Statistical Analysis of Frequency Estimation Methods of Vibration Signal

In the fault diagnosis of a machine, frequencies of its vibration are important indicators to show conditions of the machine. There are two main categories of methods to estimate frequency. One is based on the fast Fourier transform, and the other is on the signal subspace decomposition. Using FFT directly to estimate frequency may introduce larger estimation error, several approaches are proposed to correct or decrease the error, which comprise phase difference, energy centrobaric, interpolation and search method. The signal subspace decomposition method (SSDM) consists of Pisarenko harmonic decomposition, multiple signal classification. In order to assess the performance of these methods, the Cramer-Rao bound is used to compare with the error variance of difference frequency estimation methods, and simulations are based on Monte Carlo experiments for various record sizes and signal-to-noise ratios (SNR's). The results show that there is a turning point about 25 dB for FFT based methods, above which FFT based methods are less sensitive to the noise, and SSDM achieves higher precision estimation at higher SNR and for the short time series, but produces poor accuracy at lower SNR's.