11 Wavelets — Concepts and Applications Pol D. Spanos

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Rice University

Giuseppe Failla Universita` degli Studi

Mediterranea di Reggio Calabria Nikolaos P. Politis

Rice University

11.1 Introduction ....................................................................... 11-1

11.2 Time – Frequency Analysis ................................................ 11-2

Gabor Transform † Wavelet Transform † Wavelet

Families

11.3 Time-Dependent Spectra Estimation of Stochastic

Processes ............................................................................. 11-11

11.4 Random Field Simulation ................................................ 11-14

11.5 System Identification ......................................................... 11-15

11.6 Damage Detection ............................................................. 11-17

11.7 Material Characterization ................................................. 11-18

11.8 Concluding Remarks ......................................................... 11-19

Summary

Section 11.1 provides a brief introduction to wavelet concepts in vibration-related applications. Aspects of time –

frequency analysis are discussed in Section 11.2. Specifically, the Gabor and wavelet transforms are outlined.

Further, several wavelet families commonly used in vibration-related applications are presented. Estimation of

time-dependent spectra of stochastic processes is considered in Section 11.3. Section 11.4 to Section 11.7 discuss

applications of wavelet analysis in vibration-related applications. In particular, applications in random field

simulation, system identification, damage detection, and material characterization are examined. Section 11.8

provides an overview and concluding remarks on the applicability and usefulness of the wavelet analysis in

vibration theory. To enhance the usefulness of this chapter, a list of readily available references in the form of books

and archival articles is provided.

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