Gear fault diagnosis is crucial for ensuring the efficient and safe operation of rotating machinery. However, since the actual gear fault vibration signals are often contaminated by substantial noise and interference, the diagnostic performance of conventional signal decomposition methods is severely limited. In this connection, this paper proposes a novel variable multilevel random feature decomposition (VMRFD) method. First, VMRFD employs sparse random feature expansion to define the random feature energy spectrum of the signal, so that signal decomposition can be achieved through spectrum segmentation. Subsequently, based on the Fourier-model fitting method, a variable multilevel spectral trend segmentation framework is established to adaptively determine the segmentation boundaries of the spectrum. This framework not only reduces the complexity of the spectrum, but also increases the diversity and accuracy of frequency band division. In addition, a spectral energy threshold denoising scheme is formulated to weaken redundant noise in the segmented frequency bands. Eventually, an adaptive mode extraction strategy assisted by the envelope-derivative operator periodic harmonic-to-noise ratio metric is designed to iteratively derive several independent random mode components from the components corresponding to different denoising frequency bands, which ensures that the periodic fault components of interest can be accurately separated. The analysis results of simulation and experimental cases show that VMRFD has superior decomposition performance and can effectively diagnose gear fault.
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