Methods for Uncertainty Quantification and Comparison of Weld Residual Stress Measurements and Predictions

Abstract

Weld residual stress (WRS) is a major driver of primary water stress corrosion cracking (PWSCC) in safety critical components of nuclear power plants. Accurate understanding of WRS is thus crucial for reliable prediction of safety performance of component design throughout the life of the plant. However, measurement uncertainty in WRS is significant, driven by the method and the indirect nature in which WRS must be measured. Likewise, model predictions of WRS vary due to uncertainty induced by individual modeling choices. The uncertainty in WRS measurements and modeling predictions is difficult to quantify and complicates the use of WRS measurements in validating WRS predictions for future use in safety evaluations. This paper describes a methodology for quantifying WRS uncertainty that facilitates the comparison of predictions and measurements and informs design safety evaluations. WRS is considered as a function through the depth of the weld. To quantify its uncertainty, functional data analysis techniques are utilized to account for the two types of variation observed in functional data: phase and amplitude. Phase variability, also known as horizontal variability, describes the variability in the horizontal direction (i.e., through the depth of the weld). Amplitude variability, also known as vertical variability, describes the variation in the vertical direction (i.e., magnitude of stresses). The uncertainty in both components of variability is quantified using statistical models in principal component space. Statistical confidence/tolerance bounds are constructed using statistical bootstrap (i.e., resampling) techniques applied to these models. These bounds offer a succinct quantification of the uncertainty in both the predictions and measurements as well as a method to quantitatively compare the two. Major findings show that the level of uncertainty among measurements is comparable to that among predictions and further experimental work is recommended to inform a validation effort for prediction models.

A geometric approach for computing tolerance bounds for elastic functional data

“…This is due to the fact that the bounds were computed in a cross-sectional manner without accounting for warping variability. Figure 7(b) presents the tolerance bounds calculated using the approach of Lewis et al [18]. Again, comparing these bounds with those presented in Figure 5, we see some structural differences.…”

“…Corresponding estimated confidence values using the methods in [24] and [18]. upper and lower bounds do not accurately capture the true underlying shape of the given data.…”

“…Nonetheless, the simulated values are very close to the correct confidence levels. For comparison, we also list the estimated confidence values computed using the methods defined in [24] and [18]. For both methods, the estimated confidence values are much lower than expected.…”

“…Again, comparing these bounds with those presented in Figure 5, we see some structural differences. Both the [24] 75.00 70.00 67.00 Lewis et al [18] 71.00 67.00 64.00 Table 1. Simulated confidence values of 90% coverage tolerance using the bootstrap-based approach (top).…”

“…A couple of papers in recent literature have taken into account the phase variability in the application of monitoring functional data. Lewis et al [18] expanded upon the generative model presented in [33], and used a bootstrap approach to generate tolerance bounds. However, the phase variability in this approach was discarded, and as a result, the generated tolerance bounds did not maintain the shape of the original data.…”