Crack Location in Beams Using Wavelet Analysis

This paper applies a methodology for damage detection in beams proposed by the authors. The methodology is based on a continuous wavelet analysis of the difference of mode shapes between a damaged state and a reference state. The wavelet transform is used to detect changes in the mode shapes induced by damage. The wavelet coefficients for each mode are added up and normalized to unity in order to obtain a clear and precise damage assessment. A curve fitting approach reduces the effect of experimental noise in the mode shapes. When only a small number of measuring points are available, a cubic spline interpolation technique provides additional “virtual” measuring points. The interpolation technique may also be used when measuring points are not equally spaced. It also serves as a softening technique of the mode shapes when applied, and no curve fitting approach is used in that case. An antisymmetric extension at both ends of the mode shapes is used to avoid the edge effect in the wavelet transform. The paper presents the results obtained for steel beams with an induced crack. Several sizes and locations of the crack have been considered. The paper addresses several issues affecting the accuracy of the proposed methodology, such as the number of measuring points and the effect of the extension, curve fitting and interpolation techniques.