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

10

5

and others are newherein. A total of 24 combined DIs using 51 directional DIs (17 in each of 3 directions) are employed in the damage detection software. Their nomenclature is (method)(DSF)(R or S), and for ease each combined DI will be identified by the presented method number. Note that some incompatibilities exist in Table 1. The COMAC method is applied for DI calculation only based upon mode shape and modal curvature as in literature. Similarly, a Z-normalization method is only used to calculate DIs using modal flexibility and modal strain energy. Since the probability method is based upon Z normalized DIs, only modal flexibility-based and modal strain energy-based DIs are used to further generate DIs using the probability method. The CDF method is only used for modal curvature as from literature.

Table 1. Summary of combined damage indices. Method Mode Shape

Flexibility

Curvature

Strain Energy

COMAC

1. COMACφjR 1

–

9. COMACκjS 3 10. COMACκjR 3

–

Difference

2. DiffφjR 1

4. DiffFjR

11. DiffκjS 3 12. DiffκjR 3 13. DivκjS 14. DivκjR

17. DiffUjS 18. DiffUjR 19. DivUjS 20. DivUjR 21. PercUjS 22. PercUjR

Division

3. DivφjR

5. DivFjR

Percentage

–

6. PercFjR

–

Z-score

– – –

7. Z MFI jR 2 8. P MFI jR

– –

23. ZγjR 5 24. PγjR

Probability

CDF

–

15. CDFκjS 4

–

16. CDFκjR 4 Sources 1: Lieven and Ewins (1988); 2: Sun et al. (2001); 3: Baghiee et al. (2009); 4: Chandrashekhar and Ganguli (2009); 5: Cornwall et al. (1999) 3. GA implementation

Three-dimensional resultant analysis produced 24 broad indices to assist inspectors in evaluating structural damage. These indices likely differ from another because method sensitivity certainly varies with damage location, type and extent. Thus, an improved tool is needed to better advise and assist an inspector. Genetic algorithm is a choice for structures with a limited amount of input information; that is, data is often limited by cost, access, time, and so on. An appropriate objective function must be selected that is sensitive to physical damage through index changes; an ineffective objective function would cause false positives and false negatives in damage detection. The goal of implementing GA is to combine all 24 DIs into one single best-fit index. However, the magnitude for each DI could dramatically vary by algorithm. To avoid numerical imbalance in combining DIs, each index should be normalized so that all the values are in the range of 0 and 1, showing percent possibility of damage. To force the optimized DI to also be a possibility of damage, a weighted average function is built. If m nodes are measured, let P be a m × 1 vector that combines the 24 DIs. The damage in the structure may then be localized by the combination of damage indices which is written 24 1 1 1 2 2 24 24 24 1 2 24 1 i i i i i         = =   +  + +   = = + + +   (6) The term α i is the weight co efficie nt of the i th DI and the I i is the m × 1 i th DI. The weight co efficie nts are unknown prior to GA processing, but the value of each weight co efficie nt ranges from 0 to 1, indicating that the i th DI’s co ntribution to the optimized damage detection result. GA aims to minimize the difference between the current weighted DI iteration and the suspected actual damage