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NASA NTRS1991

Some Aspects of uncertainty in computational fluid dynamics results

Uncertainties are inherent in computational fluid dynamics (CFD). These uncertainties need to be systematically addressed and managed. Sources of these uncertainty analysis are discussed. Some recommendations are made for quantification of CFD uncertainties. A practical method of uncertainty analysis is based on sensitivity analysis. When CFD is used to design fluid dynamic systems, sensitivity-uncertainty analysis is essential.

Mehta, U. B.↗

NASA NTRS2017

Overview of the AVT-191 Project to Assess Sensitivity Analysis and Uncertainty Quantification Methods for Military Vehicle Design

A NATO symposium held in 2008 identified many promising sensitivity analysis and un-certainty quantification technologies, but the maturity and suitability of these methods for realistic applications was not known. The STO Task Group AVT-191 was established to evaluate the maturity and suitability of various sensitivity analysis and uncertainty quantification methods for application to realistic problems of interest to NATO. The program ran from 2011 to 2015, and the work was organized into four discipline-centric teams: external aerodynamics, internal aerodynamics, aeroelasticity, and hydrodynamics. This paper presents an overview of the AVT-191 program content.

Benek, John A.↗

NASA NTRS1995

Impact of uncertainty on modeling and testing

A thorough understanding of the uncertainties associated with the modeling and testing of the Space Shuttle Main Engine (SSME) Engine will greatly aid decisions concerning hardware performance and future development efforts. This report will describe the determination of the uncertainties in the modeling and testing of the Space Shuttle Main Engine test program at the Technology Test Bed facility at Marshall Space Flight Center. Section 2 will present a summary of the uncertainty analysis methodology used and discuss the specific applications to the TTB SSME test program. Section 3 will discuss the application of the uncertainty analysis to the test program and the results obtained. Section 4 presents the results of the analysis of the SSME modeling effort from an uncertainty analysis point of view. The appendices at the end of the report contain a significant amount of information relative to the analysis, including discussions of venturi flowmeter data reduction and uncertainty propagation, bias uncertainty documentations, technical papers published, the computer code generated to determine the venturi uncertainties, and the venturi data and results used in the analysis.

Coleman, Hugh W.↗

DOE OSTI2020

Nuclear data uncertainty propagation and modeling uncertainty impact evaluation in neutronics core simulation

Uncertainty analysis is a critical requirement in reactor simulation as it is used to quantify the reliability of best-estimate calculation. A comprehensive uncertainty analysis should characterize all sources of uncertainties in a computationally-feasible and scientifically-defendable manner. Here we employ a well-established reduced order modeling (ROM) based uncertainty quantification methodology to propagate uncertainties throughout neutronic calculations. ROM relies on recent advances in randomized data mining techniques applied to large data streams. In our proposed implementation, the nuclear data uncertainties are first propagated from multi-group level through lattice physics calculation to generate few-group parameter uncertainties, described using a vector of mean values and a covariance matrix. Employing an ROM-based compression of the covariance matrix, the few-group uncertainties are then propagated through downstream core simulation in a computationally efficient manner. This straightforward approach, albeit efficient as compared to brute force forward and/or adjoint-based methods, often employs a number of assumptions that have been unquestioned in the literature of neutronic uncertainty analysis. This manuscript argues that these assumptions could introduce another source of uncertainty referred to as modeling uncertainties, whose magnitude needs to be quantified in tandem with nuclear data uncertainties. Thus, our primary goal is to explore the interactions between these two uncertainty sources in order to assess whether modeling uncertainties have an impact on parameter uncertainties. To explore this endeavor, the impact of a number of modeling assumptions on core attributes uncertainties is quantified. The study employs a CANDU reactor model, with Serpent and NEWT as lattice physics solvers and NESTLE-C as core simulator. The modeling assumptions investigated include those related with the uncertainty propagation method employed, e.g., deterministic vs. stochastic, the few-group energy structure employed to represent the cross-sections, the resonance treatment in lattice physics calculation, the reference values for the cross-section, and the number of samples employed to render ROM compression. Results indicate that some of the modeling assumptions could have a non-negligible impact on the core responses propagated uncertainties, highlighting the need for a more comprehensive approach to combine parameter and modeling uncertainties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

The STAT7 Code for Statistical Propagation of Uncertainties in Steady State Thermal Hydraulics Analysis of Plate Fueled Reactors

