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At least 613 records · Page 34

Data driven modeling of plastic deformation

In this paper the application of machine learning techniques for the development of constitutive material models is being investigated. A flow stress model, for strain rates ranging from 10 –4 to 10 12 (quasi-static to highly dynamic), and temperatures ranging from room temperature to over 1000 K, is obtained by beginning directly with experimental stress-strain data for Copper. An incrementally objective and fully implicit time integration scheme is employed to integrate the hypo-elastic constitutive model, which is then implemented into a finite element code for evaluation. Accuracy and performance of the flow stress models derived from symbolic regression are assessed by comparison to Taylor anvil impact data. The results obtained with the free-form constitutive material model are compared to well-established strength models such as the Preston-Tonks-Wallace (PTW) model and the Mechanical Threshold Stress (MTS) model. Here, preliminary results show candidate free-form models comparing well with data in regions of stress-strain space with sufficient experimental data, pointing to a potential means for both rapid prototyping in future model development, as well as the use of machine learning in capturing more data as a guide for more advanced model development.

36 MATERIALS SCIENCE↗

Utilizing the deuterium-tritium fusion resonance to diagnose thermal runaway in igniting plasmas

For high-efficiency inertial confinement fusion implosions, it is predicted that a burning hot spot will successfully encompass all surrounding fuel and then transition into a thermal runaway where the internal energy increase from fusion occurs on a timescale faster than the expansion of the fuel is able to quench the fusion chain reaction after ignition occurs. Observation of this dynamic phase transition would indicate distinct burn properties and indicate an implosion's robustness. A technique for diagnosing the presence of thermal runaway from measurements of nuclear reaction history is presented. The technique is based on taking the logarithmic derivative of the nuclear reaction history, called the 𝛼 curve, and allowing a mathematical decoupling of the mass, volume, and thermal reactivity in the fusion reaction rate equation. During thermal runaway, where the thermal temperature dominates the burn dynamics, a maximum in the 𝛼 curve is found where there is a maximum in the first derivative of the thermal fusion reactivity, an effect to the deuterium-tritium (DT) fusion cross-section resonance. This provides a distinct signature related to the fundamental nature of the DT fusion nuclear resonance and signifies the transition into the fusion thermal instability. Impacts of charged particle transport on the effect are also assessed and the analytical formulas are compared and found to be in agreement with radiation hydrodynamic codes.

high-energy-density plasmas↗

Cavern leaching at SPR associated with 2017 oil sales and exchanges

In 2017 small-scale drawdowns at the Strategic Petroleum Reserve (SPR) supported oil sales for the Bipartisan Budget Act of 2015 and the 21st Century Cures Act of 2015 as well as exchanges supporting relief efforts for hurricane Harvey. These drawdowns may affect cavern stability and available drawdowns, thus is important to assess the leaching effects on the cavern shape. Cavern shape estimates from the SANSMIC solution mining code suggest the shapes of 28 caverns were altered in 2017 to varying degrees depending on the total volume of water injected, the initial cavern shape and the distance between the hanging string depth and the oil-brine interface depth. A flaring of the cavern floor occurred in 13 caverns, a geomechanically unfavorable outcome that may require operational changes to preserve cavern integrity. Of the three caverns with post-sale sonars, SANSMIC predictions compared favorably to two but underpredicted the third.

04 OIL SHALES AND TAR SANDS↗

Tools for Water Ingress Testing

The Safety Storage and Engineering Team, as part of the Production Support Services division (PSS-2), is tasked with ensuring the safety of containers used for handling and storage of nuclear materials. As part of this work, water ingress tests are conducted to evaluate the water-tightness of containers intended for in-glovebox use. In collaboration, the statistics group of the Computer and Computational Sciences Division (CCS-6) provided support in developing a statistically defensible approach for determining appropriate sample sizes for water ingress testing. Water ingress testing involves multiple measurements on multiple containers. Our approach uses a simple random effects model to analyze a pilot data set, implementing prediction limits to evaluate the efficacy of collecting additional data. Although this study capitalizes on available data, our approach can be used with estimates of the ratio of between and within variability and average values, often available from past testing or expert knowledge. An interactive Shiny tool was developed as a final user-friendly product for future testing. The Shiny interface is an open-source package providing a framework for building web applications. Raw data exploration and prediction interval-based sample size assessments can quickly be conducted by the engineering team without needing to interact with the underlying code.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

