Adaptive spectrum segmentation Ramanujan decomposition and its application to gear fault diagnosis

Ramanujan Fourier mode decomposition (RFMD) is a novel non-stationary signal decomposition method, which can decompose a complex signal into several components and extract the periodic characteristics of the signal. However, the mode generation method adopted by RFMD does not consider the physical meaning of the component signal, which makes over-decomposition when dealing with real-life gear signals with complex modulation characteristics, thus destroying the integrity of the signal sideband, increasing the difficulty of subsequent analysis, and even losing key fault information. The iterative envelope-segmentation algorithm combines the modulation characteristics of the local fault gear signal and divides the original signal into a limited number of dominant frequency bands containing the modulation region in the Fourier spectrum, thereby ensuring that the obtained frequency bands contain rich fault information. Based on the above algorithm, a new adaptive decomposition method is proposed in this paper, which is adaptive spectrum segmentation Ramanujan decomposition (ASSRD). ASSRD uses fault envelope harmonic noise ratio as the index to evaluate the fault information content of component signals and uses it to assist the iterative envelope-segmentation algorithm to complete the adaptive segmentation of the Fourier spectrum. Finally, based on the segmentation result, the inverse RFT reconstruction of each frequency band is performed. Thus, the signal is decomposed into a finite number of component signals containing rich fault information. In addition, through the experiment on the gear simulation signal and the measured crack fault gear signal, the ASSRD method is compared with the original RFMD method and the existing ensemble empirical mode decomposition (EMD), variational mode decomposition, empirical wavelet transform, and singular spectrum decomposition method, verifying the feasibility and superiority of ASSRD in gear fault diagnosis. Besides, a comparative experiment based on compound faults diagnosis is carried out, in which ensemble EMD, Fourier decomposition method, empirical wavelet transform, and sparse decomposition are involved. The results show that the proposed method can extract the local fault information in the gear signal more effectively, and the performance is better than the comparison method.