# Time Series Analysis of Acoustic Emissions in the Asinelli Tower during Local Seismic Activity

^{*}

## Abstract

**:**

_{1}, have been derived from the AE time series in order to identify the approach of the monitored structural element to a “critical state” in relation to the earthquake occurrence.

## 1. Introduction

## 2. Materials and Methods

## 3. Results

#### 3.1. Correlation between AE and Earthquakes

#### 3.2. b-Value versus Natural Time Analyses of AE Time Series

_{1}of the natural-time transformed time series [25,26,27].

_{b-min}= 501 h (marked in bottom diagram of Figure 4). It is worth remembering that b-values close to unity correspond to the growth of macro-fractures in the monitored element [38,39].

_{k}= k/N to the k-th event of energy Q

_{k}[25,26,27].

_{k}≡ Q

_{k}/Σ

_{k}

_{=1}

^{N}Q

_{i}as the probability distribution of the discrete variable χ

_{k}, the variance ${\kappa}_{1}\equiv {\chi}^{2}-{\chi}^{2}$, is considered a key parameter for identifying the approach to a critical state, and defined as follows:

_{k}and p

_{k}are rescaled upon the occurrence of any additional hit, κ

_{1}results to be an evolutionary parameter.

_{1}, evolving hit by hit, approaches the value 0.07.

- (1)
- the parameter κ
_{1}must approach the value 0.07 “by descending from above”; - (2)
- the entropies S and S
_{rev}(entropy upon time reversal) must be lower than the entropy of uniform noise, S_{u}= 0.0966, when κ_{1}coincides to 0.07. The entropy S is defined as$$S\equiv \u2039\chi \text{}\mathrm{ln}\chi \u203a-\u2039\chi \u203a\text{}\mathrm{ln}\text{}\u2039\chi \u203a$$

_{1}and entropies S and S

_{rev}of the natural-time transformed AE time series {χ

_{k}} has been studied, where the event energy Q

_{k}is derived from the amplitude A

_{k}through the relation Q

_{k}= cA

_{k}

^{1.5}, where c is a constant of proportionality [51,52]. Plotting all natural-time quantities as functions of the conventional time t provides a visual way to reveal the possible entrance point to “critical stage,” corresponding to the fulfillment of criticality Conditions (1) and (2). An entrance point to critical stage has been identified at time t

_{crit}= 492 h (criticality initiation time, marked by a vertical dashed line in Figure 4 and by a vertical dotted line in Figure 6), i.e., 9 h before the b-value reaches its minimum. Remarkably, this critical point corresponds to the middle-height peak in the AE rate (highlighted by the dashed line before the highest peak in Figure 4) and to the appearance of high-amplitude AE signals.

_{1}of the natural-time transformed AE series can be identified as a pre-failure indicator, before the onset of non-reversible damage—supposedly revealed by the minimum b-value—within the bulk of the structural element.

## 4. Conclusions

_{1}[47,48,49,50], as a possible early failure precursor. Future investigations in similar surveys would hopefully include the use of a seismometer, installed together with the AE system to record possible small seismic events affecting the observations.

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) The Asinelli Tower (with Garisenda Tower on the left) in the city centre of Bologna; (

**b**) Monitored portion of the masonry wall with the applied AE transducers, printed from [30]; (

**c**) AE transducer adopted for the monitoring; (

**d**) Typical AE signal formed by the sequence of P-, S- and surface waves.

**Figure 2.**(

**a**) Time series of the AE signals count rate and nearby earthquakes (extracted from http://www.ingv.it/it/, see Supplementary Materials) printed from [28]; (

**b**) Expansion of the dashed frame: the red line marks the occurrence time t

_{EQ}= 486 h of 13 October; earthquake (EQ).

**Figure 3.**Map showing the epicenter of the 4.1-magnitude earthquake (yellow point) occurred on 13 October 2010 with epicenter 100 km far from the monitoring site in Bologna (red point).

**Figure 4.**From top to bottom: accumulated number of AE signals; AE signals count rate; time series of AE signals frequencies (derived from signal duration and ring-down count) and amplitudes; b-value over time calculated using groups of, respectively, 300 (yellow squares), and 800 (blue squares) numbers of signals. The dashed line indicates a critical point revealed by the natural time analysis.

**Figure 6.**Time evolution of natural-time quantities κ

_{1}, S and S

_{rev}. Horizontal dashed lines represent the characteristics value κ

_{1}= 0.07 and S

_{u}= 0.0966 defining the criticality initiation time t

_{crit}. Note the relative positions of t

_{crit}and t

_{b-min}along the time-axis (the inset shows the approach of natural-time quantities to the critical point).

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**MDPI and ACS Style**

Carpinteri, A.; Niccolini, G.; Lacidogna, G.
Time Series Analysis of Acoustic Emissions in the Asinelli Tower during Local Seismic Activity. *Appl. Sci.* **2018**, *8*, 1012.
https://doi.org/10.3390/app8071012

**AMA Style**

Carpinteri A, Niccolini G, Lacidogna G.
Time Series Analysis of Acoustic Emissions in the Asinelli Tower during Local Seismic Activity. *Applied Sciences*. 2018; 8(7):1012.
https://doi.org/10.3390/app8071012

**Chicago/Turabian Style**

Carpinteri, Alberto, Gianni Niccolini, and Giuseppe Lacidogna.
2018. "Time Series Analysis of Acoustic Emissions in the Asinelli Tower during Local Seismic Activity" *Applied Sciences* 8, no. 7: 1012.
https://doi.org/10.3390/app8071012