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User Guidelines and Best Practices for CASL VUQ Analysis Using Dakota

Sandia’s Dakota software (available at http://dakota.sandia.gov) supports science and engineering transformation through advanced exploration of simulations. Specifically it manages and analyzes ensembles of simulations to provide broader and deeper perspective for analysts and decision makers. This enables them to enhance understanding of risk, improve products, and assess simulation credibility. In its simplest mode, Dakota can automate typical parameter variation studies through a generic interface to a physics-based computational model. This can lend efficiency and rigor to manual parameter perturbation studies already being conducted by analysts. However, Dakota also delivers advanced parametric analysis techniques enabling design exploration, optimization, model calibration, risk analysis, and quantification of margins and uncertainty with such models. It directly supports verification and validation activities. Dakota algorithms enrich complex science and engineering models, enabling an analyst to answer crucial questions of - Sensitivity: Which are the most important input factors or parameters entering the simulation, and how do they influence key outputs?; Uncertainty: What is the uncertainty or variability in simulation output, given uncertainties in input parameters? How safe, reliable, robust, or variable is my system? (Quantification of margins and uncertainty, QMU); Optimization: What parameter values yield the best performing design or operating condition, given constraints? Calibration: What models and/or parameters best match experimental data? In general, Dakota is the Consortium for Advanced Simulation of Light Water Reactors (CASL) delivery vehicle for verification, validation, and uncertainty quantification (VUQ) algorithms. It permits ready application of the VUQ methods described above to simulation codes by CASL researchers, code developers, and application engineers.

97 MATHEMATICS AND COMPUTING↗

Uniting Surface Properties With Hydrodynamic Roughness in Shallow Overland Flow Models

Describing flow resistance from the properties of an underlying surface is a challenge in surface hydrology. Runoff models must specify a resistance formulation or “roughness scheme”—describing the functional relationship between flow resistance and flow depth/velocity—and its parameters. Uncertainty in runoff predictions derives from both the selected roughness scheme (e.g., Darcy Weisbach, Manning's, or laminar flow equations), and its parameterization with a roughness coefficient (e.g., Manning's n). Both choices are informed by model calibration to data, usually discharge, and, if available, velocity. In this study, a Saint Venant Equation-based runoff model is calibrated to discharge and velocity data from 112 rainfall simulator experiments. The results are used to identify the optimal roughness scheme among four widely-used options for each experiment, and to explore whether surface properties can be used to select the optimal roughness scheme and its coefficient. Among the tested roughness schemes, a transitional flow equation provided the best fit to the plurality of experiments. The most suitable roughness scheme for a given experiment was not related to measured surface properties. Regression models predicted the calibrated roughness coefficients with adjusted values between 0.48 and 0.54, depending on the roughness scheme used. Litter cover was the best predictor of the roughness coefficient, followed by soil cover and average canopy gap size. The results suggest that selection of an optimal roughness scheme based on surface properties alone remains difficult, but that once a scheme is selected, roughness coefficients can be estimated from surface properties.

54 ENVIRONMENTAL SCIENCES↗

Utilizing Environmental Tracers to Reduce Groundwater Flow and Transport Model Parameter Uncertainties

Abstract Non‐uniqueness in groundwater model calibration is a primary source of uncertainty in groundwater flow and transport predictions. In this study, we investigate the ability of environmental tracer information to constrain groundwater model parameters. We utilize a pilot point calibration procedure conditioned to subsets of observed data including: liquid pressures, tritium ( 3 H), chlorofluorocarbon‐12 (CFC‐12), and sulfur hexafluoride (SF 6 ) concentrations; and groundwater apparent ages inferred from these environmental tracers, to quantify uncertainties in the heterogeneous permeability fields and infiltration rates of a steady‐state 2‐D synthetic aquifer and a transient 3‐D model of a field site located near Riverton, Wyoming (USA). To identify the relative data worth of each observation data type, the post‐calibration uncertainties of the optimal parameters for a given observation subset are compared to that from the full observation data set. Our results suggest that the calibration‐constrained permeability field uncertainties are largest when liquid pressures are used as the sole calibration data set. We find significant reduction in permeability uncertainty and increased predictive accuracy when the environmental tracer concentrations, rather than apparent groundwater ages, are used as calibration targets in the synthetic model. Calibration of the Riverton field site model using environmental tracer concentrations directly produces infiltration rate estimates with the lowest uncertainties, however; permeability field uncertainties remain similar between the environmental tracer concentration and apparent groundwater age calibration scenarios. This work provides insight on the data worth of environmental tracer information to calibrate groundwater models and highlights potential benefits of directly assimilating environmental tracer concentrations into model parameter estimation procedures.

