Keywords: damage, detection, spline, vibration, monitoring, ambient.

As a result of the advances in sensor technology, data acquisition systems and data interpretation algorithms, monitoring techniques based on the analysis of the response recorded in structure, are becoming a widespread method to monitor structural health conditions. Damage produces changes in the dynamic characteristics of the structure hence several indices have been proposed in the literature to detect and localize damage through the analysis of variations in modal parameters between the damaged and the undamaged states of the structure. In recent years a number of damage indices based on parameters related to the deformation of the structure have been proposed that appear more reliable with respect to other quantities when damage localization is involved. These methods can be classified as modal [1] or non-modal [2] methods according to whether they rely on modal or "non-modal" deformed shapes.

In order to obtain an accurate description of deformation of the structure from recorded data (in terms of both modal and non modal quantities), responses should be available at a large number of locations in the structure. On the other hand, due to economic reasons, concerning the cost related to data acquisition and, or to the inaccessibility of some degrees of freedom, structures are usually instrumented with a limited number of sensors.

In this paper the accuracy of a technique to detect and locate damage, denoted as IDDM (interpolation damage detection method), formerly proposed by the author and applied considering a large number of sensors [3] is checked assuming that a limited number of recording sensors are available.

The method is based on the analysis of the deviation from the smooth behaviour of the deformed shape of the structure or, in other words, on the variation of the accuracy of a smooth spline function to interpolate the deformed shape of the structure. The method belongs to the family of non-modal methods and can be applied considering the response to vibrations induced by base excitation such as an earthquake or by ambient excitations such as wind or traffic.

In this paper the method is applied to model of one of the landmarks in Milan, the Pirelli skyscraper designed in the 1950s by the well known architect Gio Ponti and the engineer Pier Luigi Nervi.

Several damage scenarios characterized by one, two or three damaged storeys have been considered. A comparison of results from the IDDM with those given by two well known modal damage detection methods is also reported in order to show the feasibility of the IDDM approach to detect even very small amount of damage. The analysis shows that, as expected, the capability of the IDDM to correctly locate damage decreases with the number of available recorded responses however, for the example considered herein, up to a reduction higher then 60% of the total number of sensors (hence of the cost of instrumentation) the method is still able to detect both the existence and the location of the damage accurately.

1

J.T. Kim, N. Stubbs, "Improved damage identification method based on modal information", Journal of Sound and Vibration, 252(2), 223-238, 2002. doi:10.1006/jsvi.2001.3749

2

R.P.C. Sampaio, N.M.M. Maia, J.M.M. Silva, "Damage detection using the frequency response function curvature method", Journal of Sound and Vibration, 226(5), 1029-1042, 1999. doi:10.1006/jsvi.1999.2340

3

M.P. Limongelli, "A damage detection approach based on responses interpolation", IOMAC 2009, Portonovo di Ancona, Italy, May 2009.

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