PSI - Issue 52

Sidney Goossens et al. / Procedia Structural Integrity 52 (2024) 647–654 Sidney Goossens / Structural Integrity Procedia 00 (2023) 000 – 000

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The temperature compensation between the inspection and the baseline measurement is then performed as follows. First, the reverse relation of (1) is used to determine the temperature T from the Bragg wavelength λ B of every FBG sensor. The median value of these 120 temperature values is chosen as the actual temperature of the panel. The median is immune to λ B outliers coming from e.g. residual strain changes due to a possible BVID. Next, relation (1) is used to calculate the predicted λ B,i for this median te mperature. Finally, the difference Δλ B,i between the measured and reconstructed λ B,i is calculated. The resulting Δλ B,i are now temperature-compensated, and except for compensation errors, only the wavelength shift due to a BVID is left (Goossens, Berghmans, Sharif Khodaei, et al., 2021). The compensation errors can be used to determine a detection limit, or detection threshold τ (Goossens, Berghmans, Sharif Khodaei, et al., 2021). From all temperature calibration measurements, the compensation errors are calculated as mentioned above. All compensation errors are combined into one dataset, and the Gamma distribution of the absolute value of these errors is computed. From the cumulative distribution function (CDF) of the Gamma distribution, the near certainty interval at 98 % confidence bound is defined as detection threshold. Only if Δλ B,i > τ, is the wavelength shift attributed to the residual strain change due to a BVID, and else (Δλ B,i < τ) it is attributed to an effect of temperature. We previously showed that this algorithm can be used to define a global damage index (GDI) that quantifies and tracks the health of a subcomponent due to sequential BVIDs (Goossens, Berghmans, Muñoz, et al., 2021; Goossens et al., 2023). 3. Results and discussion 3.1. Temperature calibration and damage detection threshold Fig. 3 (a) shows the temperature calibration of one FBG sensor. The average λ B of 60 measurements per temperature step is shown in blue circles, and the cubic fit is shown in solid blue line. In addition, a linear fit (red dotted line) is performed for each sensor, which allowed for determining the temperature sensitivity of 10.2 ± 1.7 pm/ ℃ . The cubic fit allowed for obtaining the relation shown in equation (1) for each individual FBG sensor. Relation (1) is then used for temperature compensation, as explained in section 2.3. When applying this temperature compensation approach to the pristine baselines acquired during the temperature calibration on all 120 sensors and for all temperature steps (such as the data values shown in Fig. 3(a) for one sensor), the temperature compensation errors can be computed and gathered into one dataset. The histogram of the absolute value of these compensation errors is shown in Fig. 3(b). When computing the Gamma distribution, and corresponding CDF for this dataset, the 98 % confidence bound was calculated and chosen as the damage detection threshold τ. As can be seen in Fig. 3 (b), τ = 8.07 pm for the sensors on this curved panel. This means that all wavelength shifts after temperature compensation that are larger than this value are considered to be the effect of a BVID.

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Fig. 3. (a) Temperature calibration of an individual FBG sensor; (b) compensation error histogram and Γ -CDF.