Structural Damage Detection by Derivative-Based Wavelet Transforms

In practical applications of wavelet transform, engineers and practitioners encounter challenges that arise due to the disparity between wavelet theory, which deals with continuous functions, and the digital nature of signals in engineering contexts. In particular, wavelet transform theory does not consider the effect of changes in digital signals on the result of the wavelet transform. This paper emphasizes the influence of the type of digital signals on the accuracy of wavelet transform in engineering applications and proposes an efficient wavelet function based on the derivative of the signal for better damage detection in beam structures. For this purpose, the obtained signals from the mode shapes of the steel beam are used to examine the efficiency of the proposed derivative-based wavelet transform. The effects of changes in boundary conditions, location of damage, and level of damage on the performance of the proposed method, are evaluated. Findings show that when we use the derivate of the signal in the wavelet transform, the location of damage in all damage scenarios is detected with high accuracy. This research demonstrates the importance of the type of signal used in the wavelet transform for enhancing the precision of fault and damage detection in signals.