## 2 1/_f_ Noise in Damaging Structures: Laboratory Tests
Therefore, a fluctuation of \(f^{\gamma\gamma}\) (\(\gamma\approx 0.29\)) is found, which reveals a source noise basically \"white\" (\"white\" or random noise: \(1/f^{0}\)). Figure 1: Concrete specimens subjected to compression test monitored by means of Acoustic Emission (**a**); Experimental set-up (**b**). Figure 4 shows the log-log plot of AE power spectrum versus frequency for signals detected after the peak load. For the compression test of the specimen with \(\lambda\) = 1.0 a fluctuation of \(f^{\gamma}\) (\(\gamma\approx\) 0.9) is found, which reveals a source noise basically \"pink\" (\"pink\" or correlated noise: \(\gamma\) \(\sim\) 1.0 for \(1/f^{\gamma}\)). Furthermore, the results obtained from the compression test of specimen with \(\lambda\) = 2.0 are represented in Figures 5-7. Also in this case, \(1/f^{\gamma}\) distribution of AE signals is divided into two time windows (Figure 5): before the achievement of the peak load, and after peak load. In Figure 6 the log-log plot of AE power spectrum versus frequency for signals detected before the peak load is reported, and a fluctuation of \(f^{\gamma}\) (\(\gamma\approx\) 0.33) is found, which reveals a source noise basically \"white\" (\"white\" or random noise: \(1/f^{0}\)). Figure 3: Log-log plot of AE power spectrum versus frequency for the concrete specimen (\(\lambda\) = 1): \(1/f^{\gamma}\) noise before peak load, with \(\gamma\) = 0.29. White noise source (Random phenomena). Figure 2: Concrete specimen with \(\lambda\) = 1: Load vs. time diagram; Cumulated AE (hits) versus time diagram. Red line refers to the peak load occurrence. Figure 4: Log-log plot of AE power spectrum versus frequency for the concrete specimen (\(\lambda=1\)): \(1/f^{\gamma}\) noise after peak load, with \(\gamma=0.90\). Pink noise source (Correlated phenomena). Figure 5: Concrete specimen with \(\lambda=2\): Load vs. time diagram; Cumulated AE (hits) versus time diagram. Red line refers to the peak load occurrence. Analogously, in Figure 7 the log-log plot of AE power spectrum versus frequency for signals detected after the peak load is shown. During the compression test of specimen with \(\lambda=2.0\) a fluctuation of \(f^{\gamma\gamma}\) (\(\gamma\approx 0.84\)) is found, which reveals a source noise basically \"pink\" (\"pink\" or correlated noise: \(1/f^{1}\)). Summarizing, the frequency fluctuation data obtained by the compression tests carried out on concrete cylindrical specimens show how, before the achievement of the peak load, AE signals reveal a source noise basically \"white\" (\(1/f^{0}\)) that is characteristic of prominent random phenomena. On the contrary, after peak load, the source noise revealed by AE signal is characterized as \"pink\" (\(1/f^{1}\)), that is distinctive of correlated phenomena. See, for the sake of synthesis, the graph of Figure 8 that represents the behaviour under compression of the specimen having slenderness 1. Additionally, \(b\)-values of the specimen with \(\lambda=1.0\) are reported in Figure 9 both for pre-peak (\(b\cong 1.40\)), and post-peak loading phases (\(b\cong 1.02\)), confirming the \(1/f\) noise as a very suitable indicator of both the critical states and those that precede global or local collapses [25; 26]. As a matter of fact, as it is well known in the literature [7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21], the statistical interpretation to the variation in the \(b\)-value during the evolution of damage detected by AE captures the transition from the condition of diffused criticality to that of imminent failure localization. More precisely, in the pre-peak loading phase of the specimen with \(\lambda=1.0\), to the white noise envisaged by the \(1/f\) analysis, corresponds the critical  
Figure 6: Log-log plot of AE power spectrum versus frequency for the concrete specimen (\(\lambda=2\)): \(1/f^{\gamma}\) noise before peak load, with \(\gamma=0.33\). White noise source (Random phenomena).