Blaschke mode decomposition: algorithm and application

Gear fault modulation information is often obscured by noise, and existing signal decomposition methods do not directly address the modulation characteristics of the gear, making it difficult to fully extract fault-related information. To overcome this challenge, this paper proposes a novel signal decomposition method, Blaschke mode decomposition (BMD). First, BMD proposed the weighted Chebyshev index and, based on this, develops the Chebyshev-based Blaschke transform, which effectively reveals weak modulation information hidden within the signal. Second, BMD incorporates a feature-constrained spectral segmentation strategy that divides the Blaschke spectrum into segments with distinct modulation characteristics, effectively suppressing noise interference. Finally, BMD constructs an ideal zero-phase filter bank to decompose the signal into components that clearly exhibit modulation characteristics. As an innovative signal decomposition method, BMD excels at extracting gear fault characteristics while significantly reducing noise interference. Experimental results demonstrate that BMD provides superior signal decomposition performance, enhancing the accuracy of mechanical fault diagnosis and showcasing its practical value.