PSI - Issue 64

Ina Reichert et al. / Procedia Structural Integrity 64 (2024) 145–152 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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The model parameter results of the last stages of different combinations, sensor distances and noise levels are given in Tables 3, 4 and 5. Here, the cost function value with its corresponding model parameter V S is displayed for all three selected fault size and position combinations for all considered noise levels and the sensor distances of 1 m, 5 m and 10 m. The weighting factors for the cost function calculation are 1 2 0.5 w w   . The trend of the cost function value depending on the sensor distance for no noise and several signal-to-noise ratios is plotted in Figure 5 for the three chosen fault size and position combinations.

Fig. 5. Trend of cost function value depending on the sensor distances for different noise levels for a) combination 1, b) combination 2 and c) combination 3

Table 3. Display of model parameter V S for last iterations stage of FWI for selected sensor distances and noise levels, cost function value and size and position of real ellipse marked with red dashed line for combination 1 combination 1 no noise sn = 100 sn = 50 sn = 20 sn = 10 Δs = Δr = 1 m

C f = 44.3073

C f = 44.3096

C f = 44.3168

C f = 44.3357

C f = 48.4501

Δs = Δr = 5 m

C f = 68.3427

C f = 67.3693

C f = 57.8663

C f = 56.4414

C f = 68.4321

Δs = Δr = 10 m

C f = 79.1351

C f = 79.4586

C f = 78.2765

C f = 79.6262

C f = 87.3340