Blaschke transform-based Weight Soft Voting Denoise Method and its applications in gear fault diagnosis

Hardy space is a distinctive space of holomorphic functions on the unit disk, with far-reaching implications in mathematical analysis, control theory, and scattering theory due to its favorable growth and boundary properties. Building upon the Hardy space, this paper proposes a novel denoising method, Blaschke Transform-based Weight Soft Voting (BT-WSV). Firstly, BT-WSV defines Blaschke Transform. Operating within the theoretical framework of the complex Hardy space, Blaschke Transform employs the specific Szegő kernel projection, which represents signals as a linear combination of quasi-periodic Blaschke mono-components. Blaschke Transform can map complex signals to the optimal power series space, and its derived Blaschke spectrum can intuitively illustrate the energy distribution of quasi-periodic components, facilitating the analysis of the intrinsic characteristics. Secondly, BT-WSV restructures the Blaschke mono-components based on soft thresholds, effectively sifting out the strongly quasi-periodic characteristic information within the signal. Finally, BT-WSV defines a weight voting strategy, which effectively refines the fault information, protects sideband characteristics, and eliminates noise interference. Applying BT-WSV to gear fault diagnosis, both simulation and experimental signal analysis results demonstrate the excellent performance of the proposed method in gear fault diagnosis.