54 ENVIRONMENTAL SCIENCES↗

Evolutionary Tuning of Building Models to Monthly Electrical Consumption

Building energy models of existing buildings are unreliable unless calibrated so they correlate well with actual energy usage. Calibrating models is costly because it is currently an art which requires significant manual effort by an experienced and skilled professional. An automated methodology could significantly decrease this cost and facilitate greater adoption of energy simulation capabilities into the marketplace. The Autotune project is a novel methodology which leverages supercomputing, large databases of simulation data, and machine learning to allow automatic calibration of simulations to match measured experimental data on commodity hardware. This paper shares initial results from the automated methodology applied to the calibration of building energy models (BEM) for EnergyPlus (E+) to reproduce measured monthly electrical data.

Garrett, Aaron↗

A fast particle-based approach for calibrating a 3-D model of the Antarctic ice sheet

We consider the scientifically challenging and policy-relevant task of understanding the past and projecting the future dynamics of the Antarctic ice sheet. The Antarctic ice sheet has shown a highly nonlinear threshold response to past climate forcings. Triggering such a threshold response through anthropogenic greenhouse gas emissions would drive drastic and potentially fast sea level rise with important implications for coastal flood risks. Previous studies have combined information from ice sheet models and observations to calibrate model parameters. These studies have broken important new ground but have either adopted simple ice sheet models or have limited the number of parameters to allow for the use of more complex models. These limitations are largely due to the computational challenges posed by calibration as models become more computationally intensive or when the number of parameters increases. Here, we propose a method to alleviate this problem: a fast sequential Monte Carlo method that takes advantage of the massive parallelization afforded by modern high-performance computing systems. We use simulated examples to demonstrate how our sample-based approach provides accurate approximations to the posterior distributions of the calibrated parameters. The drastic reduction in computational times enables us to provide new insights into important scientific questions, for example, the impact of Pliocene era data and prior parameter information on sea level projections. These studies would be computationally prohibitive with other computational approaches for calibration such as Markov chain Monte Carlo or emulation-based methods. We also find considerable differences in the distributions of sea level projections when we account for a larger number of uncertain parameters. For example, based on the same ice sheet model and data set, the 99th percentile of the Antarctic ice sheet contribution to sea level rise in 2300 increases from 6.5 m to 13.1 m when we increase the number of calibrated parameters from three to 11. With previous calibration methods, it would be challenging to go beyond five parameters. Here, this work provides an important next step toward improving the uncertainty quantification of complex, computationally intensive and decision-relevant models.

54 ENVIRONMENTAL SCIENCES↗

A variational phase-field model For ductile fracture with coalescence dissipation

A novel phase-field model for ductile fracture is presented. The model is developed within a consistent variational framework in the context of finite-deformation kinematics. A novel coalescence dissipation introduces a new coupling mechanism between plasticity and fracture by degrading the fracture toughness as the equivalent plastic strain increases. The proposed model is compared with a recent alternative where plasticity and fracture are strongly coupled. Several representative numerical examples motivate specific modeling choices. In particular, a linear crack geometric function provides an “unperturbed” ductile response prior to crack initiation, and Lorentz-type degradation functions ensure that the critical fracture strength remains independent of the phase-field regularization length. In addition, the response of the model is demonstrated to converge with a vanishing phase-field regularization length. Additionally, the model is then applied to calibrate and simulate a three-point bending experiment of an aluminum alloy specimen with a complex geometry. The effect of the proposed coalescence dissipation coupling on simulations of the experiment is first investigated in a two-dimensional plane strain setting. The calibrated model is then applied to a three-dimensional calculation, where the calculated load-deflection curves and the crack trajectory show excellent agreement with experimental observations. Finally, the model is applied to simulate crack nucleation and growth in a specimen from a recent Sandia Fracture Challenge.

