Application of two-dimensional wavelet transform to detect damage in steel plate structures

Abstract

Wavelet Transforms (WT) have been receiving an increasing attention for the detection of damage in structures based on vibration response. The existence of the problem of boundary distortion in WT may lead to unreliable results at and around the boundaries of the structure. Previous studies have applied methods such as signal extension, zero padding and windowing to avoid border distortion. However, these methods try to avoid border distortion by distorting/reducing the original signal to prevent the distortion at the boundaries of the signal from occurring, thus altering the original signal and leading to unreliable damage identification. In this study, a WT-based method is proposed to solve boundary distortion problem. To achieve this, the mode shape difference of a structure is applied for WT decomposition. By using mode shape difference, the problem of border distortion is solved by reducing the effect of sudden change in stiffness that occurs at boundaries. A two-dimensional Continuous Wavelet Transform (CWT) is applied to decompose the difference between the damaged and the undamaged first mode shape signal. The damaged mode shape is subtracted from the undamaged mode shape to obtain the difference, and the difference is decomposed to detect and locate the damage. This method is demonstrated via numerical and experimental examples of a square steel plate. The reliability of the method is demonstrated through different damage intensities and locations. The numerical study involves applying a square plate model with two boundaries formats: all four sides fixed, and two opposite sides fixed and free. The mode shape and mode shape difference are decomposed and the coefficients of the two are compared to show the advantage of this method. The experimental example was applied to a square steel plate with all four sides fixed to verify the efficiency of the method. The numerical results showed that the problem of boundary distortion is resolved by using the mode shape difference and damage at all locations are detected, while applying mode shape provided unreliable results for both numerical models even at 25% severity. The sensitivity of the proposed method to noise is investigated by introducing various levels of signal to noise ratios and showed the detection of damage with 5% severity when mode shape difference was applied in presence of noise.