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- Resumen es exacto "This thesis investigates processes of stochastic systems, with complex and multiple interactions using time series that are observably emerging from them. Such series have stochastic components with a high degree of correlation, are non-linear and nonstationary. Therefore their analyses must be carried out with appropriate methods, such as those used in this Thesis. The Wavelet Transform is within the mathematical field of harmonic analysis and provides the optimal resolution in the time-frequency plane, thus allowing an excellent characterization of non-stationary series. Wavelet Coherence allows determining the similarity of two series in the time-frequency plane. If this information is complemented by appropriate dynamic models, a cause-effect relationship between phenomena can be determined. The non-linear internal or/and external system´s interactions give place to nonlinear emerging time series. So, this determines the necessity of applying advanced analytical methods, which were generated and improved in the last two decades. The empirical decomposition in modes allows the analysis of the series with an a posteriori basis, obtained through an algorithm that works directly with the data. The modes are zero-mean oscillating functions with a high degree of mutual orthogonality and the obtained decomposition is complete. The components have bandwidths at successively decreasing frequencies. When no more oscillations can be extracted, the remaining function is uniformly increasing or decreasing and represents the trend of the series. Applying the Hilbert transform to the components or modes defines instantaneous frequency. The complete procedure is called the Hilbert-Huang transform and provides a precision degree in the time-frequency plane that in many cases exceeds the one obtained with Wavelet Transform. The degree of information about the highly random studied systems was evaluated by calculating the Shannon Entropy, which indicates the ordering degree of the time series, and the Mutual Information, which is a measure of the dependence, linear or not, between two random variables. In this Thesis, the described analyses were implemented in four applications, two of them to themes and signals related to the climate of the South Atlantic, and the other two to topics and signals of Acoustic Emission from the fracture of reinforced concrete in building structures through seismic tests.In the first topic related to climate, the multidecadal variability of the temperature series of the Orcadas meteorological station was studied, which has more than 100 years of observational data. Non-linear models were applied to determine the variability for the different seasons of the year and an analysis was carried out on the trend of the series looking for the possible anthropogenic influence on global warming. In the second climate-related study, we investigated the concordance of the different definitions and calculations of the Southern Annular Mode (SAM) index, one of the most important patterns of climate variability in the middle and upper latitudes of the Southern Hemisphere.
In the topics related to fracture of reinforced concrete, the Acoustic Emission series coming from seismic tests were analyzed. The first structure studied was a reinforced concrete slab subjected to increasing loads that simulate an earthquake. The damage of the structure was in the form of fractures since concrete is an essentially brittle material. The successive tests were with increasing acceleration and it was possible to follow the successive stages of micro fractures that coalesce producing macro fractures and then some of them when stopped in some barrier produce new micro fractures. Damage evaluation was achieved by applying the Wavelet Transform to the Acoustic Emission signals and determining characteristic frequencies associated with the formation of macro fractures, responsible for the highest levels of damage. In the last application, fracture assessment was enhanced by studying the local damage on the column beam junction in a structure subjected to seismic loads. It was possible to define a new damage index called energy b-value, based on the Wavelet Transform. Series originating in apparently so different systems could be conveniently analyzed with the techniques used in this Thesis because they are all generated by nonstationary and nonlinear stochastic processes that ultimately involve a high degree of similarity."
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