42 ENGINEERING↗

Bayesian model updating with finite element vs surrogate models: Application to a miter gate structural system

Bayesian finite element (FE) model updating using direct model evaluations of large-scale high-fidelity FE models is extremely computationally expensive. Surrogate models can be used as fast emulators of FE models to accelerate the model calibration process. The physics/mechanics-based FE models are still the underpinning behind the surrogate models. Here, this paper evaluates the loss in accuracy and the gain in computational time while performing Bayesian model updating by using surrogate model evaluations compared to using direct FE model evaluations. This evaluation is crucial before entirely relying on surrogate models in model updating for structural health monitoring (SHM) and damage prognosis (DP) purposes. This paper also demonstrates Bayesian updating and surrogate model construction of large-scale high-fidelity FE models of infrastructure systems. In this regard, the miter gate structural system is considered as the testbed structure. Three predominant damage modes (loss of contact between gate and wall, loss of thickness due to corrosion, and loss of tension in the diagonal rods) are considered for model updating purposes. Bayesian model updating is performed using direct FE evaluations by leveraging parallel computing. Two types of surrogates, namely polynomial chaos expansion (PCE) and Gaussian process regression (GPR), are developed for the miter gate. Model updating is performed again using the trained surrogate models, and the updating results are compared with their counterparts obtained using the direct FE evaluation results. The posterior distribution of the FE model parameters obtained using the trained surrogates are sufficiently accurate with respect to the posterior obtained utilizing the direct FE evaluations. In addition, an approximate 4-fold decrease in the computational time was observed when using surrogate model evaluations instead of direct FE evaluations for model updating.

42 ENGINEERING↗

A hierarchical Bayesian model for background variation in radiation source localization

In this paper, we apply a new model to account for varying background radiation in radiological source localization. We present a hierarchical Bayesian model that simultaneously infers background and source location parameters without requiring separate estimation of the background radiation at each detector location. We employ a simplified photon transport model to reduce the computational expense of Bayesian model calibration. Furthermore, we demonstrate the model accuracy by localizing a cesium-137 source in a simulated city block, and we analyze experimental field measurements with varying background. In both cases, the model provides sufficient fidelity that we can locate the source while simultaneously estimating background radiation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Impala

SAND2025-07450O Impala is a software tool that performs Bayesian model calibration for emulator-based models. The program uses R code to perform the calculations. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Tucker, James [Sandia National Lab. (SNL-CA), Live↗

Model files for estimating snow dynamics and stable water isotopes across the East River, CO.

A coupled hydrologic and snowpack stable water isotope model is used to assesses controls on isotopic inputs across the East River, Colorado, a large, mountainous basin. The hydrologic model uses the semi-empirical, spatially distributed and publicly available U.S. Geological Survey numerical code Precipitation-Modelling Runoff System (PRMS). Water and energy are tracked daily through the atmosphere, canopy and subsurface at a 100-m grid resolution. The isotope mass balance model follows previous work by Ala-aho et al. (2017) to track stable isotopes entering the soil system as snowmelt or rain. Water stores and fluxes needed for the isotope model use hydrologic model output for each timestep and model modeled grid location. This data package provides all files related to the hydrologic model (executable, input and output files), the isotopic model calibration and the historic isotopic model (water years 2015-2020). The isotope model source code and executable are provided. The file "readme.txt" includes information on the file structure, steps to run the model, and description of included folders.

