Developing frugal wavelet transform for damage detection of laminated composite beams

This paper investigates detecting damages in laminate composite beams using a novel method called Frugal Wavelet Transform (FrugWT). Based on the first-order shear deformation theory and using the Finite Element Method (FEM), the discretized governing equations of motion have been obtained. The proposed frugal wavelet transform is developed based on the one-dimensional discrete wavelet transform and multi-resolution analysis at the first level of decomposition. Three different most commonly used damage detection methods, i.e., derivative of mode shape, one-dimensional discrete wavelet transform (1D-DWT), and one-dimensional continuous wavelet transform (1C-DWT), are compared with the frugal wavelet transform. Results show that the FrugWT can detect the damages at different levels and locations in the laminated composite beam (LCB) with higher accuracy. Findings show that the frugal wavelet transform is robust to a given level of noise in the signal, and its performance in noisy conditions is better than the derivative of the signal, 1D-DWT, and 1D-CWT.