Wavelet Analysis of Vibration: Part 2—Wavelet Maps

Abstract

Wavelet maps provide a graphical picture of the frequency composition of a vibration signal. This paper, which is Part 2 of a pair, describes their construction and properties. In the case of harmonic wavelets, there are close similarities between wavelet maps and sonograms. A range of practical examples illustrate how the wavelet method may be applied to vibration analysis and some of its advantages.

Application of Wavelet Transform for Fault Diagnosis in Swash Plate Pump’s Control Unit Causing Pipes Flutter

“…It employs two sets of functions, called scaling functions and wavelet functions [12], [13], which are associated with low and high pass filters, respectively. The discrete signal is passed through a high pass filter (H) and a low pass filter (g), resulting in two vectors at the first level; approximation coefficient (A 1 ) and detail coefficient (D 1 ) [14], [15]. Application of the same transform on the approximation (A 1 ) causes it to be decomposed further into approximation (A 2 ) and detail (D 2 ) coefficients at the second level.…”

Non-stationary seismic response of MDOF systems by wavelet transform

“…On substituting equations (26) and (27) in equation (20), we get the expression for E[W x i (a p ; b q )] 2 in terms of the wavelet co-e cients of the input acceleration process. This expression can now be used to obtain the total expected energy of the response, x i (t) as (as in equation (10) …”

Research on vibration of rotor by application of the improved harmonic wavelet

“…The existence of many kinds of nonlinear factors in the process defect, as well as in rotor, bears system of changeable operating mode and complicated flow field and often can not avoid leading to his vibration signal to show out the stronger non-smooth and steady specific property when referring to machinery revolving [16][17][18]. The harmonic wavelet is analyzed for improving it, which provides a great convenience frequently [19][20][21].…”