Time-Frequency Analysis by Evolutionary Periodogram With Application in Gear Fault Diagnosis

Abstract

The evolutionary periodogram has been introduced to mechanical fault diagnosis and relationship between the evolutionary periodogram and time-frequency spectrogram has been investigated. The evolutionary periodogram is unveiled as an especially windowed spectrogram, and is applied to gearbox fault diagnosis. It has been shown that the window used in the evolutionary periodogram is not a single function but a combination of a set of functions. Two cases of gearbox diagnosis are presented as examples of application. Vibration signals and a synchronous signal are collected for the analysis. The time synchronous averaging is used to reduce background noise or random transients to enhance the periodicity of a specific gear rotation. The performance of the evolutionary periodogram has been compared with the spectrogram for gear diagnosis, showing that the evolutionary periodogram is an alternative technique in time-frequency analysis for fault detection and better resolution can be obtained as more choices are offered by the way of constructing the window.

Generalized Paley–wiener Theorems

“…1,[3][4][5]9 The study is initiated by two topics, one is the non-harmonic Fourier transform, 6 the other is the real variable description of the Paley-Wiener type theorem discovered by Bang, 2 Tuan and Zayed. 7, 8 We briefly review both of them below.…”

Joint Estimation of Doppler Stretch and Time Delay of Wideband Echoes for LFM Pulse Radar Based on Sigmoid-FRFT Transform under the Impulsive Noise Environment

“…To suppress the impulsive noise interference, many parameter estimation algorithms based on the fractional lower-order statistics (FLOS) have been proposed [7][8][9][10][11][12][13]. Li (DOA) in impulsive noise [7].…”

“…Time-frequency distribution is a useful tool to extract helpful information of the received signal. Various time frequency distribution methods based on fractional lower order statistics have been proposed, such as short time Fourier transform based on fractional lower order statistics [10], Wigner-Ville distributions based on fractional lower order statistics [11], fractional power spectrum density based on fractional lower order statistics [12], and fractional correlation based on fractional lower-order statistic [13]. Li et al proposed a novel method that combines the fractional lower order statistics and fractional power spectrum density (FLOS-FPSD) for suppressing the impulsive noise and estimating parameters for a bistatic multiple input and multiple output (MIMO) radar system in the impulse noise environment [12].…”