Wave-Based Damage Identification in Composite Strips and 2D Solids Using Inverse Multiresolution Wavelet Methods

Abstract

An inverse procedure for damage identification on 1D and 2D solids based on wave propagation using the multiresolution finite wavelet domain (MR-FWD) method is presented. The forenamed method utilizes Daubechies wavelet and scaling functions for the approximation of state variables and as such, it involves two types of solutions, the coarse and the fine solutions. In that way, the multiresolution nature of the method can be utilized for efficient damage estimation in experimental applications since the fine solutions of the method have manifested remarkable localization and isolation capabilities and high sensitivity to damage. In order to fully take advantage of the additional benefits of the MR-FWD method, full-field displacement measurements of the wave propagation are taken into consideration. Wavelet decomposition using Daubechies wavelets is now applied on the measurements, leading to approximation and detail components that are directly comparable to the coarse and fine solutions of the multiresolution simulation, respectively. Therefore, MR-FWD models can be created using the same Daubechies wavelets as the decomposition of the experimental data, so as to compare the simulation results with the measured ones. Numerical results reveal that comparing the detail component of the experiments with the fine solution of the simulations using appropriate metrics can lead to efficient damage identification. In such manner, an optimization process can be conducted in order to characterize the investigated damage scenarios. This procedure can lead to more sensitive and accurate damage estimation due to the advantages of the multiresolution analysis.