PSI - Issue 37

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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would cause unreasonable flexibility which would affect the detection of local damage. Thus, the bottom of each columns is defined as fixed. ABAQUS ® pre-processing produces the natural frequencies and their associated mode shapes for the fifty-two selected nodes in x , y , z directions.

Fig. 2. Test frame schematic diagram.

True structural damage can have numerous deleterious effects. Some damage can be simulated as a reduction in stiffness, such as due to bolt loosening, corrosion, and cracking due to cyclic loading [28]. Here, damage is induced by reducing the Y oung’s modulus E by 60% ( E = 0 . 4 E steel ) on one second floor beam, Beam 7. Five nodal responses may differ: Nodes 22, 23, and 24 are located directly on the altered beam, but Nodes 21 and 25 will also be affected by Columns 15 and 16, respectively. For each model, seventymodes were found up to 200 Hz. The mode shapes from the two scenarios were compared, and 39 pairs of modes were identified as matched. Those natural frequencies and modes shapes were used to calculate 24 combined normalized damage indices. As input for GA, the DIs are then assembled as an m × n array where m and n denote the number of measured locations (52) and the number of resultant indices (24), respectively. The target vector values corresponding to Nodes 22, 23, and 24 on damaged Beam 7 are set as 1 (fully damaged) while the values of all other nodes are set to 0 (no change). Note that this assumes that Columns 15 and 16 will affect end Nodes 21 and 25 far more than local Beam 7. For viewing ease, the optimized detection result is visualized by the structure’s configuration with color-coded circled number using thresholds. Figure 3(a) and 3(b) plots the employed target vector adopted for GA optimization and corresponding optimized detection, respectively. Note that the undamaged members are represented by blue solid lines while the damaged member is represented by red dash line. The numbers are the optimized best-fit detection results in percentage. The optimized detection successfully identified the damaged beam; values at Nodes 22 to 24 on Beam 7 are 61%, 94% and 61% respectively, which are significantly greater than the nodes at the undamaged members. An inspector would need understand that the reading of 94% is relative: that node is weaker than it was prior to damage. The 94% does not mean collapse is imminent since there is still remaining strength and nearby strength. The GA scheme successfully identifies the location of damage with no false positives. Using the 20% threshold, weight co efficie nts were found for the second and third rounds. The GA scheme still identifies the location of damage with minimal false positives. The maximum value at the damage location decreases from 94% in the first round to 79% in the second round and then 65% in the third round. Nodes 14 and 15 on Beam 5 also have increased values of 39%, which is fairly large and might be considered false positives.