PSI - Issue 41

Mikhail Bannikov et al. / Procedia Structural Integrity 41 (2022) 518–526 Author name / Structural Integrity Procedia 00 (2019) 000–000

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in the MathWorksMatlab application package in the form of separate scripts that implement the algorithms used, in which text files with the results of measurements of the energy of acoustic emission events and the distribution of fluctuations of deformation fields of composite samples under various loadings act as input data, and as output data – images visualizing the results of processing. The energy of acoustic emission events E(t) was recorded using acoustic emission sensors as a discrete signal. Fig. 3.1 a, b shows the typical energy distributions of acoustic emission events for samples made from a unidirectional fibrous composite material under conditions of uniaxial quasi-static and cyclic loading, respectively. The measured energy values of discrete acoustic emission signals were converted into a logarithmic scale. The algorithm for calculating the dependence of the energy of acoustic emission events on the rate of its change consisted in calculating the derivative of the function E(t) using a difference analogue. Typical dependences of the energy of acoustic emission events on the rate of its change, calculated by this algorithm and presented using the modified Euclidean metric for cluster analysis (see relation (1)), are shown in Fig. 3 c, d. �� � �� �� � �� � �� � ��� � � � �� �� � �� � �� � �� �� � �� � ��� � (1) where indices 1, 2 denote the numbers of points between which the distance is determined. As can be seen from Fig. 3, under conditions of cyclic loading, the spatio-temporal dynamics of the multiscale development of damage to composites is characterized by two clusters (see Fig. 3 d, cluster 1 - red markers, cluster 2 - blue markers). While under the conditions of a quasi-static load, division into clusters is not possible (Fig. 3 c). Clustering was carried out on the basis of an agglomerative hierarchical clustering approach [9], which is as follows: 1) the similarity or difference between each pair of points in the data set is determined; 2) grouping of points located in close proximity into a binary hierarchical tree of clusters is performed; 3) large clusters stand out. In the case of dividing the studied set of points into clusters, an algorithm for calculating multifractal spectra based on the wavelet leader method was used [10] for each cluster separately. This method is analogous to the method of maxima of the wavelet transform modules (wavelet transform maxima modulus - WTMM) and was used in this work because the studied signals were discrete. Fig. 4 shows multifractal spectra constructed for two clusters of experimental data of the dependence E(t) (Fig. 3, d). As can be seen from the obtained results, the cluster spectra are monofractal.

Fig. 4 - Multifractal spectra built for the entire set of points of the dependence of E on ∂E / ∂t (red line) and for cluster 2 (blue line), shown in Fig. 3,d