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In this work, we propose a two steps method for localizing damages in multi-layer composite structures. The signals of the dynamic responses of the healthy and damaged structures are initially decomposed using the analysis into wavelet packages and then rebuilt. Then, energies of these last signals are used to define an indicator of variation of energy called WPEVI ``Wavelet Packages based Energy Variation Index''. The robustness of this damage localization index is tested in the case of composite beams with respectively two and three damages.
To ascertain the quality of the results, the sensitivity of the proposed method to structural damage is studied. In this respect, we define the threshold sensibility of a damage vibration indicator based on wavelet package decomposition of structural vibration responses before and after the occurrence of structural damage. Each of these structural vibration responses is decomposed to the jth order wavelet package sub-signals. The structure is subdivided into a certain number of finite elements. For a structure with one particular finite element perturbed to a certain rate, the damage indicator is then defined as the maximum of all energy variations of the wavelet package sub-signals of the structural vibration response before and after the occurrence of some structural damage. The indicator is called "maximum energy variation" (MEV). For the same mono-excitation, this indicator is then evaluated for all the elements of the discretization with the same perturbation rate. The values of this indicator are then represented on a graph in terms of the number of the finite element. Once we have determined the element whose damage indicator value is minimum, further trials are carried out in order to draw the curve representing the indicator in terms of the different rates of damage. From the graph, we determine the least detectable damage rate using the wavelet package decomposition of structural response. A mapping of the structure is carried out as to the least detectable damaged element of the structure.
With this tool in hand, we may ascertain or not each of the damage localization results.