The STAT7 software was developed to perform steady-state thermal hydraulic analyses. Application of the software is for non-power research and test reactors, including conversion to low-enriched uranium fuel of U.S. High-Performance Research Reactors such as MITR-II. Since it can be necessary to repeat analysis during fuel reloading, STAT7 accommodates flexibility in analyzing many realistic aspects of reactor fuel management. STAT7 uses a Monte Carlo approach to model common fabrication parameters and other key reactor analysis uncertainties required for research and test reactor thermal hydraulic analyses. These safety calculations are ultimately intended to protect against high fuel plate temperatures due to critical heat flux or departure from nucleate boiling or onset of flow instability; but additional margin is obtained by basing the limiting safety settings on avoiding onset of nucleate boiling. STAT7 can simultaneously analyze all of the axial nodes of all of the fuel plates and all of the coolant channels for one lateral stripe of a fuel element. The stripes run the length of the fuel, from the bottom to the top. Power splits are calculated for each axial node of each plate to determine how much of the power goes out each face of the plate. By running STAT7 multiple times, full core analysis can be performed by analyzing the margin to onset of nucleate boiling and onset of flow instability for each axial node of each stripe of each plate of each element in the core.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS2016

Uncertainty and Sensitivity Analysis of Afterbody Radiative Heating Predictions for Earth Entry

The objective of this work was to perform sensitivity analysis and uncertainty quantification for afterbody radiative heating predictions of Stardust capsule during Earth entry at peak afterbody radiation conditions. The radiation environment in the afterbody region poses significant challenges for accurate uncertainty quantification and sensitivity analysis due to the complexity of the flow physics, computational cost, and large number of un-certain variables. In this study, first a sparse collocation non-intrusive polynomial chaos approach along with global non-linear sensitivity analysis was used to identify the most significant uncertain variables and reduce the dimensions of the stochastic problem. Then, a total order stochastic expansion was constructed over only the important parameters for an efficient and accurate estimate of the uncertainty in radiation. Based on previous work, 388 uncertain parameters were considered in the radiation model, which came from the thermodynamics, flow field chemistry, and radiation modeling. The sensitivity analysis showed that only four of these variables contributed significantly to afterbody radiation uncertainty, accounting for almost 95% of the uncertainty. These included the electronic- impact excitation rate for N between level 2 and level 5 and rates of three chemical reactions in uencing N, N(+), O, and O(+) number densities in the flow field.

West, Thomas K., IV↗

NASA NTRS1991

Risk analysis of an RTG on the Space Shuttle

As part of the effort to review the Ulysses Final Safety Analysis Report and to understand the risk of plutonium release from the Ulysses spacecraft General Purpose Heat Source-Radioisotope Thermal Generator (GPHS-RTG), the Interagency Nuclear Safety Review Panel (INSRP) and the author performed an integrated, quantitative analysis of the uncertainties of the calculated risk of plutonium release from Ulysses. Using state-of-the-art probabilistic risk assessment technology, the uncertainty analysis accounted for both variability and uncertainty of the key parameters of the risk analysis. The results show tht INSRP had high confidence that risk of fatal cancers from potential plutonium release associated with calculated launch and deployment accident scenarios is low.

Frank, Michael V.↗

DOE OSTI2025

LTAU-FF: Loss Trajectory Analysis for Uncertainty in atomistic Force Fields

Model ensembles are effective tools for estimating prediction uncertainty in deep learning atomistic force fields. However, their widespread adoption is hindered by high computational costs and overconfident error estimates. In this work, we address these challenges by leveraging distributions of per-sample errors obtained during training and employing a distance-based similarity search in the model latent space. Our method, which we call LTAU (Loss Trajectory Analysis for Uncertainty), efficiently estimates the full probability distribution function of errors for any test point using the logged training errors, achieving speeds that are 2–3 orders of magnitudes faster than typical ensemble methods and allowing it to be used for tasks where training or evaluating multiple models would be infeasible. We apply LTAU towards estimating parametric uncertainty in atomistic force fields (LTAU-FF), demonstrating that it produces well-calibrated confidence intervals and predicts errors that correlate strongly with the true errors for data near the training domain. Furthermore, we show that the errors predicted by LTAU-FF can be used in practical applications for detecting out-of-domain data, tuning model performance, and predicting failure during simulations. We believe that LTAU will be a valuable tool for uncertainty quantification in atomistic force fields and is a promising method that should be further explored in other domains of machine learning.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2013

