Damage detection in Euler–Bernoulli beams via spatial wavelet analysis

A spatial wavelet transform (WT) is used for damage detection in Euler–Bernoulli beams subject to static loads. It is shown that by applying the WT on the difference between the displacement responses of the damaged and the undamaged beams for various loading conditions, boundary effects are eliminated and damage-related local maxima are clearly identified in the WT modulus map. Estimates of damage locations and amplitudes are then obtained by two separate optimization procedures, in which each damaged section is modelled by an equivalent ‘reduced-stiffness’ spring. The effectiveness of the method is assessed using digitally-simulated data obtained via cubic interpolation on a finite number of nodal displacements. In this context, results pertaining to multi-crack beams prove quite accurate even for small damage amplitudes