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Fault diagnosis under time-varying operational conditions is always the challenge in industrial systems. The chirplet transform (CT) provides an effective first-order approximation approach, but the slow operation speed and the drawback for high-order signal analysis limit its uses. Focusing on this problem, a fast nonlinear chirplet dictionary-based sparse decomposition (FNC-SD) method for nonlinear signal analysis is proposed. By replacing the time–frequency inclination parameter in the CT with a frequency bending parameter, the proposed method can track the nonstationary signals by arbitrary order polynomial law with time by an additional degree. Considering that too many parameters will slow down the operation speed, a frequency bending operator estimation algorithm is also proposed in this paper based on the calculated rotating frequency. Therefore, a laser vibrometer is needed in the experiment to collect the impulse signals, which can represent rotating speed signals. Then, the FNC-SD method is used to construct a redundant dictionary for signal sparse time–frequency representation. The high similarity between signals and atoms can make the method prefer to choose the right atoms, instead of being influenced by noise. Therefore, the proposed method also shows a strong noise robustness. Two simulation experiments are constructed to verify the performance of the proposed method. Finally, the FNC-SD method is used to diagnose a faulty motor with broken bar. The analyzed results and comparisons with respect to the state-of-the-art methods are illustrated in detail, as well as the convergence accuracy and speed, which highlight the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

As wind power attracts increasing attention and wind turbines (WTs) capacity expands, fault diagnosis of WT is playing a more and more important role in improving reliability, minimizing down time, reducing maintenance costs, and providing reliable power generation. In this paper, a novel sparse time-frequency representation (STFR) method is proposed to increase the diagnostic precision of incipient faults. The proposed method can be applied once the condition is detected as abnormal according to the VDI3834 vibration threshold standard in WT fault diagnosis systems. The proposed method is a novel signal representation method based on the sparse representation theory and Wigner–Ville distribution (WVD), which can overcome the limitations of traditional basis functions expansion and time-frequency analysis methods. In this method, a union of redundant dictionary (URD) is constructed on the basis of the underlying prior information of the oscillate characteristics with multicomponent coupling effect and different morphological waveforms. Therefore, the vibration signal can be sparsely represented over the URD. Then, the sparse coefficients and corresponding atoms can be obtained by solving the basis pursuit denoising problem via alternating direction method of multipliers. Based on the combination of the WVD of each atom and corresponding sparse coefficient, the time-frequency distribution of the vibration signal can be obtained. To verify the effectiveness of the STFR method, a simulation and two field tests in the wind farm are performed. The comparison results with state-of-the-art methods illustrate the superiority and robustness of the proposed method in the engineering applications. [ABSTRACT FROM AUTHOR]