Abstract
Conventional time-frequency spectral analysis, typically conducted with discrete Fourier transforms (DFTs), represents a signal as the sum of complex harmonic exponentials, and results in an analysis that has the same time and frequency resolution at all frequencies represented in the DFT. However, some processes are better represented as the sum of functions at different time scales rather than at different frequencies. Wavelet analysis provides such a representation, and under certain conditions can be interpreted as an analysis whose time and frequency resolutions change with frequency, as opposed to the constant time and frequency resolution of the DFT. Two different types of processes associated with rotating machinery, bearing vibrations, and periodic mechanical transients, are shown from physical considerations to have time scale properties that are appropriate for wavelet analysis. Measurements of bearing vibrations and mechanical transients were made and both Fourier and wavelet analyses were applied to each of the measurements to demonstrate their associated time-scale properties and the potential benefits of wavelet analysis for machinery diagnostics. [Work supported by ONR.]
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