11.1 Introduction

Back

Wavelets-based representations offer an important option for capturing localized effects in many signals.

This is achieved by employing representations via double integrals (continuous transforms), or via

double series (discrete transforms). Seminal to these representations are the processes of scaling and

shifting of a generating (mother) function. Over a period of several decades, wavelet analysis has been set

on a rigorous mathematical framework and has been applied to quite diverse fields. Wavelet families

associated with specific mother functions have proven quite appropriate for a variety of problems. In this

context, fast decomposition and reconstruction algorithms ensure computational efficiency, and rival

classical spectral analysis algorithms such as the fast Fourier transform (FFT). The field of vibration

analysis has benefited from this remarkable mathematical development in conjunction with vibration

monitoring, system identification, damage detection, and several other tasks. There is a voluminous body

11-1

© 2005 by Taylor & Francis Group, LLC

of literature focusing on wavelet analysis. However, this chapter has the restricted objective of, on one

hand, discussing concepts closely related to vibration analysis, and on the other hand, citing sources that

can be readily available to a potential reader. In view of this latter objective, almost exclusively books and

archival articles are included in the list of references. First, theoretical concepts are briefly presented; for

more mathematical details, the reader may consult references [1 – 23]. Next, the theoretical concepts are

supplemented by vibration-analysis-related sections on time-varying spectra estimation, random field

synthesis, structural identification, damage detection, and material characterization. It is noted that most

of the mathematical developments pertain to the interval [0,1] relating to dimensionless independent

variables derived by normalization with respect to the spatial or temporal “lengths” of the entire signals.

Навигация