Lessons Learned During TBCC Design for the NASA-AFRL Joint System Study

NASA and the Air Force Research Laboratory are involved in a Joint System Study (JSS) on Two-Stage-to-Orbit (TSTO) vehicles. The JSS will examine the performance, operability and analysis uncertainty of unmanned, fully reusable, TSTO launch vehicle concepts. NASA is providing a vehicle concept using turbine-based combined cycle (TBCC) propulsion on the booster stage and an all-rocket orbiter. The variation in vehicle and mission requirements for different potential customers, combined with analysis uncertainties, make it problematic to define optimum vehicle types or concepts, but the study is being used by NASA for tool assessment and development, and to identify technology gaps. Preliminary analyses were performed on the entire TBCC booster concept; then higher-fidelity analyses were performed for particular areas to verify results or reduce analysis uncertainties. Preliminary TBCC system analyses indicated that there would be sufficient thrust margin over its mission portion. The higher fidelity analyses, which included inlet and nozzle performance corrections for significant area mismatches between TBCC propulsion requirements versus the vehicle design, resulted in significant performance penalties from the preliminary results. TBCC system design and vehicle operation assumptions were reviewed to identify items to mitigate these performance penalties. The most promising items were then applied and analyses rerun to update performance predictions. A study overview is given to orient the reader, quickly focusing upon the NASA TBCC booster and low speed propulsion system. Details for the TBCC concept and the analyses performed are described. Finally, a summary of "Lessons Learned" are discussed with suggestions to improve future study efforts.

Snyder, Christopher A.↗

DOE OSTI2023

Quantifying uncertainty in analysis of shockless dynamic compression experiments on platinum. I. Inverse Lagrangian analysis

Absolute measurements of solid-material compressibility by magnetically driven shockless dynamic compression experiments to multi-megabar pressures have the potential to greatly improve the accuracy and precision of pressure calibration standards for use in diamond anvil cell experiments. Here, to this end, we apply characteristics-based inverse Lagrangian analysis (ILA) to 11 sets of ramp-compression data on pure platinum (Pt) metal and then reduce the resulting weighted-mean stress–strain curve to the principal isentrope and room-temperature isotherm using simple models for yield stress and Grüneisen parameter. We introduce several improvements to methods for ILA and quasi-isentrope reduction, the latter including calculation of corrections in wave speed instead of stress and pressure to render results largely independent of initial yield stress while enforcing thermodynamic consistency near zero pressure. More importantly, we quantify in detail the propagation of experimental uncertainty through ILA and model uncertainty through quasi-isentrope reduction, considering all potential sources of error except the electrode and window material models used in ILA. Compared to previous approaches, we find larger uncertainty in longitudinal stress. Monte Carlo analysis demonstrates that uncertainty in the yield-stress model constitutes by far the largest contribution to uncertainty in quasi-isentrope reduction corrections. We present a new room-temperature isotherm for Pt up to 444 GPa, with 1-sigma uncertainty at that pressure of just under ±1.2%; the latter is about a factor of three smaller than uncertainty previously reported for multi-megabar ramp-compression experiments on Pt. The result is well represented by a Vinet-form compression curve with (isothermal) bulk modulus K 0 = 270.3 ± 3.8 GPa, pressure derivative K$^{'}_{0}$= 5.66 ± 0.10, and correlation coefficient $R_{K_{0},K^{'}_{0}}$= –0.843.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2014

The NASA Langley Multidisciplinary Uncertainty Quantification Challenge

This paper presents the formulation of an uncertainty quantification challenge problem consisting of five subproblems. These problems focus on key aspects of uncertainty characterization, sensitivity analysis, uncertainty propagation, extreme-case analysis, and robust design.

Crespo, Luis G.↗

NASA NTRS1977

Monte Carlo analysis of uncertainty propagation in a stratospheric model. 2: Uncertainties due to reaction rates

A concise stratospheric model was used in a Monte-Carlo analysis of the propagation of reaction rate uncertainties through the calculation of an ozone perturbation due to the addition of chlorine. Two thousand Monte-Carlo cases were run with 55 reaction rates being varied. Excellent convergence was obtained in the output distributions because the model is sensitive to the uncertainties in only about 10 reactions. For a 1 ppby chlorine perturbation added to a 1.5 ppby chlorine background, the resultant 1 sigma uncertainty on the ozone perturbation is a factor of 1.69 on the high side and 1.80 on the low side. The corresponding 2 sigma factors are 2.86 and 3.23. Results are also given for the uncertainties, due to reaction rates, in the ambient concentrations of stratospheric species.

