PSI - Issue 18

574 Danilo D’ Angela et al. / Procedia Structural Integrity 18 (2019) 570–576 Danilo D’Angela et al. / Structural Integrity Procedia 00 (2019) 000–000 5 Fig. 4 shows the boxplots of the Entropy values corresponding to the failure for both Shannon and relative Entropy formulations: (a) cumulative Entropy at the failure ( ) over the median value ( � ), and (b) logarithmic cumulative Entropy at the failure ( ). The dispersion of the relative Entropy values at the failure is significantly smaller than the Shannon Entropy one, considering both over � and . Damage correlations are identified considering both Shannon and relative Entropy curves. Crack initiation is correlated to the transition between stage (2) and (3) for the Shannon Entropy, and to the initiation of the stage (3) for the relative Entropy (Fig. 3). Crack propagation is associated with the stage (3) for both Shannon Entropy and relative Entropy (Fig. 3). Fracture failure corresponds to the occurring of the stage (4) for the Shannon Entropy (Fig. 3), and to a threshold value for the relative Entropy (Fig. 4). The damage correlations related to the Shannon Entropy are more qualitative than the ones related to the relative Entropy; however, the former can be reasonably considered as more robust and consistent. As a matter of fact, the trend of the Shannon Entropy curves is more regular and clearly sub staged, as well as it is less affected by the testing/sample conditions. Furthermore, damage criteria based on more gradual response (e.g., smooth knee) are easier to be assessed by real-time monitoring. The cumulative Shannon Entropy is evaluated considering several sets of random monitoring processes , which are more representative of real structural health monitoring processes. A random monitoring process consists of randomly selected sequential detection windows , during which AE data are recorded and the Entropy is assessed. A set of random processes can be defined by (a) the number of detection windows ( N DW ) over the structural lifetime ( L t ), (b) the time duration of the detection windows ( T DW ), and (c) a set of rules for the random selection of the detection windows. T DW should be significantly smaller than L t in order to be consistent with realistic monitoring. The minimum time interval between the end of the previous detection windows and the beginning of the following ( Δ T ) is the main rule for the random selection of the detection windows. Fig. 5 shows the logarithmic cumulative Shannon Entropy (log Σ H S ) evaluated according to the abovementioned procedure applied to the A 2 case. A number of 500 curves is considered for each set of values of N DW . In particular, five sets of N DW are considered (ranging from 10 to 100), T DW is assumed equal to 0.005 L t , and Δ T is assumed equal to 10 T DW . The global Entropy curve is also shown in Fig. 5. The trend of the Entropy curves is proven to not be affected by (a) time-discontinuous detection, (b) random selection of the detection windows, and (b) variation of N DW . The increase of N DW (with the consequent increase of total monitored time) translates the curves towards the global Entropy curve without affecting the relative shape and trend of the curves. The sets of random curves have the same trend of the global curve, even if a much-reduced total monitored time is considered (e.g., smaller than 0.1 L t ). The damage criteria verified for the time-continuous global curve (e.g., curve knee and plateau in Fig. 3) are also valid in the considered conditions (Fig. 4), which simulate more realistic structural health monitoring processes.

(a) (b) Fig. 4. Boxplots of failure Entropy values for both Shannon and relative Entropy formulations: (a) cumulative Entropy at the failure ( ���� ) over the median value ( � ���� ), and (b) logarithmic cumulative Entropy at the failure ( ���� ).