Wavelet-based multi-scale finite element modeling and modal identification for structural damage detection

Wavelet techniques enable multi-resolution analysis that can represent a function (either field or signal function) in a multi-scale manner. This article presents a damage detection method with dynamically changed scales in both temporal and spatial domains, by taking advantage of the wavelet-based multi-resolution analysis. This method combines a wavelet-based finite element model (WFEM) that employs B-spline wavelet as shape functions and wavelet-based modal identification method to detect structural damage progressively. High-fidelity modal information can be computed or identified with minimized computation cost by lifting the wavelet scales in the wavelet-based finite element model and in signal processing individually according to the actual requirements. Numerical examples demonstrate that the accuracy of damage detection is improved considerably by this lifting strategy during the damage detection process. Besides, fewer degrees of freedom are involved in the wavelet-based finite element model than those of traditional finite element method. The computational efficiency can be improved to large extent and computation resources can be utilized more rationally using the proposed multi-scale approach.