Wavelet Analysis

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.