Keywords: structural damage, damage identification, wave propagation in solids, particle swarm optimization, hybrid identification method.

In a companion paper, the damage influence on the vibrational behavior and on the wave propagation issues of a slender Euler-Bernoulli beam was investigated. The theoretical formulation and the numerical implementation of the direct problem was taken into account. Besides, different damage scenarios were considered with the aim of assessing the sensitivity of the two approaches. In the present work, one is concerned about the inverse problem of damage identification from the point of view of wave propagation approach. The damage scenarios of the companion paper are now considered for damage identification. Time-history responses, obtained from a pulse-echo experiment performed on the damaged beams, are used to identify both the damage position and profile. The required responses are the regressive waves (echoes) propagating along the beam due to an excitation given as a longitudinal impact at one end of it. The damage identification problem is, then, defined as a finite dimensional minimization one as follows. A functional is defined as the norm of the difference between the echo predicted by the model and that measured in an experiment. Then, in order to minimize this functional, the cross section area of the elements in the spatially discretized model are sought. In order to solve the damage identification problem, different optimization methods were considered: the deterministic Levenberg-Marquardt method, the stochastic Particle Swarm Optimization, and a hybrid method combining the aforementioned ones. The damage identification, for different damage scenarios, was firstly performed considering time responses not corrupted with noise. Besides, different levels of signal to noise ratio - varying from 30 to 0 dB - were introduced in the time responses in order to account for noise corrupted data. It is shown that the damage identification procedure built on the wave propagation approach succeeded, for all optimization methods considered, even for highly corrupted noisy data. For the noise-free data, the LM and PSO-LM methods yielded the exact inverse problem solution in all damage scenarios. The PSO method also yielded a quite satisfactory result, with errors lower than 0.4%. Even in the absence of noise, the numerical analysis showed that to the improve the convergence of the LM method, different values of the relaxation parameter must be considered and, besides, the method may diverge if a unsuitable value is adopted. The same did not occur with the PSO-LM technique, which was run with only one value for this parameter in all cases. For the noise corrupted data tests, the performance of all methods were almost the same for the lower signal to noise ratios (30 and 20 dB). For the moderate (10 dB) and high (0 dB) signal to noise ratios, the performance was shown to be still good, with the PSO method presenting the worse identification, for all damage tested.

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