PSI - Issue 5
Andreas Kyprianou et al. / Procedia Structural Integrity 5 (2017) 1192–1197 Andreas Kyprianou / Structural Integrity Procedia 00 (2017) 000 – 000
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characteristics can be exploited to devise algorithms for damage detection, location and size Doebling et al. (1996+. Varying environmental and operational conditions of structures under monitoring also induce changes to dynamic behavior that could potentially cause a damage detection algorithm to wrongly attribute them to damage In the context of structural health monitoring (SHM) various methodologies were proposed to deal with separating the dynamic changes due to damage from those due to changing environmental and operating condtions. Recent surveys on these methodologies and their rationale can be found in Tjirkallis (2013) and Fahit (2014) and the references therein. These methodologies were classified according to whether the damage detection algorithm utilizes or not information about the actual environmental and operating conditions Worden et al. (2002) and Sohn (2007). This article proposes the use of spatio temporal continuous wavelet transform (SPT-CWT) to detect damage under varying environmental conditions by analysing a sequence of time responses of a cantilever subjected to pink noise excitation. The proposed method does not require knowledge of the actual environmental conditions. It is an extension of earlier work on separating structural dynamic changes due to damage from changes due to environmental and/or operating conditions by exploiting the multiscale nature of structural time responses \ Tjirkallis (2013) and Tjirkallis et al. (2016). A mathematical tool that reveals the multiscale nature of time domain signal is the continuous wavelet tranform (CWT). In particular, its ability of detecting singularites has been widely used to characterize the multiscale nature of both time domain signals and images Mallat et al. (1992). In structural damage detection this capability of CWT was utilized in Douka (2003) to determine the location and the size of the crack in beam using the fundamental mode of vibration. Furthermore, in Gentile et al. (2003) it was demonstrated that CWT could be used to detect damage location and crack size by analysing both noisy and noise-free data. In this work edges were extracted from a sequence of images of the response of a cantilever subjected to pink noise both under constant and varying temperature conditions. The edges were subsequently processed to yield a sequence of time series measurements on 439 points of the vibrating beam. This sequence was then analyzed by the spatio temporal wavelet transform (SPT-CWT) to characterize its multiscale nature. This characterization at once unveiled the effects of damage and changing temperature on the cantilever. The rest of the article is organized as follows: Section 2 presents the experimental test rig and expalins how the data was organized to become amenable for SP-CWT analysis. The theory of the spatio-temporal wavelet transform is given in section 3 and the results of this application are discussed in 4. The article ends with the conclusions given in section 5.
2. Experimental set-up and data organization
2.1. Test set-up and conditions
The experimental test rig, shown in fig.1, consists of a cantilever beam made up of steel of density, ρ = 7.87x10 6 kg/mm 3 , and Young modulus, E =200x10 6 mN/mm 2 . Its thickness is 1.5 mm and its second moment of area is 8.44 mm 4 . The beam is excited by an LDS V201 permanent magnet shaker, which is connected to the beam via a stringer rod, attached to the beam, at a distance of 100 pixels from the fixed end (top end) of the beam, to minimize the interaction between the shaker and the structure. Damage is introduced in the beam by cutting a crack of depth, d =0.75mm, width, b =2 mm, and opening, e =2 mm, at a distance of 302 pixels from the fixed end of the beam. The beam was excited by pink noise both under constant temperature and varying temperature conditions. The varying temperature conditions were created manually by heating the beam.
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