Relative frugal wavelet transform to detect damages in functionally graded tapered beams made of porous material

Purpose This study aims to enhance singularity detection in non-stationary signals by introducing the frugal wavelet transform (FrugWT), a novel variation of the wavelet transform. Design/methodology/approach The frugal wavelet transform, based on a modified first-level discrete wavelet transform decomposition, is compared with traditional discrete wavelet transform. The performance of these transforms is evaluated using signals derived from finite element analysis of a functionally graded tapered beam made of porous material. Findings The frugal wavelet transform significantly outperforms the discrete wavelet transform in detecting singularities within the analyzed signals. It offers more accurate detection of singularities and local abrupt changes, demonstrating its effectiveness for signal analysis. Originality/value This paper contributes to the field by proposing the relative frugal wavelet transform as a novel enhancement of the frugal wavelet transform. It provides a significant improvement in detecting subtle singularities in one-dimensional signals, with potential applications in advanced signal processing and analysis across various scientific domains such as electrical engineering, automotive, aerospace engineering, civil engineering, marine engineering and medical signal processing.