# Long-Range Correlations and Natural Time Series Analyses from Acoustic Emission Signals
###### Abstract  
This work focuses on analyzing acoustic emission (AE) signals as a means to predict failure in structures. There are two main approaches that are considered: (i) long-range correlation analysis using both the Hurst (H) and the detrended fluctuation analysis (DFA) exponents, and (ii) natural time domain (NT) analysis. These methodologies are applied to the data that were collected from two application examples: a glass fiber-reinforced polymeric plate and a spaghetti bridge model, where both structures were subjected to increasing loads until collapse. A traditional (AE) signal analysis was also performed to reference the study of the other methods. The results indicate that the proposed methods yield reliable indication of failure in the studied structures. acoustic emission; long-range correlations; natural time analysis; heterogeneous materials +
Footnote †: journal: _sciences_  
inside the material (rupture, dislocation, among other causes) using sensors on the surface's structure. Each \"waves' source\" is called an event. The register of an event in an AE sensor is a signal or hit. Notice that there is no guarantee that an isolated signal informs of only one event since the waves from different events can affect the sensor simultaneously. Damage evolution is represented by the spatial-temporal distribution of the events, identified by a series of global parameters that are calculated from these signals, the most popular one being called \(b\)-value. This parameter could be related to the fractal dimension where the damage develops [11], being regarded in several works as a reliable precursor for the collapse, such as in [PERSON] et al. [12; 13; 14]. Other parameters are also used with the same goal. See, for instance, [PERSON] and [PERSON] 2006 [15] and [PERSON] et al., 2021 [16]. There is an identifiable pattern in complex systems in several science fields as they come close to instability, as illustrated by [PERSON], 1979 [17] with the normalization group theory. This method's central idea is that when a system approaches its critical collapse, its associated process has characteristics that do not depend on its geometry and boundary conditions because all scales are activated. This fact is observed in economics [18; 19], solid-state physics [20], and mechanical systems [21], among other fields. Several AE parameters present typical behavior that indicates when a system is close to its critical state. In this work, we investigate the behavior of long-range correlations of the temporal series that are studied using rescaled range (\(R\)/S*) analysis (or Hurst method-\(H\)) [22] and detrended fluctuation analysis (DFA) [23]. In addition, we analyze the temporal series using the natural time (NT) domain, a tool that was introduced by [PERSON] et al., 2001 [24] and subsequently employed by [PERSON] et al., 2013 [25]. These two approaches are used to analyze AE signals in two examples from previous works which employed classical AE techniques. First is a polymer plate that is reinforced by glass fibers that was studied by [PERSON] et al., 2020 [26]. The second was previously analyzed by [PERSON] et al., 2021 [27] and consisted of a spaghetti bridge structure that was built from spaghetti sticks and monitored while the structure was loaded up to reach the failure. The proposed parameters from the AE signals are of interest, not only because of their potential as precursors of failure in the studied systems but also because they illustrate their underlying principle: all systems present the same basic patterns when they approach criticality. As shown in this work, this feature is an effective alternative to identify damage in structures. Notice that the purpose of the present work is to present the parameters that are related to DFA, \(R\)/S*, and NT analyses, which could be used in a concomitant way with other strategies of analysis that are used nowadays. The focus here is different from applying the DFA, \(R\)/S*, and NT analyses to practical engineering problems.