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Shock and Vibration
Volume 19, Issue 3, Pages 287-299

Structural Damage Identification and Location Using Grammian Matrices

D.D. Bueno,1 C.R. Marqui,1 V. Lopes Jr.,1 M.J. Brennan,1 and Daniel J. Inman2

1UNESP – Univ Estadual Paulista, Faculdade de Engenharia de Ilha Solteira, Grupo de Materiais e Sistemas Inteligentes – GMSINT, Av. Brazil, n. 56, Centro, 15385-000, Ilha Solteira, SP, Brazil
2Center for Intelligent Material Systems and Structures, Virginia Tech, Blacksburg, VA, USA

Received 9 December 2010; Revised 9 December 2010

Copyright © 2012 Hindawi Publishing Corporation. 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.


In this paper, an approach using observability and controllability grammian matrices is proposed to determine if structural damage has occurred together with an estimate of its location. The theory is outlined and simulations are carried out on a simple structure to demonstrate the method. Experimental tests were also carried out to demonstrate the validity of the approach using real signals. The dynamic properties of the structure are identified using the eigensystem realization algorithm (ERA) and a reduced order state-space model of the system subsequently constructed. Either the observability or controllability grammians can then be used depending on the number of sensors available. It is shown that these are sensitive to both the degree and location of the damage and offer promise for structural health monitoring applications.