Keywords: subspace identification, subspace fitting, modal analysis, damage localization, finite elements.

Vibration-based damage detection [1] is often implemented by identifying changes in the structural dynamic properties before and after damage. Most vibration-based damage detection methods require the modal properties (i.e. the eigenfrequencies, the eigenshapes as well as the modal damping factors) that are obtained from measured signals through the system identification techniques. They normally need intact structural states (undamaged state) or baseline finite element model so that structural damage can be identified.

For a linear dynamical system, the subspace identification method is well suited for capturing the system eigenstructure under operational conditions (i.e under deterministic or stochastic excitation). The key idea behind subspace identification algorithms is to consider a block Hankel matrix and formulating an observability matrix that contains the dynamics of the system. Different algorithms [2] allow access to an observability matrix and performing a 'shift invariance' procedure of this observability matrix provides infomation on the recovered modal state space. Unfortunately, if the observability matrix is contaminated by noise, introduces errors.

It is therefore preferable to use the subspace fitting method [3,4], in which the observability matrix is minimised through a theoretical observability matrix. Although iterative, this method has the advantage of incorporating prior information about the system.

In this paper, a method is proposed, in which prior information, from modal data of the coarse finite element model of the healthy structure, is introduced in a subspace fitting procedure. When the noise increases, the subspace fitting improves the identification of the modal frequencies compared to the shift invariance. Incorporating the prior information from the eigenvectors reduces the CPU costs without reducing the accuracy of the identification. The method is used for damage identification of a mechanical system. The method is able to localise and estimate the severity of damage.

1

S.W. Doebling, C.R. Farrar, M.B Prime, "A summary review of vibration-based damage identification methods", Shock and Vibration Control, 30, 91-105, 1998. doi:10.1177/058310249803000201

2

P. Van Overschee, B. De Moor, "Subspace identification of linear systems: Theory, Implementation, Applications", Kluwer Academic Publishers, 1996.

3

A. Swindlehurst, R. Roy, B. Ottersten, T. Kailath, "A Subspace Fitting Method for Identification of Linear State-Space Models", Automatic Control, 40(2), 311-316, 1995. doi:10.1109/9.341800

4

R. Serra, M. Raffy, C. Gontier, "A subspace fitting method for structure modal identification in time domain", ISMA25 Conference, Leuven, 13-15 September 2000.

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