FAST-1.1: A Computer Code for Thermal-Mechanical Nuclear Fuel Analysis under Steady-state and Transients (Developed under NQA-1-2017)

Fuel Analysis under Steady-state and Transients (FAST) is the U.S. Nuclear Regulatory Commission (NRC)’s computer code that calculates the steady-state and transient response of nuclear reactor fuel rods during long-term in-reactor burnup, anticipated operational occurrences (AOOs), design basis accidents (DBAs), and dry storage conditions. The code calculates the temperature, pressure, and deformation of a fuel rod as functions of time-dependent fuel rod power and coolant boundary conditions. The phenomena modeled by the code include: * heat conduction through the fuel and other materials * heat transfer from the cladding-to-coolant * cladding elastic and plastic deformation, including creep * fuel-cladding mechanical interaction * fission gas release from the fuel * rod internal pressure and void volume * cladding oxidation The code contains necessary material and coolant properties, as well as clad-to-coolant heat transfer correlations, for normal operation through postulated accidents and AOOs for today’s U.S.-based light water reactor (LWR) fuel designs. FAST-1.1 also contains preliminary materials and models for new LWR fuel concepts, such as accident tolerant fuel (ATF), and non-LWR fuel concepts such as metallic fuels for sodium fast reactors (SFRs). FAST has been developed for use on Windows and Linux operating systems. This document describes FAST-1.1 and is one of a series of documents on the code; the other documents detail the material properties used by FAST as well as its integral assessment to experiments and commercial data.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

FAST-1.2: A Computer Code for Thermal-Mechanical Nuclear Fuel Analysis under Steady-state and Transients

Fuel Analysis under Steady-state and Transients (FAST) is the U.S. Nuclear Regulatory Commission (NRC)’s computer code that calculates the steady-state and transient response of nuclear reactor fuel rods during long-term in-reactor burnup, anticipated operational occurrences (AOOs), design basis accidents (DBAs), and dry storage conditions. The code calculates the temperature, pressure, and deformation of a fuel rod as functions of time-dependent fuel rod power and coolant boundary conditions. The phenomena modeled by the code include: • heat conduction through the fuel and other materials • heat transfer from the cladding-to-coolant • cladding elastic and plastic deformation, including creep • fuel-cladding mechanical interaction • fission gas release from the fuel • rod internal pressure and void volume • cladding oxidation The code contains necessary material and coolant properties, as well as clad-to-coolant heat-transfer correlations, for normal operation through postulated accidents and AOOs for today’s U.S.-based light water reactor (LWR) fuel designs. FAST-1.2 also contains preliminary materials and models for new LWR fuel concepts, such as accident tolerant fuel (ATF), and non-LWR fuel concepts such as metallic fuels for sodium fast reactors (SFRs). FAST has been developed for use on Windows and Linux operating systems. This document describes FAST-1.2 and is one of a series of documents on the code; the other documents detail the material properties used by FAST as well as its integral assessment to experiments and commercial data.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Development and Assessment of CTFFuel

This milestone report documents an approach that seeks to develop a standalone fuel solver to simulate steady-state and transient thermo-mechanical responses of light-water reactor fuel rods and assess its temperature predictions against analytical solutions, and a well-known and validated fuel performance code. This manuscript focuses on five major topics: (1) development of the CTFFuel, (2) discussion of the newly implemented fuel deformation models in dynamic gap conductance model of CTFFuel, (3) enabling the dynamic gap conductance model in VERA-CS, (4) verification of the solid conduction solution and comparison of the CTFFuel with respect to the workhorse code, CTF, and (5) benchmark of the thermal conductivity degradation using the burnup dependent fuel thermal conductivity models and benchmark of the fuel centerline temperature using the dynamic gap conductance model with Halden measurements and FRAPCON-4.0 simulation results. CTFFuel temperature predictions are compared to predictions from FRAPCON-4.0 for UO 2 , UO 2 +Gd 2 O 3 and MOX fuels through reactor’s life. The main motivation is to understand discrepancies between CTFFuel and FRAPCON-4.0’s temperature predictions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

FAST-1.2.2: A Computer Code for Thermal-Mechanical Nuclear Fuel Analysis under Steady-state and Transients

