Empirical mixed Ramanujan Fourier decomposition and its application to early fault diagnosis of planetary gears

The noise robustness of adaptive empirical Fourier decomposition (AEFD) is not ideal, and Ramanujan Fourier mode decomposition (RFMD) often occurs over decomposition, causing the fault information to be dispersed. Based on this, an original method called empirical mixed Ramanujan Fourier decomposition (EMRFD) is proposed for nonlinear and non-stationary signal analysis. Firstly, EMRFD obtains the coefficients of mixed Ramanujan Fourier transform (MRFT) through the new mixed transform matrix. Then, EMRFD obtains the partition boundary through adaptive frequency band division. Finally, the mode components named mixed Ramanujan Fourier intrinsic band functions (MRFIBFs) of frequency bands are obtained by inverse MRFT. The simulation and experimental signal analysis results show that EMRFD not only has excellent signal decomposition accuracy, but also has effective ability of extracting periodic components, which is a valid method for early fault diagnosis of planetary gears.