## 3 1/_f_ Noise in Damaging Structures: In-Situ AE Monitoring
The signals acquisition threshold was settled at 100 \(\upmu\)V.  
The monitoring period of the structural supports of the chapel began on 28 April 2011 and ended on 4 June 2011, it lasted about 900 h [32]. As results from the monitoring campaign, the vertical crack monitored on the North wall of the chapel presents a distribution of cracks on a surface domain, clearly proved by the \(b\)-value in the range (0.95, 1.15). Concerning the monitored frescos detachment, the decorated surface tends to evolve towards metastable conditions, and the acquired signals showed high frequency characteristics (<400 kHz). Moreover, a distribution of microcracks in the volume is obtained for the analyzed region [32]. The results obtained by the application of the AE sensors are represented in a log-log plot of power spectrum versus frequency (Figure 13), with a fluctuation of \(f^{\gamma}\) (\(\gamma\) = 0.92). Also in this case, the source noise revealed by AE signals sounds \"pink\", supporting the evidences of the cracking process found during the monitoring campaigns [24; 28; 32]. Finally, the log-log plot of the AE power spectrum versus frequency for a monitored masonry arch [33], belonging to the Racconigi Castle (Figure 14a,b) in Piedmont (Italy) is proposed. This last example has been presented in order to demonstrate that a \"white\" response is obtained on a masonry structural element in which the post-peak loading phase is far from being achieved. From Figure 15, it results \(1/f^{\gamma}\) noise with \(\gamma\) \(\sim\) 0.0, that characterizes white sources, generated by small defects random diffused in the structural volume. Figure 14: External view of the Racconigi Castle (Italy) (**a**) and the monitored masonry arch inside the Castle (**b**). Figure 13: Log-log plot of AE power spectrum versus frequency for the Chapel XVII of the Sacred Mountain of Varalló: \(1/f^{\gamma}\) noise, with \(\gamma\) = 0.92. Pink noise source (Correlated phenomena). Comparing the results obtained during the laboratory compression tests, and the data collected from in-situ structural monitoring, we remark a sophistication of the \"pink music\", that suggests that \(1/f\) noise may have an essential role in self-organized criticality and correlated processes. By applying it to damage analysis of materials, the distribution \(1/f\) behaves as a very suitable indicator of critical states. At last, recalling the elastic-softening constitutive law for the structural response [26; 34], when microcracks are organized on preferential fracture surfaces, the damaging structure \"produces\" pink noise. It is possible to find out in the previous discussion a parallel with the statistical distribution analysis of AE events, the so-called \(b\)-value [7; 8; 9; 35; 36; 37; 38; 39; 40]. Therefore, the emitted energy modalities are identified during the monitoring process by determining the \(b\)-value variations. \(b\)-value extreme cases are: the critical conditions \(b=1.5\), when the energy emission takes place through small defects diffused homogeneously in the structural volume; and \(b=1.0\), when energy emission takes place throughout preferential fracture surfaces. A diffused damage in the former case is observed (\(2b=D\simeq 3.0\), i.e., the cracks are distributed in a fractal domain near a volume [41; 42; 43]), whereas in the latter, two-dimensional macroracks are formed leading to the separation of the structural element (\(2b=D\simeq 2.0\), i.e., the cracks are distributed in a fractal domain close to a surface [41; 42; 43]). Like the \(b\)-value analysis, the proposed \(1/f^{\gamma}\) noise model analyzes the transition from the diffused damage condition to that of imminent collapse, when damaging structures sound \"pink\".