Order Tracking Analysis Using Generalized Fourier Transform With Nonorthogonal Basis

Abstract

The nonorthogonal basis generalized Fourier transform is used as orders extraction technique during machinery speed-up and slow-down tests due to nonstationary nature of vibration signals in these tests. The kernels of this transform have time-dependent frequency which is related to the operating speed of the machine. Since these kernels may belong to different groups or shafts, they are generally nonorthogonal. The actual amplitudes and phases of the orders can be found by solving the system of linear equations resulting from decomposition process which is proposed in this work as an improvement to the time variant discrete Fourier transform (TVDFT) method. The proposed scheme is proved to be efficient and the processing time is very small as compared to other schemes such as the Vold–Kalman order tracking (VKOT) method. The accuracy and efficiency of the proposed scheme are investigated using simulated vibration signal and also actual signals.

Diagnosis of Inter-Turn Faults Based on Fault Harmonic Component Tracking in LSPMSMs Working Under Nonstationary Conditions

“…Instead, the transient MCSA, as an extension of MCSA to transient conditions [13], should be used to analyze transient current signals in these conditions. The short-time Fourier transform (STFT) [14], Hilbert-Huang transform (HHT) [15], wavelet transform (WT) [6], Wigner-Ville distribution (WVD) [16], and Gabor transform [17] are methods to analyse the nonstationary signals. In these methods, a current signal in the time-domain (1D) is converted into a spectrogram in the t-f plane by special transform techniques [18].…”

“…These methods are capable of reconstructing harmonic orders in their time history and extracting a specified frequency/order component. As time history allows instantaneous determination of values such as frequency and amplitude at any time, any FHC of a signal can be easily traced using these methods [14]. Although Gabor-OT and VKF-OT are the most accurate techniques for nonstationary signal analysis, their most important drawbacks are that they require excessive calculations.…”