Stolarski, R. S.↗

DOE OSTI2021

Uncertainty quantification for Multiphase-CFD simulations of bubbly flows: a machine learning-based Bayesian approach supported by high-resolution experiments

In this paper, we developed a machine learning-based Bayesian approach to inversely quantify and reduce the uncertainties of multiphase computational fluid dynamics (MCFD) simulations for bubbly flows. The proposed approach is supported by high-resolution two-phase flow measurements, including those by double-sensor conductivity probes, high-speed imaging, and particle image velocimetry. Local distributions of key physical quantities of interest (QoIs), including the void fraction and phasic velocities, are obtained to support the Bayesian inference. In the process, the epistemic uncertainties of the closure relations are inversely quantified while the aleatory uncertainties from stochastic fluctuations of the system are evaluated based on experimental uncertainty analysis. The combined uncertainties are then propagated through the MCFD solver to obtain uncertainties of the QoIs, based on which probability-boxes are constructed for validation. The proposed approach relies on three machine learning methods: feedforward neural networks and principal component analysis for surrogate modeling, and Gaussian processes for model form uncertainty modeling. The whole process is implemented within the framework of an open-source deep learning library PyTorch with graphics processing unit (GPU) acceleration, thus ensuring the efficiency of the computation. The results demonstrate that with the support of high-resolution data, the uncertainties of MCFD simulations can be significantly reduced. The proposed approach has the potential for other applications that involve numerical models with empirical parameters.

42 ENGINEERING↗

DOE OSTI2022

THERMAL MODELING OF HANFORD LEAD CANISTER’S HEATER BENCH TESTS

A computational fluid dynamics (CFD) model was built to simulate planned testing of heater assemblies for the Hanford Lead Canister (HLC) project. The HLC is a canister storage system that will contain heaters to simulate the decay heat of nuclear material and provide the canister storage system with environmental conditions equivalent to the operating conditions on a dry storage pad. The HLC will be equipped with long-term data collection and monitoring systems to provide an early warning of corrosion, pitting, cracking, or other signs of canister degradation that might threaten the integrity of the containment boundary over the potentially long term of dry storage. An important part of the HLC development is to confirm the function and ability of the electric heater assemblies that were specially designed to provide heating similar to the decay heat of nuclear material contained within the canister storage system. Heater bench testing is planned for early 2022 in a test configuration that does not include the canister. The goal of the bench testing is to verify that the heaters can replicate the decay heat of a canister with nuclear material and to validate the thermal models, which are critical to understanding the HLC’s thermal environment, including the local air flow within the canister storage system. Testing of the heater assemblies inside the canister system are planned in the future to validate canister level thermal models, and rigorous pre-deployment testing of the complete HLC cask and canister system is intended to be completed before the HLC is deployed in the 2025-2026 timeframe. This study presents the pre-test temperature predictions of the bench testing. A description of the heater assemblies and planned bench testing is presented. The model was developed with the commercial CFD code STAR-CCM+. An uncertainty analysis was run with the CFD model to determine the uncertainty in the temperature predictions and provide a range over which the predicted temperatures are expected to vary. The uncertainty analysis was performed by coupling STAR-CCM+ with the software Dakota, which provides advanced parametric analyses, including quantification of margins and uncertainty with computational models. This work is expected to provide insight into SNF canister behavior.

Suffield, Sarah R.↗

DOE OSTI2024

THERMAL MODELING OF HANFORD CESIUM AND STRONTIUM CANISTERS DURING SIMULATED LOADING

A computational fluid dynamics (CFD) model was built to simulate planned testing of heater assemblies within a canister and overpack for the Hanford Lead Canister (HLC) project. The HLC is a canister storage system that will contain heaters to simulate the decay heat of nuclear material and provide the canister storage system with environmental conditions equivalent to the operating conditions on a dry storage pad. The HLC will be equipped with long-term data collection and monitoring systems to provide an early warning of corrosion, pitting, cracking, or other signs of canister degradation that might threaten the integrity of the containment boundary over the potentially long term of dry storage. An important part of the HLC development is to make pretest numerical predictions for the behavior of the heated canister during the simulated radiolytic decay heat testing, which simulates the dry storage system during loading operations. The simulated radiolytic decay heat test is planned for mid-2024 in a configuration that includes the heater assembly, overpack, and canister, but with the lids removed to allow loading cesium and strontium capsules into the canister. One of the goals of the test is to evaluate the thermal behavior of the canister and overpack assembly in the ambient air of the test facility, which will provide data critical to validating the thermal models and understanding how the HLC will perform as a system once deployed. To best approximate real-world conditions, the CFD model includes the full air volume of the mock-up truck bay the heated canister test will be performed in, enabling detailed investigation of how the heated canister affects airflow around it. Rigorous pre-deployment testing of the complete HLC cask and canister system is intended to be completed before the HLC is deployed in the 2028 timeframe. This study presents the pre-test temperature predictions of the simulated radiolytic decay heat test. A description of the heater assembly, canister, and overpack system is presented. The model was developed with the commercial CFD software STAR-CCM+. An uncertainty analysis was run with the CFD model to determine the uncertainty in the temperature predictions and provide a range over which the predicted temperatures are expected to vary. The uncertainty analysis was preformed by coupling STAR-CCM+ with the software Dakota, which provides advanced parametric analyses, including quantification of margins and uncertainty with computational models. This work is expected to provide insight into SNF canister behavior.

