Multiscale recursive mode decomposition: theory and application
Under strong background noise, the weak incipient fault features of mechanical equipment are easily obscured by environmental noise, thereby hindering effective feature extraction. Inspired by the decomposition mode of wavelet packet transform, a multiscale recursive mode decomposition (MRMD) method is proposed based on a tree-structured decomposition framework in this paper. The MRMD constructs a multi-level recursive decomposition framework that hierarchically partitions the signal across different scales, thereby enhancing the adaptivity of the decomposition process. Moreover, by employing a tree-based binary-splitting strategy, the method reduces the multi-parameter optimization problem inherent in conventional approaches to a single dominant tuning parameter focused on filter length, which substantially improves computational efficiency and parameter stability. To ensure that selected components preserve high fault-information density and periodic characteristics, the harmonic energy to background is used as the component evaluation criterion and is supplemented by a harmonic-matching verification mechanism to quantitatively identify and screen candidate components. Simulation and experimental results indicate that MRMD reliably identifies fault features across a range of signal-to-noise ratios while maintaining high diagnostic accuracy and markedly improving decomposition efficiency and adaptivity.