Keywords: damage detection, particle swarm optimization, dynamic parameters, finite element model, incomplete data, beam structures.

The use of structural dynamic parameters to develop non-destructive damage detection methodologies could be limited by several issues. Some of them are: low sensitivity of the dynamic parameters in relation to the damage, high complexity level of the technique used to determine the damage scenario, and the possibility of the dynamic parameters being affected by factors different to the damage and incomplete measurements [1]. Concerning the latter issue, and if modal parameters are used, the incompleteness is related to the fact that it is not possible to excite all vibration modes of the structure and measure the mode shapes in all degrees of freedom, (DOFs), in the finite-element model that represents the undamaged structure [2].

Herein, the damage is considered a reduction in the stiffness matrix of the damaged element. This reduction is obtained by using a stiffness reduction factor. The element does not present damage if the stiffness reduction factor assumes a value equal to 0, and it is completely damaged if this factor is equal to 1.

The damage detection in a structure is studied as an optimization problem and it is solved by using an adaptive particle swarm optimizer. The objective function is based on natural frequencies and mode shapes and the optimization variables correspond to the set of stiffness reduction factors of each element in the structure. The proposed methodology was applied to detect simple and multiple damage scenarios on a beam-type structure, but considering that the modal data were incomplete. In this sense, several settings of modal data were considered, for which it was varied the quantity of points in the beam where measurements were carried out and the quantity of measured modes. The sensors were considered to be uniformly distributed across the beam.

It was observed that an optimal quantity of modal information exists that permits the detection of most of the possible damage scenarios. If a lower quantity is used, then the methodology can fail to detect the real damage scenario. Also, different damage scenarios can be detected with different reliability levels for a same quantity of modal information available. In general, simple damage scenarios are detected more reliably than the multiple ones. Finally, the computational cost involved in the determination of the optimal quantity of modal information is high because many combinations of modal information have to be tested. It is important to observe that this set of values is limited by technical conditions, such as the available number of sensors and the quantity of excitable modes.

1

J. Humar, A. Bagchi, H. Xu, "Performance of vibration-based techniques for the identification of structural damage", Structural Health Monitoring, 5, 215-227, 2006. doi:10.1177/1475921706067738

2

W.X. Ren, G. De Roeck, "Structural damage identification using modal data. II: test verification", Journal of Structural Engineering, 128(1), 96-104, 2002. doi:10.1061/(ASCE)0733-9445(2002)128:1(96)

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