The Differential Evolution method applied to continuum damage identification via flexibility matrix

In the present work, a structural damage identification approach, built on the flexibility matrix, is proposed. Here, the damage state of the structure is continuously described by a cohesion parameter, which, in turn, is spatially discretized by the finite element method. Then, the inverse problem of damage identification is defined as an optimization one, where the objective is to minimize, with respect to the nodal cohesion parameters, a functional based on the difference between the experimentally obtained flexibility matrix and the corresponding one predicted by a finite element model of the structure. The Differential Evolution stochastic optimization method was considered for solving the resulting damage identification problem. The assessment of the proposed approach has been performed by means of numerical simulations on a simply supported Euler–Bernoulli beam. A brief analysis of the influence of different damage positions and severities on the undamped natural frequencies and on the flexibility matrix of the structure is presented. Then, the influence of damage and different levels of noise on the mode shapes of the structure is also considered. In the damage identification problem, different damage scenarios and noise levels were addressed. For comparison purposes, other stochastic optimization methods, namely, Particle Swarm Optimization, Luus–Jaakola and Simulated Annealing, were also considered for the identification of one damage scenario in the presence of noise corrupted data.