFA based on optimized empirical mode decomposition (MFDFAoemd). In MFDFAoemd, instantaneous frequency of a signal component is estimated using normalized Hilbert transform and Teager energy operator and a criterion for distinguishing a fractal component from a truly noisy component is established. Moreover, the effectiveness of MFDFAoemd is compared with MFDFA and MFDFAemd by probing a multifractal signal generated by a multifractal cascade model. The comparison displays superiority of MFDFAoemd over MFDFA and MFDFAemd. Next, the performance of MFDFAoemd is further benchmarked against MFDFA and MFDFAemd by analyzing gearbox vibration signals containing different types of single-point fault and those containing different types of compound gear fault. The results show that MFDFAoemd can remedy the shortages of MFDFA and MFDFAemd and has an advantage in diagnosing both single-point gear faults and compound gear faults.