Fuel Analysis under Steady-state and Transients (FAST) is the U.S. Nuclear Regulatory Commission (NRC)’s computer code that calculates the steady-state and transient response of nuclear reactor fuel rods during long-term in-reactor burnup, anticipated operational occurrences (AOOs), design basis accidents (DBAs), and dry storage conditions. The code calculates the temperature, pressure, and deformation of a fuel rod as functions of time-dependent fuel rod power and coolant boundary conditions. The phenomena modeled by the code include heat conduction through the fuel and other materials, heat transfer from the cladding-to-coolant, cladding elastic and plastic deformation (including creep), fuel-cladding mechanical interaction, fission gas release from the fuel, rod internal pressure, void volume, and cladding oxidation. The code contains necessary material and coolant properties, as well as clad-to-coolant heat transfer correlations, for normal operation through postulated accidents and AOOs for today’s U.S.-based light water reactor (LWR) fuel designs. FAST-1.2.2 also contains preliminary materials and models for new LWR fuel concepts, such as accident tolerant fuel (ATF), and non-LWR fuel concepts such as metallic fuels for sodium fast reactors (SFRs). FAST has been developed for use on Windows and Linux operating systems. This document describes FAST-1.2.2 and is one of a series of documents on the code; the other documents detail the material properties used by FAST as well as its integral assessment to experiments and commercial data.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NON-LTE INVERSIONS OF THE Mg ii h and k AND UV TRIPLET LINES

The Mg ii h and k lines are powerful diagnostics for studying the solar chromosphere. They have become particularly popular with the launch of the Interface Region Imaging Spectrograph ( IRIS ) satellite, and a number of studies that include these lines have lead to great progress in understanding chromospheric heating, in many cases thanks to the support from 3D MHD simulations. In this study, we utilize another approach to analyze observations: non-LTE inversions of the Mg ii h and k and UV triplet lines including the effects of partial redistribution. Our inversion code attempts to construct a model atmosphere that is compatible with the observed spectra. We have assessed the capabilities and limitations of the inversions using the FALC atmosphere and a snapshot from a 3D radiation-MHD simulation. We find that Mg ii h and k allow reconstructing a model atmosphere from the middle photosphere to the transition region. We have also explored the capabilities of a multi-line/multi-atom setup, including the Mg ii h and k, the Ca ii 854.2 nm, and the Fe i 630.25 lines to recover the full stratification of physical parameters, including the magnetic field vector, from the photosphere to the chromosphere. Finally, we present the first inversions of observed IRIS spectra from quiet-Sun, plage, and sunspot, with very promising results.

79 ASTRONOMY AND ASTROPHYSICS↗

Systematic and objective evaluation of Earth system models: PCMDI Metrics Package (PMP) version 3

Systematic, routine, and comprehensive evaluation of Earth system models (ESMs) facilitates benchmarking improvement across model generations and identifying the strengths and weaknesses of different model configurations. By gauging the consistency between models and observations, this endeavor is becoming increasingly necessary to objectively synthesize the thousands of simulations contributed to the Coupled Model Intercomparison Project (CMIP) to date. The Program for Climate Model Diagnosis and Intercomparison (PCMDI) Metrics Package (PMP) is an open-source Python software package that provides quick-look objective comparisons of ESMs with one another and with observations. The comparisons include metrics of large- to global-scale climatologies, tropical inter-annual and intra-seasonal variability modes such as the El Niño–Southern Oscillation (ENSO) and Madden–Julian Oscillation (MJO), extratropical modes of variability, regional monsoons, cloud radiative feedbacks, and high-frequency characteristics of simulated precipitation, including its extremes. The PMP comparison results are produced using all model simulations contributed to CMIP6 and earlier CMIP phases. An important objective of the PMP is to document the performance of ESMs participating in the recent phases of CMIP, together with providing version-controlled information for all datasets, software packages, and analysis codes being used in the evaluation process. Among other purposes, this also enables modeling groups to assess performance changes during the ESM development cycle in the context of the error distribution of the multi-model ensemble. Quantitative model evaluation provided by the PMP can assist modelers in their development priorities. In this paper, we provide an overview of the PMP, including its latest capabilities, and discuss its future direction.

