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Spatial DIC Errors due to Pattern-Induced Bias and Grey Level Discretization

Digital image correlation (DIC) is an optical metrology method widely used in experimental mechanics for full-field shape, displacement and strain measurements. The required strain resolution for engineering applications of interest mandates DIC to have a high image displacement matching accuracy, on the order of 1/100th of a pixel, which necessitates an understanding of DIC errors. In this paper, we examine two spatial bias terms that have been almost completely overlooked. They cause a persistent offset in the matching of image intensities and thus corrupt DIC results. We name them pattern-induced bias (PIB), and intensity discretization bias (IDB). We show that the PIB error occurs in the presence of an undermatched shape function and is primarily dictated by the underlying intensity pattern for a fixed displacement field and DIC settings. The IDB error is due to the quantization of the gray level intensity values in the digital camera. In this paper we demonstrate these errors and quantify their magnitudes both experimentally and with synthetic images.

47 OTHER INSTRUMENTATION↗

Connecting Large‐Scale Meteorological Patterns to Extratropical Cyclones in CMIP6 Climate Models Using Self‐Organizing Maps

Abstract Extratropical cyclones (ETCs) are responsible for the majority of cool‐season extreme events in the northeastern United States (NEUS), often leading to high‐impact weather conditions that can have wide‐ranging socioeconomic impacts. Evaluating the ability of climate models to adequately simulate ETC dynamics is essential for improving model performance and increasing confidence in future projections used by stakeholders and policymakers. ETCs are traditionally studied using techniques such as case studies and synoptic typing, however, these approaches can be time‐consuming, require subjective analysis, and do not necessarily identify the coincident large‐scale meteorological patterns (LSMPs). Here, we apply self‐organizing maps (SOMs) as an automated machine‐learning approach to characterize the LSMPs and associated frequency and intensity of discrete ETC events over NEUS. The dominant patterns of geopotential height variability are identified through SOM analysis of five reanalysis products during the last four decades. ETC events are tracked using TempestExtremes and are integrated with SOMs to classify the accumulated cyclone activity (ACA) associated with each pattern. We then evaluate the skill of CMIP6 historical experiments in simulating the LSMPs and ETC events identified in the SOM. Our results identify a robust bias toward more zonal patterns, with models struggling to reproduce the more amplified patterns typically associated with the highest cyclone activity. While model resolution has some impact on simulation credibility, model configuration appears to be more important in LSMP representation. The vast majority of CMIP6 models produce too few ETCs, although model errors are distributed around historical reanalyses when ACA is normalized by storm frequency.

54 ENVIRONMENTAL SCIENCES↗

A neural network‐enhanced reproducing kernel particle method for modeling strain localization

Abstract Modeling the localized intensive deformation in a damaged solid requires highly refined discretization for accurate prediction, which significantly increases the computational cost. Although adaptive model refinement can be employed for enhanced effectiveness, it is cumbersome for the traditional mesh‐based methods to perform while modeling the evolving localizations. In this work, neural network‐enhanced reproducing kernel particle method (NN‐RKPM) is proposed, where the location, orientation, and shape of the solution transition near a localization is automatically captured by the NN approximation via a block‐level neural network (NN) optimization. The weights and biases in the blocked parameterization network control the location and orientation of the localization. The designed basic four‐kernel NN block is capable of capturing a triple junction or a quadruple junction topological pattern, while more complicated localization topological patters are captured by the superposition of multiple four‐kernel NN blocks. The standard RK approximation is then utilized to approximate the smooth part of the solution, which permits a much coarser discretization than the high‐resolution discretization needed to capture sharp solution transitions with the conventional methods. A regularization of the NN approximation is additionally introduced for discretization‐independent material responses. The effectiveness of the proposed NN‐RKPM is verified by a series of numerical verifications.

Baek, Jonghyuk↗

Ratio method for estimating uncertainty in calculated gamma cascades

The assessment of uncertainty on deduced quantities obtained through both measurement and modeling must include contributions from both components. There are several methods to estimate the uncertainty due to modeling, such as the parametric uncertainty and that stemming from model bias. However, in the case where experimental data exists for partial cross sections, such as discrete gammas emitted in the de-excitation of the product nucleus following the reaction, the discrepancy between the measured and modeled gamma cascades provides more information and allows for uncertainty estimation that can account for all types of model and data uncertainty. This work presents a method for estimating that uncertainty, using ratios of gammas to get a measure of the accuracy of different parts of the modeled gamma cascade. The gamma with the lowest intensity uncertainty is shown to be the best for determining the channel cross section with realistic uncertainties, indicating that it should be used rather than the most intense gamma or a sum of gammas. In conclusion, this method provides both a simple procedure for calculating realistic uncertainties and identifies the best gamma for use in converting a set of measured partial gamma cross sections to the deduced total channel cross section.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

High Order Implicit Residual-Based Spatial Discretization Error Estimation for S N Neutron Transport

This work demonstrates our novel residual source spatial discretization error estimator (LeR/TEAD) for a DGFEM-1 discretization and assesses it along with two contemporary estimators, Ragusa and Wang's h -refinement estimator (RW) and Duo, Azmy, and Zikatanov's explicit residual-based estimator (DAZ), on a suite of Method of Manufactured Solutions (MMS) 2D problems and three realistic problem geometries. LeR/TE-AD is attractive because it directly estimates the local error in the angular flux, as opposed to a mere indicator of the error's behavior, on the same mesh and method order as the original numerical solution, thus typically being less computationally intensive than a refinement-based method. On the MMS suite, LeR/TE-AD consistently displayed a reduced performance versus its DGFEM-0 results in terms of accuracy and precision metrics, though it was not typically grossly inaccurate. This is attributed to the irregularities in the true solution across singular characteristics limiting the local accuracy of the numerical flux solution, leading to poor derivative approximations used in the residual approximations. The error transport problem then spreads the error in the residual to nearby cells, causing a greater degree of imprecision that did not afflict DAZ or RW. In testing the estimators on realistic problem geometries, however, LeR/TE-AD fared better. In practice, the true error is much larger in non-idealized geometries like in MMS, and a superlinear true solution means that RW and DAZ are not beneficially biased for DGFEM-1 error estimation. LeR/TE-AD was typically first or second in accuracy, primarily competing with RW, but the latter usually consumed 2-4 times the computational time as LeR/TE-AD, and requires a solution with four times as many unknowns. Furthermore, RW and LeR/TE-AD can be used to compute direct estimates of the error in any quantity of interest that is based on the angular ux solution, such as the fission rate density in a fuel pin, whereas DAZ requires a heuristic extension due to its norm-based nature.

97 MATHEMATICS AND COMPUTING↗