PSI - Issue 52

Ilias N. Giannakeas et al. / Procedia Structural Integrity 52 (2024) 655–666 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 4: Posterior estimations of ̃ under the assumption of perfect information is available. The effectiveness of the predictions to estimate the true damage area values can be quantified using the accuracy and precision as metrics. The detection and localization results from the impacts on the flat panels have been presented and studied extensively in previous publications by the authors (Yue, Khodaei, and Aliabadi 2021; Giannakeas, Sharif Khodaei, and Aliabadi 2022). Based on these results, it is possible to extract the uncertainties associated with ̃ , ̃ and ̃ . It is assumed that the detection and localization parameters follow a normal distribution defined as ̃ ~ ( , ) , ̃ ~ ( , ) and ̃ ~ ( , ) . The underlying uncertainties may affect both the mean and the standard deviation for each parameter. A Monte Carlo (MC) approach is followed to propagate the uncertainty and provide an estimate for ̃ . The MC consists of drawing samples from one of the inputs parameters. Then Eq. 8 is used to draw 5000 samples from the posterior distribution using NUTS. The final estimate of ̃ is extracted by pooling together the = ×5000 samples. By setting = , = , = and = = =0 , we revert to the case where there is no uncertainty in the inputs and we have perfect information from the detection and localization modules. The extracted damage sizes for the perfect information scenario are illustrated in Fig. 4. In the same figure, the mean ( ̃ ) and standard deviation ( ̃ ) of each histogram is reported. In the following sections we assess the influence of uncertainty on the damage size estimations based on the changes in the ̃ and ̃ . We consider the case of perfect information as the benchmark situations and compare the rest of the cases with this one. 3. Results 3.1. Influence of Health Indicator Uncertainty In this section the influence of the uncertainty on ̃ is studied. Temperature uncertainty is one of the main uncertainty contributors in GWSHM systems. Many investigations have concluded that even small temperature variations can lead to fictitious HI that are high enough to impair the reliability and robustness of the SHM system. Temperature variations cause changes in the propagation characteristics of the guided waves and can mask the existence of damage as well as raise false positive indicators. Although various temperature compensation methods have been developed to reduce the temperature effects, residuals remain (Yue and Aliabadi 2020). Here the experimental signals are used to quantify the uncertainty in . Using the healthy flat panels signals, the value is computed for different temperature difference levels. The baseline temperature is assumed to be at 0 =25℃ while the current temperature varies in the range 25℃≤ 1 ≤40℃ . The effects of temperature are compensated following the method described in (Giannakeas, Sharif Khodaei, and Aliabadi 2022; Yue and Aliabadi 2020). Because of the temperature difference between the baseline and the current signals it is expected that as the temperature difference increases the uncertainty in also increases. The values computed for ∆ = 1 − 0 are reported in Fig. 5. Although no damage is included in these signals and the temperature difference is compensated, non-zero values are obtained.