54 ENVIRONMENTAL SCIENCES↗

304L Can Crush Validation Studies

Accurate prediction of ductile behavior of structural alloys up to and including failure is essential in component or system failure assessment, which is necessary for nuclear weapons alteration and life extensions programs of Sandia National Laboratories. Modeling such behavior requires computational capabilities to robustly capture strong nonlinearities (geometric and material), rate- dependent and temperature-dependent properties, and ductile failure mechanisms. This study's objective is to validate numerical simulations of a high-deformation crush of a stainless steel can. The process consists of identifying a suitable can geometry and loading conditions, conducting the laboratory testing, developing a high-quality Sierra/SM simulation, and then drawing comparisons between model and measurement to assess the fitness of the simulation in regards to material model (plasticity), finite element model construction, and failure model. Following previous material model calibration, a J 2 plasticity model with a microstructural BCJ failure model is employed to model the test specimen made of 304L stainless steel. Simulated results are verified and validated through mesh and mass-scaling convergence studies, parameter sensitivity studies, and a comparison to experimental data. The converged mesh and degree of mass-scaling are the mesh discretization with 140,372 elements, and a mass scaling with a target time increment of 1.0e-6 seconds and time step scale factor of 0.5, respectively. Results from the coupled thermal-mechanical explicit dynamic analysis are comparable to the experimental data. Simulated global force vs displacement (F/D) response predicts key points such as yield, ultimate, and kinks of the experimental F/D response. Furthermore, the final deformed shape of the can and field data predicted from the analysis are similar to that of the deformed can, as measured by 3D optical CMM scans and DIC data from the experiment.

36 MATERIALS SCIENCE↗

ROSE: A reduced-order scattering emulator for optical models

A new generation of phenomenological optical potentials requires robust calibration and uncertainty quantification, motivating the use of Bayesian statistical methods. These Bayesian methods usually require calculating observables for thousands or even millions of parameter sets, making fast and accurate emulators highly desirable or even essential. Emulating scattering across different energies or with interactions such as optical potentials is challenging because of the nonaffine parameter dependence, meaning the parameters do not all factorize from individual operators. Here we introduce and demonstrate the reduced-order scattering emulator ( ROSE ) framework, a reduced basis emulator that can handle nonaffine problems. ROSE is fully extensible and works within the publicly available band framework software suite for calibration, model mixing, and experimental design. As a demonstration problem, we use ROSE to calibrate a realistic nucleon-target scattering model through the calculation of elastic cross sections. This problem shows the practical value of the ROSE framework for Bayesian uncertainty quantification with controlled trade-offs between emulator speed and accuracy as compared to high-fidelity solvers. Finally, planned extensions of ROSE are discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Determination of elemental impurities in plastic calibration standards using laser induced breakdown spectroscopy

Dual-energy computed tomography (CT) scanning is a rapidly emerging imaging technique employed in nondestructive evaluation of various materials. CT has been used for characterizing rocks and visualizing multiphase flow through rocks for over 25 years. The most common technique for dual-energy CT scanning relies on homogeneous calibration standards to produce the most accurate decoupled data. However, the use of calibration standards with impurities increases the probability of error in the reconstructed data and results in poor rock characterization. Laser-induced breakdown spectroscopy was used to determine impurity concentration in a set of commercially purchased calibration standards used in dual-energy scanning for material identification with coal samples. Two calibration models were developed by using univariate calibration with the internal ratio method and multiple linear regression. Seven elements (Al, Fe, Mg, Na, Ni, Sr, and Ti) were examined in five different samples containing varying amounts of each ion to compare calibration from univariate data analysis and from multivariate data analysis. The contaminant concentrations were also measured by a commercially available inductively coupled plasma optical emission spectroscopy instrument, and the data were used as a reference in developing calibration curves for a modified version of the single linear regression model and the multiple linear regression model.

