Robust Fractional Low-Order Multiple Window STFT for Infinite Variance Process Environment

Mechanical fault vibration signal is a typical non-Gaussian process, they can be characterized by the infinite variance process, and the noise within these signals may also be the process in complex environments. The performance of the traditional cross-term reduction algorithm is compromised, sometimes yielding incorrect results under the infinite variance process environment. Several robust fractional lower order time–frequency representation methods are proposed including fractional low-order smoothed pseudo Wigner (FLOSPW), fractional low-order multi-windowed short-time Fourier transform (FLOMWSTFT), and improved fractional low-order multi-windowed short-time Fourier transform (IFLOMWSTFT) utilizing fractional low-order statistics and short-time Fourier transform (STFT) to mitigate cross-terms, enhance time–frequency resolution, and accommodate the infinite variance process environment. When compared to traditional methods, simulation results indicate that they effectively suppress the pulse noise and function effectively in lower mixed signal noise ratio (MSNR) in an infinite variance process environment. The efficacy of the proposed time–frequency algorithm is validated through its application to mechanical bearing outer ring fault vibration signals contaminated with Gaussian noise and subjected to an α infinite variance process.