54 ENVIRONMENTAL SCIENCES↗

Lighting Policy Options to Incentivize the Circular Economy

Energy codes and energy efficiency policy are primed for significant shifts in the coming decade. Consumers are increasingly asking manufacturers to take responsibility for products over the course of the product lifespan, including at end-of-life. Consumer demand for social and environmental responsibility may push new codes and policies that incentivize the circular economy. Within the lighting sector, for example, rapid innovations have created large energy savings but also created a complex waste stream. Traditional energy code approaches to lighting efficiency have considered only lighting power density or energy-based metrics. Shifting codes and policy to consider environmental impacts of the product lifecycle could include circular economy mechanisms such as product deposits or service-based business models. In this paper we consider the possible structures for both codes and policies, and provide an analysis of the merits of each policy using life cycle assessment and sustainability index (SI).

Dillon, Heather↗

Uniformly Ordered Binary Decision Algorithm for Benchmark Experiment Correlations in Whisper Validation

When performing a validation exercise for determining the upper subcritical limit of a nuclear criticality safety application, an analyst should select and perform a statistical analysis on a population of benchmark experiments that are neutronically similar to the application. The size of this population should be sufficiently large such that the statistical analysis has a high degree of confidence that the bias plus bias uncertainty (calculational margin) has been accurately quantified. A complication arises because many benchmark experiments share common components, leading to correlations in their measured effective multiplication factors. Correlations between benchmark experiments within the population reduces its predictive power. This motivates the need for methods that consider benchmark experiment correlations and ensure adequate statistical significance of results. The Whisper code is a statistical analysis pack- age that incorporates nuclear data sensitivity coefficients from MCNP to assess benchmark experiment similarity and then performs an extreme-value analysis to estimate the bias plus bias uncertainty. The original methodology in Whisper does not consider the effect of benchmark experiment correlations when making this estimation, and this summary proposes the uniformly ordered binary decision algorithm to address this shortcoming. The original methodology in Whisper computes similarity coefficients ck for an application compared to all benchmark experiments in its library and develops weighting factors for a selected population proportional to the ck values. The methodology can be interpreted as statistically emulating a validation exercise for a particular application where the weighting factors may be viewed as the likelihood that an analyst would include a particular benchmark experiment within the population. The effective sample size of the population is the expected or mean number of benchmark experiments in the population. The uniformly ordered binary decision algorithm identifies clusters of correlated benchmark experiments within the population and then computes adjusted weighting factors based on the magnitude of the correlation coefficients within the cluster to compute a reduced effective sample size accounting for the lower information content because of correlations. Benchmark experiments within the cluster are ordered randomly with equal probability and probabilistic decisions are made as to whether a benchmark. experiment within the cluster should treated as redundant with a previous one; if two redundant benchmark experiments are included, then the conservative worst case bias plus bias uncertainty is used and the pair is counted as a single benchmark experiment in the population. Results are provided for HEU solutions in a research version of the Whisper software using benchmark experiment correlations provided by DICE, the Database for the International Criticality Safety Benchmark Evaluation Project (ICSBEP). These show that there can be a significant increase in the bias plus bias uncertainty because the effective sample size is reduced, and therefore the algorithm, needing to meet sample size requirements, expands the benchmark experiment population by accepting less similar benchmark experiments that would have otherwise not been included.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Software Dependability for Digital Instrumentation and Control Systems in Nuclear Power Plants - Lessons Learnt from a DOE Sponsored Project

