In this paper, a new wavelet-based approach for crack identification in beam-like structures is presented and applied to simply-supported beams with single or multiple cracks. A novel damage index, based on finding the difference between two sets of detail coefficients obtained by the use of the Stationary Wavelet Transform (SWT) of two reconstructed sets of modal displacement data of the cracked beam-like structure, is proposed for single crack detection or multiple crack detection. These two sets of mode shape data represent the left half and the modified right half of the modal data of the structure. Currently, SWT is widely used in the field of image processing for image noise reduction and image quality improvement. However, because it can provide an accurate estimate of the variances at each scale and facilitate the identification of salient features in a signal, SWT has great potential in the field of structural damage detection. In this paper, the modal responses of the damaged simply supported beams used are computed using the finite element method (FEM). The modal data generate is decomposed by SWT into a smooth curve, called approximation coefficient, and detail coefficient. It is shown that the detail coefficient includes crack information that is useful for structural damage detection. Therefore, a novel damage index, the difference of the SWT detail coefficients of two reconstructed sets of modal displacement data, is proposed and employed. The numerical simulation results show that the proposed wavelet-based method has a good anti-noise ability and it does not require the modal parameters of an intact structure as a baseline for crack detection. Therefore, it can be recommended for real applications in structural health monitoring and damage detection.
Modified gravitational search algorithm and its application to structural damage detection