Continuous wavelet analysis of mode shapes differences for damage detection

Abstract

This paper presents a new damage detection methodology for beams. It applies wavelet analysis to locate the damage from changes in the mode shapes (geometric based analysis). The proposed methodology requires the mode shapes of a reference undamaged state as well as those of the potentially damaged one. Once obtained, a continuous wavelet transform is applied to the difference of the mode shape vectors to obtain information of the changes in each of them. Finally, the results for each mode are added up to compute an overall result along the structure. For the addition, the wavelet coefficients of each mode are weighted according to the corresponding variation of the natural frequency. By doing so, emphasis is given on those modes that are more likely to be affected by damage. On the other hand, mode shapes that have not changed their natural frequencies are disregarded. The proposed methodology also includes mathematical techniques to avoid wavelet transform edge effect, experimental noise reduction in mode shapes and creation of new virtual measuring points. It has been validated by experimental analysis of steel beams with cracks of different sizes and at different locations. The results show that the method is sensitive to little damage. The paper analyses the severity threshold of damage and the required number of sensors to obtain successful results.