Two-dimensional frugal wavelet transform for single and multiple damage detection in sandwich plates

Frugal Wavelet Transform (FrugWT) is a wavelet-based technique derived from the Discrete Wavelet Transform (DWT). Unlike the conventional DWT, it does not proceed with the full multi-resolution analysis; instead, it stops after the first decomposition step and applies its modified processing thereafter. Unlike the conventional multi-resolution DWT, which involves n decomposition steps, FrugWT uses only two steps to identify singularities in signals, achieving improved results with lower computational effort. In this paper, we extend this approach to two dimensions and introduce the two-dimensional Frugal Wavelet Transform (2D-FrugWT) for detecting singularities in two-dimensional signals and images. The method is applied to the damage detection of two-dimensional mode shape signals in sandwich plates under both single- and multiple-damage scenarios. Numerical and experimental validations demonstrate that 2D-FrugWT outperforms the traditional 2D-DWT, providing higher accuracy while substantially reducing the computational cost of singularity detection in two- dimensional signals.