Carpenter-Graffy, Dina E.↗

NASA NTRS2015

Considering Risk and Resilience in Decision-Making

This paper examines the concepts of decision-making, risk analysis, uncertainty and resilience analysis. The relation between risk, vulnerability, and resilience is analyzed. The paper describes how complexity, uncertainty, and ambiguity are the most critical factors in the definition of the approach and criteria for decision-making. Uncertainty in its various forms is what limits our ability to offer definitive answers to questions about the outcomes of alternatives in a decision-making process. It is shown that, although resilience-informed decision-making would seem fundamentally different from risk-informed decision-making, this is not the case as resilience-analysis can be easily incorporated within existing analytic-deliberative decision-making frameworks.

Torres-Pomales, Wilfredo↗

DOE OSTI2025

A compact x-ray spectrometer for measurements of electron temperature distributions in inertial confinement fusion implosions at OMEGA

The Wedge Range Filter (WRF), commonly used for proton spectroscopy at the OMEGA Laser Facility and National Ignition Facility, is adapted to measure the x-ray continuum spectrum through transmission measurement using a continuous-gradient filter. Continuum x rays emitted from the hotspot of an implosion contain information about the plasma composition and electron temperature. The WRF data are leveraged to probe this distribution, specifically the electron temperature distribution. In this work, the data recorded with the WRF are forward modeled using a temperature distribution model folded with the WRF response function. An uncertainty analysis is conducted through a Bayesian regression algorithm using a Hamiltonian Monte Carlo sampler. This analysis enables the uncertainties in the instrument response to be folded into the uncertainty estimation of the electron temperature and absolute x-ray emission. Data analysis for a series of OMEGA implosions is presented and compared with radiation hydrodynamic simulations.

Lasers↗

DOE OSTI2023

Modeling the Effect of Surface Platinum–Tin Alloys on Propane Dehydrogenation on Platinum–Tin Catalysts

Uncertainty analysis, reported experimental literature data, and density functional theory were synthesized to model the effect of surface tin coverage on platinum-based catalysts for nonoxidative propane dehydrogenation to propylene. Here, this study tests four different platinum–tin skin surface models as potential catalytic sites, Pt 3 Sn/Pt(100), PtSn/Pt(100), Pt 3 Sn/Pt(111), and Pt 2 Sn/Pt(211), and compares them to the corresponding pure Pt surface sites using an uncertainty analysis methodology that uses BEEF-vdW with its ensembles (BMwE) to generate the uncertainty for the energies of the intermediates and transition states. One experimental data set with two experimental observations, selectivity to propylene and turnover frequency of propylene, was used as a calibration data set to evaluate the impact of the experimental data on informing the models. This study finds that the prior model for Pt 3 Sn/Pt(100) is the most active and Pt 2 Sn/Pt(211) is the most selective toward propylene. Active sites on the (100) facet have the highest probability of being responsible for C 1 and C 2 product formations (C–C bond cleavage). Increasing the Sn coverage on the (100) surface facet to a PtSn/Pt(100) active site leads to a significantly reduced rate and might explain the experimentally observed higher selectivity of Sn-doped catalysts relative to pure Pt catalysts. Next, this study finds that for all surfaces, except PtSn/Pt(100), the rate-controlling steps are the initial dehydrogenation steps alongside some partially rate-controlling second dehydrogenation steps. For PtSn/Pt(100), only the initial terminal dehydrogenation step to CH 3 CH 2 CH 2 * and second dehydrogenation steps are rate-controlling. Next, the calibrated models for all surfaces were found to be selective toward propylene production and model the reported turnover frequency successfully. Nevertheless, Pt 2 Sn/Pt(211) emerges as the active site with some (minor) evidence as the main active site based on Jeffreys’ scale interpretation of Bayes factors. This observation agrees with prior studies that also found step sites to be most likely the most relevant active sites for pure Pt catalysts. Overall, the results indicate that tin, in addition to affecting the binding strength of the adsorbed species, prevents deeper dehydrogenation (reducing coking) and cracking reactions through increasing activation barriers for unwanted side reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