PSI - Issue 37

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Elizabeth K. Ervin et al. / Procedia Structural Integrity 37 (2022) 6–16 Ervin and Zeng / Structural Integrity Procedia 00 (2021) 000 – 000

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Fig. 4. Damage detection thresholds considering all damage scenarios.

determined as δ = − 0 . 337FV + 1 . 154. The co efficie nt of determination R 2 is 0.939, indicating relatively high fitness. The points in Figure 4 represent scenarios in DL 1, DL 2, DL 3 and DL 4. The figure can be divided into four regions: Region I (low FV and high δ ), Region II (high FV and high δ ), Region III (low FV and low δ ), and Region IV (high FV and low δ ). Based upon GA performance, the thresholds for the average FV and the absolute difference are determined as 2.3% and 36%, respectively. Regions I and IV are colored in light green and light red, respectively, while Regions II and III are colored in light yellow. Region I represents the situation that the optimization works well and is thus green to represent successful detection. Two cases of Nodes 22, 23, and 24 for Beam 7 are shown as effective detection examples. Regions II represents the situation that the separation in δ is significant but the overall error is large. Regions III represents the situation that the overall error is small but the separation in δ is insignificant, meaning low range sensitivity. Region IV represents the situation that the optimization does not work: both the numerical error is large and the separation is insignificant. One case of Nodes 22, 23, and 24 for Beam 7 is shown to illustrate a lack of detection. Figure 4 shows that all points in DL 2 and DL 4 fall within Region I. Represen ting “small” damage, DL 2 has statistically significant change and does not reduce the degree of matching significantly. DL 4 represents “se v ere” damage, largely reducing the mode matching degree but also increasing change between the two states. Thus, optimized damage scenarios for DL 2 and DL 4 are deemed successful. Although scenarios in DL 1 have high degree of mode matching, the minor change in E might not show enough variation in modal properties. This would be similar to a local crack that was too small to affect the global structure. Thus, some scenarios in DL 1 fall in Region IV as undetectable while others are near detectable thresholds. The maximum reduction of E ( ρ ) that the GA optimization could not detect is 0.001%. DL 3 represents “medium” damage which alters both the modal properties as well as the mode matching to large extents. All points in DL 3 falls in Region I, but they are near the thresholds. Thus, “medium” damage introduces correlated noise between the physical and numerical portions of damage detection. 6. Conclusion This paper presents a genetic algorithm (GA)-based approach to optimize damage detection via combination