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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Fig. 3. Change detection with a 60% decrease in Beam 7’s E : (a) Target vector and (b) GA optimized detection.

Effective DIs and their participation factors are selected by GA for each round. For the first round with a FV of 0.657, only one effective DI is selected: the best indicator at 100% is Z γ j R, Z-normalized resultant strain energy. For the second round with a FV of 1.022, two effective DIs are COMAC on curvature (COMAC κ j S, 100%) and percent flexibility (PercF j R, 25.8%). With a FV of 1.213, the third round chooses five less effective DIs: P γ j R (100%), COMAC ϕ j R (56.0%), COMAC κ j R (50.1%), CDF κ j R (42.3%),

and Diff κ j S (29.9%) . 5. Severity analysis

As the performance of DIs may be affected by damage severity, so may be the performance of GA. Low levels of damage lead to a higher matching degree of mode shapes, but the change of modal properties might be insignificant and not reveal weakness. In contrast, high levels of damage show considerable strength change but may cause more difficult mode matching. Therefore, to investigate damage severit y’s effect on the GA scheme, multiple scenarios of damage levels are tested. Damage is represented by the reduction of Y oung’s modulus E , denoted ρ , of the target beam, Beam 7. Four levels of damage are examined for a total of 31 damage scenarios are examined. Scenarios with ρ less than 1% are classified as Damage Level 1 (DL 1) represents “ti n y” defect inside the structural member. DL 1 is used to reveal the minimum change of E that GA can detect in this structure, so 11 scenarios are studied between 1E-8 and 1E-3. DL 2 represents “small” damage and has 5 scenarios with ρ between 1% and 30%. DL 3 represents “medium” damage and has 5 scenarios with ρ between 40%and 80%. Lastly, DL 4 represents “se v ere” damage and has 10 scenarios with ρ greater than 90%. This level examines the upper limit of detection. For each scenario, the mode shapes from the undamaged and damage cases are compared and matched. The number of matched modes has a tendency of decrease as the level of damage increases, indicating lower matching degree. This is expected due to increasing difference between the compared structures, generating more mode shape changes. Using each set of matched modes, the 24 DIs are calculated and normalized by scenario. The values of the target vector corresponding to Nodes 22, 23, 24 are set as 1 while all others are set as 0. Two criteria are chosen to quantitatively evaluate the optimized damage detection: the average fitness value (FV) and the absolute difference between the mean values of undamaged and damaged nodes ( δ ). The average FV is defined as the fitness value divided by the number of measurement nodes (52 in this study). All scenarios are compared in Figure 4, and the absolute difference is negatively proportional to the average FV. The fitted linear regression is