This paper discusses the lessons learnt from a sponsored study undertaken under the sponsorship of the Department of Energy by a team of scientists at the Ohio State University in collaboration with Technology Resources and experts around the world. This paper makes recommendations for future research and studies based on these lessons learnt. The purpose of the research was to provide a software dependability quantification framework that would allow its evaluation along the software development life cycle for safety critical instrumentation and control systems (I and C) such as those found in nuclear power plants. A typical example of safety critical system is the reactor protection system. The research funded by the Department of Energy built on preliminary research carried out for the US NRC that had focused solely on software reliability quantification. Quantification of software dependability is important for safety critical I and C because the regulatory framework in use in the United States for nuclear power plants is risk informed. Quantification of risk requires quantification of all contributors to risk and those include instrumentation and control systems. The purpose of the study was to help developers of software-based I and C with an early evaluation of the potential risk an application would represent at different stages of the software development life cycle by building gates at the end of each life cycle phase. Life cycle phases of software development comprehend phases such as requirements, design, coding and test. The gates' function would be to stop development from moving forward if the assessed dependability objective for that phase were not met. Gates thresholds were to be defined based on measurements collected during the life cycle phase under evaluation and phases that preceded it and an understanding of the mechanisms that would lead to threatening the dependability objectives. The information contained in the gates would in addition help steer the development towards areas that needed improvement. The following are four high level conclusions to our study. First the study demonstrates a lack of consensus on mechanisms that will threaten the dependability attributes. This lack of consensus should be resolved. The lack of consensus appears for all measures to the exception of reliability. Second, measures should be developed for software availability and safety. Third, for all dependability attributes (with the exception of reliability) consistency of the measurement threads should evaluated and measurement-based development gates derived. Finally our ability to perform such type of research depends in a significant manner on access to vendor and/or utility data. The licensing environment and the first-of-a-kind nature of current software-based applications for nuclear I and C make it difficult to collect the relevant data. An approach which would either increase access to data by providing 'immunity' to the vendor or utility or the development of a software-based I and C for the sole purpose of data collection for research should be investigated. (authors)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

$χ$-$MeRA$: Computationally efficient adaptive mesh refinement of Monte Carlo mesh based tallies

Here, the reactor physics community is always focused on reducing the computational time and memory required for simulations. $χ$-$MeRA$, which stands for flux-based-($χ$)-Mesh tally Refinement Adaptively, was built to reduce the computational time and memory required to solve the neutronics side of a multiphysics problem when compared to traditional methods for mesh based tallies in Monte Carlo (MC) simulations. $χ$-$MeRA$ couples a MC code with an adaptive mesh refinement (AMR) algorithm to take advantage of the accuracy of a MC code and the efficiency of an AMR algorithm. Also developed within $χ$-$MeRA$ was a set of metrics to assess the effects of the refinement on various parameters in the simulation space. For a plutonium sphere, $χ$-$MeRA$ shows a reduction in memory usage and computation time when compared to a fully refined mesh by a factor of 14.7 and 6.7, respectively. When compared to an unstructured mesh, improvement of 1.3 and 4.8 was achieved for memory usage and computation time. The development of $χ$-$MeRA$ helps solve the neutronics side of a multiphysics problem in a faster, more computationally efficient manner than traditional methods, and the final mesh created contains accurate results that can be passed onto the next physics code.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Updated Economic Model for Estimation of GDP Losses in the MACCS Offsite Consequence Analysis Code RDEIM Model Report for MACCS v4.2

This report updates the Regional Disruption Economic Impact Model (RDEIM) GDP-based model described in Bixler et al. (2020) used in the MACCS accident consequence analysis code. MACCS is the U.S. Nuclear Regulatory Commission (NRC) used to perform probabilistic health and economic consequence assessments for atmospheric releases of radionuclides. It is also used by international organizations, both reactor owners and regulators. It is intended and most commonly used for hypothetical accidents that could potentially occur in the future rather than to evaluate past accidents or to provide emergency response during an ongoing accident. It is designed to support probabilistic risk and consequence analyses and is used by the NRC, U.S. nuclear licensees, the Department of Energy, and international vendors, licensees, and regulators. The update of the RDEIM model in version 4.2 expresses the national recovery calculation explicitly, rather than implicitly as in the previous version. The calculation of the total national GDP losses remains unchanged. However, anticipated gains from recovery are now allocated across all the GDP loss types – direct, indirect, and induced – whereas in version 4.1, all recovery gains were accounted for in the indirect loss type. To achieve this, we’ve introduced new methodology to streamline and simplify the calculation of all types of losses and recovery. In addition, RDEIM includes other kinds of losses, including tangible wealth. This includes loss of tangible assets (e.g., depreciation) and accident expenditures (e.g., decontamination). This document describes the updated RDEIM economic model and provides examples of loss and recovery calculation, results analysis, and presentation. Changes to the tangible cost calculation and accident expenditures are described in section 2.2. The updates to the RDEIM input-output (I-O) model are not expected to affect the final benchmark results Bixler et al. (2020), as the RDEIM calculation for the total national GDP losses remains unchanged. The reader is referred to the MACCS revision history for other cost modelling changes since version 4.0 that may affect the benchmark. RDEIM has its roots in a code developed by Sandia National Laboratories for the Department of Homeland Security to estimate short-term losses from natural and manmade accidents, called the Regional Economic Accounting analysis tool (REAcct). This model was adapted and modified for MACCS. It is based on I-O theory, which is widely used in economic modeling. It accounts for direct losses to a disrupted region affected by an accident, indirect losses to the national economy due to disruption of the supply chain, and induced losses from reduced spending by displaced workers. RDEIM differs from REAcct in in its treatment and estimation of indirect loss multipliers, elimination of double-counting associated with inter-industry trade in the affected area, and that it is intended to be used for extended periods that can occur from a major nuclear reactor accident, such as the one that occurred at the Fukushima Daiichi site in Japan. Most input-output models do not account for economic adaptation and recovery, and in this regard RDEIM differs from its parent, REAcct, because it allows for a user-definable national recovery period. Implementation of a recovery period was one of several recommendations made by an independent peer review panel to ensure that RDEIM is state-of-practice. For this and several other reasons, RDEIM differs from REAcct.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Partially coherent wavefront propagation simulations: Mirror and monochromator crystal quality assessment

