Incremental strategy for damage detection in structures
AbstractUsually, for defects detection in structures, it is necessary to establish a mathematical model for the un-damaged mechanical structure to pose a template from which deviations can be measured. The dynamic behav-iours of the analytical model and the real structure consid-ered are compared in order to detect any appearance of defect at its early stage. The presence of defects results in a difference between the measured behaviour and that given by the analytical model. The extent of the damage is ob-tained after some correction stages of this analytical model. Damage detection methods can be classified into three categories: methods of detection then correction, inverse correction methods, and simultaneous detection – correc-tion methods.The proposed method is of the third type: it re-builds the stiffness matrix considering proportional damp-ing. A frequency correlation function is used to evaluate the sensitivity of the frequency response to a defect simu-lated successively into each element of the structure. This function which varies in the interval [0, 1] informs us about the influence of a simulated defect on the frequency response of the structure. When this one is close to the unity, the defects then are located and quantified. This function indicates if one approaches or moves away from the solution when a defect is supposed in a given element. The problem then consists in determining the stiffness cor-rections which as close as possible bring the frequency responses of the analytical model and those of the experi-mental structure.The method presented here consists of determin-ing the stiffness corrections by incrementing and/or decre-menting of a step ε until as close as possible bringing the analytical model to the structure. The method thus ob-tained, applied to simulated measures for a lattice struc-ture, shows the effectiveness and the precision of this cor-rection strategy.