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Shock and Vibration
Volume 2018 (2018), Article ID 9837694, 19 pages
Research Article

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

Department DICAM, University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy

Correspondence should be addressed to Said Quqa; ti.obinu@2aquq.dias

Received 26 October 2017; Revised 24 December 2017; Accepted 18 January 2018; Published 28 February 2018

Academic Editor: Luca Zanotti Fragonara

Copyright © 2018 Said Quqa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.