On the Use of Singular Vectors for the Flexibility-Based Damage Detection under the Assumption of Unknown Structural Masses

The main purpose of this work is to investigate the usability of easily obtainable parameters instead of the modal traditional ones, in the context of a flexibility-based damage detection procedure, under the assumption of unknown structural masses. To this aim, a comparison is made between two different approaches: the first involves the calculation of the flexibility matrix by using traditional modal parameters, such as natural frequencies and modal vectors, normalized to unitary values, while the second involves the use of singular vectors, obtained through a simple matrix factorization. The modal parameters and the singular vectors necessary for the implementation of the damage detection procedure are evaluated through two different techniques: the Eigensystem Realization Algorithm and a wavelet-based procedure, for which a variant is proposed by introducing the energy reassignment concept into the original algorithm. Through the latter approach, in particular, it is possible to obtain a high number of singular vectors even in the case of reduced availability of sensors. The study is performed under the assumption of nonstationary excitation, in order to achieve general results, and the effectiveness of the procedures is evaluated through simulated tests regarding different structural schemes.

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