Sparse Feature Identification Based on Union of Redundant Dictionary for Wind Turbine Gearbox Fault Diagnosis

A primary challenge in fault diagnosis is to extract multiple components entangled within a noisy observation. Therefore, this paper describes and analyzes a novel framework, based on convex optimization, for simultaneously identifying multiple features from superimposed signals. This work adequately exploits the underlying prior information that multiple faults with similar frequency spectrum have different morphological waveforms that can be sparsely represented over the union of redundant dictionaries. Within this framework, prior information is formulated into regularization terms, and a sparse optimization problem, which can be solved through the alternating direction method of multipliers (ADMM), is proposed. Meanwhile, the convergence and computational complexity of the proposed iterative framework are profoundly investigated. Moreover, sensitivity analyses and adaptive selection rules for the regularization parameters are described in detail through a set of comprehensive numerical studies. The proposed framework is validated through performing the diagnosis of multiple faults for gearbox in a wind farm. The comparison with respect to the state of the art in the field is illustrated in detail, which highlights the superiority of the proposed framework.