01 COAL, LIGNITE, AND PEAT↗

On the Bayesian calibration of computer model mixtures through experimental data, and the design of predictive models

For many real systems, several computer models may exist with different physics and predictive abilities. To achieve more accurate simulations/predictions, it is desirable for these models to be properly combined and calibrated. Here, we propose the Bayesian calibration of computer model mixture method which relies on the idea of representing the real system output as a mixture of the available computer model outputs with unknown input dependent weight functions. The method builds a fully Bayesian predictive model as an emulator for the real system output by combining, weighting, and calibrating the available models in the Bayesian framework. Moreover, it fits a mixture of calibrated computer models that can be used by the domain scientist as a mean to combine the available computer models, in a flexible and principled manner, and perform reliable simulations. It can address realistic cases where one model may be more accurate than the others at different input values because the mixture weights, indicating the contribution of each model, are functions of the input. Inference on the calibration parameters can consider multiple computer models associated with different physics. The method does not require knowledge of the fidelity order of the models. We provide a technique able to mitigate the computational overhead due to the consideration of multiple computer models that is suitable to the mixture model framework. We implement the proposed method in a real-world application involving the Weather Research and Forecasting large-scale climate model.

97 MATHEMATICS AND COMPUTING↗

A reduced Iwan model that includes pinning for bolted joint mechanics

Bolted joints are prevalent in most assembled structures; however, predictive models for their behavior do not exist. Calibrated models, such as the Iwan model, are able to predict the response of a jointed structure over a range of excitations once calibrated at a nominal load. The Iwan model, though, is not widely adopted due to the high computational expense of implementation. To address this, an analytical solution of the Iwan model is derived under the hypothesis that for an arbitrary load reversal, there is a new distribution of dry friction elements, which are now stuck, that approximately resemble a scaled version of the original distribution of dry friction elements. The dry friction elements internal to the Iwan model do not have a uniform set of parameters and are described by a distribution of parameters, i.e., which internal dry friction elements are stuck or slipping at a given load, that ultimately governs the behavior of the joint as it transitions from microslip to macroslip. This hypothesis allows the model to require no information from previous loading cycles. Additionally, the model is extended to include the pinning behavior inherent in a bolted joint. Modifications of the resulting framework are discussed to highlight how the constitutive model for friction can be changed (in the case of an Iwan–Stribeck formulation) or how the distribution of dry friction elements can be changed (as is the case for the Iwan plasticity model). Finally, the reduced Iwan plus pinning model is then applied to the Brake–Reuß beam in order to discuss methods to deduce model parameters from experimental data.

42 ENGINEERING↗

Self-similar Reynolds-averaged mechanical–scalar turbulence models for Rayleigh–Taylor, Richtmyer–Meshkov, and Kelvin–Helmholtz instability-induced mixing in the small Atwood number limit

Analytical self-similar solutions to two-, three-, and four-equation Reynolds-averaged mechanical–scalar turbulence models describing incompressible turbulent Rayleigh–Taylor, Richtmyer–Meshkov, and Kelvin–Helmholtz instability-induced mixing in planar geometry are derived in the small Atwood number (Boussinesq) limit. The models are based on the turbulent kinetic energy K and its dissipation rate ε, together with the scalar (heavy-fluid mass fraction) variance S and its dissipation rate Χ modeled either differentially or algebraically. The models allow for a simultaneous description of mechanical and scalar mixing, i.e., mixing layer growth and molecular mixing, respectively. Mixing layer growth parameters and other physical observables relevant to each instability are obtained explicitly as functions of the model coefficients. The turbulent fields are also expressed in terms of the model coefficients, with their temporal power-law scalings obtained by requiring that the self-similar equations are explicitly time-independent. The model calibration methodology is described and discussed. Expressions for a subset of the various physical observables are used to calibrate each of the two-, three-, and four-equation models, such that the self-similar solutions are consistent with experimental and numerical simulation data corresponding to these values of the observables and to specific canonical Rayleigh–Taylor, Richtmyer–Meshkov, and Kelvin–Helmholtz turbulent flows. A calibrated four-equation model is then used to reconstruct the mean and turbulent fields, and late-time turbulent equation budgets for each instability-induced flow across the mixing layer. The reference solutions derived here can provide systematic calibrations and better understanding of mechanical–scalar turbulence models and their predictions for instability-induced turbulent mixing in the very large Reynolds number limit.

42 ENGINEERING↗