Multi-scale Ramanujan ultra-narrow band decomposition and its application in composite fault diagnosis

The reliance on a single frequency band segmentation method for composite fault signals often fails to accurately separate overlapping frequency information, resulting in misdiagnosis and missed detection of compound faults. In this regard, a novel method of considering multi-band information at different scales is proposed in this paper, called multi-scale Ramanujan ultra-narrow band decomposition (MRUD). Firstly, the MRUD method operates within a multi-scale ultra-narrow band decomposition framework to perform precise segmentation, generating multi-scale sub-modes via Ramanujan period transformation. This dual capability allows for the exact band partitioning of strongly coupled signals while simultaneously applying in-band filtering to mitigate noise’s impact on the final filter component. Secondly, the local feature enhancement index (LFEI) is introduced to quantify the fault feature intensity of these sub-modes by assessing their local energy proportion, thereby facilitating the selection of the optimal scale. Finally, filter components are derived by solving an optimisation problem, a process that preserves the integrity of fault characteristic information while effectively suppressing noise components. Simulation and experimental results on rolling bearings demonstrate that MRUD possesses superior fault feature extraction capabilities, establishing it as an effective method for composite fault identification.