Crack diagnostics in beams using wavelets, kurtosis and skewness

This paper presents a diagnostic technique using wavelets, kurtosis and skewness for detecting crack location and severity in beams. The first three mode shapes of a damaged beam are used for detecting crack locations in beams with varying boundary conditions. Damage due to an edge-crack is modelled by a conventional macroscopic torsional spring element. Multiple families of wavelets with varying scales and vanishing moments are used so as to distinguish between their ability to detect crack locations by using the mode shapes of the damaged beam. Crack detection is followed by determination of the crack size by using statistical measures of the mode shapes such as kurtosis and skewness. These two measures are highly sensitive to small changes in mode shapes resulting from crack initiation or crack propagation, and have been used in other fields of damage detection. Several simulations are presented to showcase the application of the proposed technique, and to highlight the differences between multiple wavelets and the parameters associated with the wavelets. The proposed diagnostic technique is also tested for robustness by adding noise to the mode shapes. The simulation results and preliminary experimental results indicate that the statistical measures of kurtosis and skewness can be used in conjunction with wavelets in order to provide a viable crack diagnostic technique for beam structures.