Comparing three derivative discontinuities detection methods for the localisation of cracks in beam-like structures

The fact that that a crack causes a discontinuity in the first derivative of the mode shapes (rotation) is well-known. Several methods for detecting discontinuities in piecewise smooth functions have been studied recently for application to the detection of cracks in structures. The research presented in this article has considered three different techniques which have been applied to a cracked cantilevered beam: the first is the Polynomial Annihilation Edge and derivative Detection method' the second is the Gaussian Process Regression approach and the third is the Spatial Wavelet Transform approach. The performances of these three methods which enable the detection and the localisation of the crack are compared for different levels noise and numbers of measurement points.