Application of multi-resolution analysis of wavelets to nondestructive damage evaluation: I. Theory

Abstract

A wavelet application to the vibration-based damage evaluation technique is introduced. Using a few of the lower mode shapes before and after a small damage event, the proposed method is able to provide the unique damage indices in order to detect, locate, and size damage on beam-like and plate-like structures. Based on a small damage assumption, a damage index equation is revealedn the context of elasticity. It turns out that the resulting damage index equation inherently suffers from singularities near inflection nodes. The transformation of the problem into the multi-resolution wavelet domain provides a set of coupled linear equations. With the aid of the singular value decomposition technique, the solution to the damage index equation is achieved in the Haar wavelet space. Next, the physical desired solution to the damage index equation is reconstructed from the one in the wavelet space.