Empirical Ramanujan decomposition and iterative envelope spectrum for fault diagnosis

Ramanujan Fourier mode decomposition obtains components by scanning from low frequency to high frequency, which will cause too many components, and then the fault information in mode components is incomplete. Based on this, the empirical Ramanujan decomposition (ERD) method is proposed. Firstly, ERD uses the optimized lowest minima technique to segment the spectrum and determines the segmentation boundary and the number of components. Subsequently, ERD constructs the filter bank for filtering and retains the spectral components corresponding to the main frequency band. Finally, the time domain components are recovered by the inverse Ramanujan Fourier transform. To further improve the capability of envelope spectrum (ES), an iterative ES (IES) method is proposed. IES enhances the periodic components through iterative envelope to make the fault feature more conspicuous. The analysis results of simulation and experimental signals show that the ERD and IES can extract features effectively.