PSI - Issue 13

I.Yu. Smolin et al. / Procedia Structural Integrity 13 (2018) 1059–1064 I.Yu. Smolin et al. / Structural Integrity Procedia 00 (2018) 000 – 000

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Fig. 5. Wavelet transform coefficients depending on the width and location b of the wavelet.

The wavelet analysis proves that short signal emissions are captured best by narrow wavelets while longer inhomogeneities are registered better by wider wavelets. Thus, by selecting the wavelet type and its width, it is possible to achieve the best registration of inhomogeneities of one scale or another for the time series under study. The last type of statistical research of time series in this paper is presented by the cross-correlation analysis. Figure 6 depicts a result of the cross-correlation analysis of a window moving from the left to the right with the extreme right window of the time series, on the time interval of which the catastrophic failure occurs. Throughout the multitude windows, up to the area close to the catastrophic failure, the correlation coefficients are pulsing on the graph around the zero line. Closer to the catastrophic failure zone, starting from the 7.5 s, the correlation coefficient stabilizes: it finally passes through the zero horizon and steadily increases. It is interesting to note that with an approximately two-fold increase in the window width, the envelope curve of the correlation coefficients in the region of the rightmost windows on the graph is smoothed out, and the probability of the correlation error rushes to zero, except for one peak, which, however, is much smaller than the critical value of 5 %. The region where the correlation coefficient is above zero remains unchanged. Thus, the time interval of the process at which a catastrophic event can be forecasted is extremely small without taking into account the noticeable correlation throughout the process, which is probably connected with the constantly present low frequencies when the specimen is loaded. In our opinion, this issue requires additional studies on a wider range of experimental studies, including approaches of acoustic emission analysis for damage monitoring that are presented e.g. by Mailleta et al. (2014), Panteleev et al. (2014), Whitlow et al. (2016), and Gholizadeh et al. (2018). It is also worth noting that additional useful information in this regard could be obtained from the simulation based on probabilistic approaches, as was shown by Smolin A.Yu. et al. (2016), Mikushina et al. (2015), and Mikushina et al. (2017).

Fig. 6. Cross correlation of the time series shown in Fig 1a with its extreme right window (from 7.8417 to 8.0204 s).