Frugal wavelet transform for damage detection of laminated composite beams

Frugal wavelet transform (FrugWT) is a new version of discrete wavelet transform (DWT), acting as an efficient tool for detecting signal singularities. It is proven that the frugal wavelet transform usually performs better than other versions of the wavelet transforms in detecting singularities and local abrupt changes in the signals, specifically when we use wavelet functions with lower vanishing moments. FrugWT reduces the dependence of the wavelet transform on the choice of the wavelet function and thus reduces the computational time to achieve the best results from the wavelet transform for singularity detection. Therefore, 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 gov- erning equations of motion are 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. The results demonstrate that FrugWT is capable of accurately detecting damages at various locations in the laminated composite beam (LCB), even when the damage levels are below 5%. This highlights the method’s high precision and effectiveness in identifying subtle damage scenarios. Findings show that the frugal wavelet transform is robust to a given level of noise in the signal, and its per- formance in noisy conditions is better than the derivative of the signal, 1D-DWT, and 1D-CWT.