Discrete wavelet transform is a useful means for crack identification of beam structures. However, its accuracy is severely dependent on the selecting mother wavelet and vanishing moments, which raises a significant challenge in practical structural crack identification. In this paper, a novel approach is introduced for structural health monitoring of beams to fix this challenge. The approach is based on the combination of statistical characteristics of vibrational mode shapes of the beam structures and their discrete wavelet transforms. First, this paper suggests using regression statistics between intact and damaged modes to monitor the health of beam structures. Then, it suggests extracting quasi-Pearson-based mode shape index of the beam structures to use them as an original signal in discrete wavelet transforms. Findings show that the proposed approach has several advantages compared with the conventional mode shape signal processing by the discrete wavelet transforms and significantly improves damage detection’s accuracy.

In contrast to new and modern structures, historical structures have cultural significance, and it is essential to make an effort to preserve them. For this purpose, fast and accurate damage detection of historical structures plays a crucial role. Thus, the current study introduces a novel and effective tool for detecting cracks in historic structures. A new and modified version of the Prewitt filter is proposed to detect cracks in the Si-o-se-pol Bridge, a historic bridge in Iran. Results of crack detection using vertical and horizontal Prewitt filters are compared to those obtained from the proposed improved filter. The findings show that the improved Prewitt filter has significantly better performance compared to the vertical and horizontal Prewitt filters.

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.