# Long-Range Correlations and Natural Time Series Analyses from Acoustic Emission Signals
## 4 Conclusions  
This work focused on using time series methods to analyze acoustic emission data from two experimental tests with different materials: (i) a fiber-reinforced polymer plate undergoing a three-point bending test; (ii) a spaghetti bridge model from an undergraduate-level student loading contest. The time series analysis was carried out through two approaches: calculating DFA and Hurst exponents to characterize long-range correlations and analysis in the natural time domain. The purpose was to identify the possibility of using these methodologies to predict the critical points or failure in the studied structures. From the results, one concludes that:  
* Both the Hurst and DFA exponents yielded very similar results, which indicate that no high-order trends are present in the data.
* For both applications, the DFA parameter that was calculated for the whole dataset was inconclusive. However, when considered separately, the low (\(\alpha_{low}\)) and high (\(\alpha_{high}\)) state levels indicated a critical region where one converged to extreme anti-persistent correlations, and the other, to extreme persistent ones. That highlights these parameters' usefulness in indicating the criticality of the structure.
* The analysis in the natural time domain showed that the convergence of the order parameters and the entropies could predict the structure's entry in a critical stage, whether it is calculated from the AE energy or from counting the ruptured samples.
* In both the analyzed examples it was possible to clearly perceive (see Figures 7, 9 and 11) the correlation between the critical interval that was determined by the DFA, \(R\)/S*, NT, and the \(b\)-value analyses, from which the imminent increments in the acoustic emission activity follow.
* The indexes that were analyzed here, among others used the \(b\)-value which led to identifying when the damage process approaches a critical regime. In this situation, an unstable behavior is imminent and it is characterized by an increment in the global AE activity and in the amplitude of the AE signals. However, it is worth pointing out that it may also happen that, after reaching a critical phase with a large emission of energy, if the conditions of the damage continue to evolve in the structure, another stable one follows, which can be followed by another critical one, etc. Therefore, reaching a critical phase can always be correlated with local instability, but it is not always necessarily correlated with global structural failure. See, e.g., Ref. [14].  
Conceptualization, L.F.F., A.B.C., E.S.C., I.I., G.N. and G.L.; Methodology, L.F.F., E.S.C., B.N.R.T., I.I. and G.L.; Formal analysis, L.F., E.S.C. and I.I.; Investigation, L.F.F., E.S.C., A.B.C., B.N.R.T. and L.E.K.; Writing--original draft preparation, L.F.F., A.B.C., E.S.C., I.I. and M.S.; Writing--review and editing, L.F.F., B.N.R.T., I.I., L.E.K., G.L. and M.S.; Visualization, L.F.F. and I.I.; Supervision, L.E.K., G.N., G.L. and I.I. All authors have read and agreed to the published version of the manuscript.  
This research was funded by CNPq and CAPES (Brazil), and the sponsorship guaranteed with basic research funds provided by Politecnico di Torino (Italy).  
Not applicable.  
The authors wish to acknowledge the Brazilian National Council for Scientific and Technological Development (CNPq), the Coordination for the Improvement of Higher Level of Education Personnel (CAPES) and the sponsorship guaranteed with basic research funds provided by Politecnico di Torino, Italy for their financial aids in this work.  
The authors declare no conflict of interest.