10 Stochastic Wavenumber Estimation: Damage Detection Through Simulated Guided Lamb Waves 121 Fig. 10.17 Experimental measurement setup for low quality, noisy data used to study experimental uncertainty x excitation location measurement locations 50 mm scan area Fig. 10.18 Wavenumberintensity snapshot at one pixel, where deterministic estimation fits to spurious peak causing false positive for damage 10.5.3.2 Results and Discussion In wavenumber analysis, the most common form of noise is revealed as lower wavelength, therefore higher wavenumber. When using the deterministic approach, noise which may have a higher intensity than the true wavenumber will be selected, resulting in a false positive for damage. Figure 10.18 illustrates the improvement in wavenumber estimation for one specific pixel, where the deterministic approach selects a wavenumber related to noise (which would result in a false positive for damage) while the Bayesian inference is able to better estimate the true wavenumber. Stochastic Wavenumber Estimation improves upon the deterministic approach by incorporating engineering judgment into the problem in the form of prior knowledge, as detailed in Sect. 10.4.3. For this application, in the case of corrosion, it is considered more likely that only slight thinning has occurred, as opposed to severe damage, given the environmental conditions. For these reasons, a beta prior (Eq. 10.11) with parameters ˛ equal to 5 and ˇequal to 1 is implemented for this case study. f ˇ ˇ˛;ˇ D .˛Cˇ/ .˛/ .ˇ/ ˛ 1.1 /ˇ 1; 0< <1 (10.11) Using the experimental setup described in Sect. 10.5.3.1, wavenumber-intensity curves similar to that in Fig. 10.4b are obtained for every pixel to define the experimental variability at each x–y grid point location. Assuming all model parameters are known, or determined through the procedure previously described in Sect. 10.5.2, the wavenumber estimate obtained for the pixel may used to quantify the thickness of the plate at each pixel. In this case study, the milled plate specimen was tested with a grid spacing of 120 120 pixels. Figures 10.19 and 10.20 demonstrate the improvement in both damage localization and quantification with the application of Bayesian inference with an informed prior. As shown in Fig. 10.21, the stochastic approach tends to perform better in the undamaged region of the plate while the deterministic approach performs slightly better in the damaged region. More specifically, the deterministic approach tends to underestimate the plate thickness in the undamaged region and the stochastic approach tends to overestimate the thickness in the damaged region. Underestimation of thickness with the deterministic approach is likely due to the method fitting to noise
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