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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As a consequence the SPT-CWT of f ( x , t ) can be defined by,

v        )



  ,

  dxdt x t ,

*

, , ,

F c SW (

f x t



(3)

c v , , ,  



where * denotes complex conjugation. As for the case of ordinary CWT the number F SW ( c , τ , σ , v ) denotes the correlation of f ( x , t ) with the spatially translated by c and dilated by v 0.5 σ and temporally translated τ and dilated by σ v -0.5 wavelet ψ ( x , t ). Furthermore, the square of this number measure the energy of the time sequence at the temporal and spatial translations τ and c respectively and at the temporal and spatial scales v 0.5 σ and σ v -0.5 respectively.

4. Results and discussion

The responses for the undamaged and damaged cantilever to pink noise under constant and varying temperature were analysed using the SPT-CWT transform procedure of the YAWTB matlab toolbox Yawtb (2003). The wavelet used was the two dimensional mexican hat. The spatial and temporal translations c and τα were allowed to vary whereas the dilations were fixed at σ =40 and v=0.1 The results for the beam under constant temperature from the undamaged beam are shown in fig. 3a whereas for the damaged in figure 3b. It can be seen that at the position of damage the geometrical characteristics of the results change. At this position the regions in temporal translation τ over which the correlation of the response with the wavelet are significant have become wider. This indicates that in the region around the damage the time domain characteristics at the scale of analysis of the response change. Figures 4a and 4b depict the results of the SPT-CWT analysis of the sequence of responses of undamaged and damaged cantilever beams, respectively, under varying temperature. Comparing figure 4a with 3a it is observed that heating affects the behavior at this scale also. In particular the position on which heating gun applies the heat on the cantilever, namely within the region around 200 pixels to the right of the fixed end, is clearly identified. In figure 4b both the effects of heat and damage are identified.

Fig. 3. SPT-CWT of the sequence of response time series for the cantilever under constant temperature. a) Undamaged beam b) Damaged beam