Sparsity and Periodicity-Induced Symplectic Geometry Decomposition for Incipient Fault Diagnosis of Wind Turbine Gearbox

When incipient faults of gears or bearings occur in the wind turbine gearbox, their fault information will be readily masked by intensive background noise, which may postpone the fault detection and maintenance schedule. Specifically, the phenomenon manifested in the time domain is that the fault impulse is not obvious, while in the frequency domain, it is manifested that the fault frequency is prone to submerge in other interference frequency components. However, conventional signal processing methods and matrix factorization algorithms make it difficult to intuitively characterize fault features. Complex algorithms often require some manually adjusted parameters, which is difficult to be applied in engineering practice. To balance the performance and complexity of algorithms, a sparsity and periodicity-induced symplectic geometry decomposition (SPSGD) method is proposed. The initial components are obtained by the symplectic geometry mode decomposition method. Stem from the periodicity of gear faults in the time domain and the sparsity in the frequency domain, a periodicity-induced Bayesian clustering method is proposed as a novel iteration termination condition to pursue the fault-related components in the time domain. Then, a sparsity and periodicity-induced inverse filter is designed by the Laplace operator to weigh the faulty components to reduce the noise influence. The proposed SPSGD is validated by three cases, which indicate that the noise can be reduced adaptively as well as enhance the useful fault components effectively.