Standard Article

Wavelet Analysis

Signal Processing

  1. Amy N. Robertson1,
  2. Biswajit Basu2

Published Online: 15 SEP 2009

DOI: 10.1002/9780470061626.shm048

Encyclopedia of Structural Health Monitoring

Encyclopedia of Structural Health Monitoring

How to Cite

Robertson, A. N. and Basu, B. 2009. Wavelet Analysis. Encyclopedia of Structural Health Monitoring. .

Author Information

  1. 1

    IMTECH, Boulder, CO, USA

  2. 2

    Trinity College Dublin, Department of Civil, Structural and Environmental Engineering, Dublin, Ireland

Publication History

  1. Published Online: 15 SEP 2009

Abstract

Wavelet analysis, as a time–frequency analysis tool, has shown great promise in recent years. The advantage of the wavelet transform over other time–frequency transforms is in its capabilities of flexible time windowing and computational efficiency. It is evidenced from the reported literature in this article that the wavelet transform has immense potential for application in the area of structural health monitoring (SHM). The theoretical foundations of continuous, discrete wavelet transform (DWT) and orthogonal wavelet transform have been presented. The construction of a multiresolution analysis (MRA)-based fast algorithm for calculating the DWT and its relation to filtering of signals is discussed. Also presented is the concept of wavelet packets and a brief discussion on the choice of wavelets to suit applications. Examples are presented that show the applications of continuous, discrete, and orthogonal wavelets for the detection of damage by analysis of Lamb wave propagation, and the application of wavelet packets for the identification of stiffness variation in structural systems.

Keywords:

  • time–frequency analysis;
  • continuous wavelet;
  • discrete wavelet;
  • orthogonal wavelet;
  • wavelet packets;
  • Lamb wave;
  • stiffness variation