Variational Multi-harmonic Duality Mode Pursuit

Method for extracting repetitive transient component from noisy signals

In vibration signals, repetitive transient components (RTCs) are the typical symptoms reflecting the localised defects of rotating machinery, which can be mathematically defined by feature parameters, such as the inter-arrival interval, maximum amplitude, resonance frequency, and attenuation ratio. In particular, the inter-arrival interval and maximum amplitude reveal the location and severity of failure and provide critical information for condition monitoring and fault diagnosis, which should be well retained during signal processing. A periodic RTC has a discrete and clear spectral structure. In this situation, we can recover the periodic RTC as much as possible by constructing a local narrow bandpass filter bank to extract prominent spectral lines with equal frequency intervals. However, such a band-pass filter bank is unable to extract pseudo-periodic RTCs directly because the slight random deviation of the repetition period in the time domain, namely, the fluctuating inter-arrival interval of the RTC, can cause severe spectral smearing, especially in the high-frequency regions of the spectrum.

In terms of the shape of the time-domain waveform and spectrum, a component composed of multiple harmonics is scattered in the time domain but behaves as a repetitive transient form with a local compact bandwidth in the frequency domain. Based on the duality property of the Fourier transform (FT), the functional forms of a FT pair in the time and frequency domains can be exchanged. This implies that a periodic or pseudo-periodic RTC can be expressed as an inverse Fourier transform (IFT) of a multi-harmonic duality function. Based on this idea, a complex-valued target component decomposition method called variational multi-harmonic duality mode pursuit (VMHDMP) was developed to handle complex-valued frequency signals and accurately extract the RTC occurring in the time domain. Essentially, VMHDMP provides an optimal ‘transient-pass’ inverse filter bank with compact passage only near the occurrence moment of each transient in RTC. Thus, the vital parameters closely related to the faults are fully retained, whereas the frequency-overlap noise and large-amplitude interference occurring at different moments can be effectively eliminated. Some simulated and experimental examples were used to test the effectiveness of VMHDMP.

The matlab codes permit to reproduce some results in the paper: Tingting Jiang, Qing Zhang, Junshen Zhang, Xiaohan Wei, Variational multi-harmonic duality mode pursuit method for extracting repetitive transient components from vibration signals, Measurement, 2024. In the provided matlab codes, the function called IVMHME is an embedded version specifically provided to the VMHDMP algorithm for decomposing a real-valued frequency signal. Its related details can be found in our previous work: Tingting Jiang, Qing Zhang, Xiaohan Wei, Junshen Zhang, Variational multi-harmonic mode extraction for characterising impulse envelope of bearing failures, ISA Transactions,2023.

Copyright (c) belongs to the authors of the paper. An acknowledgment for the codes and the citations about the paper above must be included in the publications as long as the codes are used.