We have applied fully-and partially-coherent synchrotron radiation wavefront propagation simulations, implemented in the “Synchrotron Radiation Workshop” (SRW) computer code, to analyse the effects of imperfect mirrors and monochromator at the Coherent Hard X-ray beamline. This beamline is designed for X-ray Photon Correlation Spectroscopy, a technique that heavily relies on the partial coherence of the X-ray beam and benefits from a careful preservation of the X-ray wavefront. We present simulations and a comparison with the measured beam profile at the sample position, which show the impact of imperfect optics on the wavefront.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Assessing Occupant and Outdoor Air Impacts on Indoor Air Quality in New California Homes

In 2008 the State of California adopted new building codes that required the use of mechanical ventilation systems in homes that meet the requirements of ASHRAE Standard 62.2. The standard requires both a dwelling unit mechanical ventilation system and exhaust fans in kitchens and bathrooms. A field study was undertaken to evaluate the IAQ and ventilation performance of homes built to these requirements. For ventilation system performance, the airflows of all mechanical ventilation systems were measured and their use was monitored for a one-week period. To evaluate IAQ, key pollutants were measured indoors and outdoors during the week, and occupants completed satisfaction surveys. The key pollutants included: formaldehyde, humidity, PM2.5 and NO2. Passive samplers were used to determine average concentrations for the week. Active samplers were used to develop time-series results that can be used to correlate pollutant concentrations with occupant activities. Other ventilation/IAQ related parameters were also recorded, such as stove top temperatures to indicate cooking, exterior door contact switches to know when large openings were being used for ventilation and sensors to determine when clothes dryers were being used. The building envelope and duct leakage were measured to enable estimates of infiltration and duct leakage effects. This paper presents an overview of the test procedures and preliminary results from several homes. The results show that although average concentrations may be reasonable compared to available standards (with the exception of formaldehyde), occupants have a strong impact on pollutant variability and source strength and that outdoor concentrations cannot be ignored. Overall, these mechanically ventilated homes have reasonable IAQ. The homes and duct systems are moderately tight, though not excessively so, by US standards. Significant concerns have been expressed regarding compliance with the ventilation requirements in the California building code. However, almost all the ventilation systems in this study complied with the ventilation air flow requirements and on average were significantly higher than the minimum required air flow rates.

Walker, IS↗

Robust verification of stochastic simulation codes

We introduce a robust verification tool for computational codes, which we call Stochastic Robust Extrapolation based Error Quantification (StREEQ). Unlike the prevalent Grid Convergence Index (GCI) [1] method, our approach is suitable for both stochastic and deterministic computational codes and is generalizable to any number of discretization variables. Building on ideas introduced in the Robust Verification [2] approach, we estimate the converged solution and orders of convergence with uncertainty using multiple fits of a discretization error model. In contrast to Robust Verification, we perform these fits to many bootstrap samples yielding a larger set of predictions with smoother statistics. Here, bootstrap resampling is performed on the lack-of-fit errors for deterministic code responses, and directly on the noisy data set for stochastic responses. This approach lends a degree of robustness to the overall results, capable of yielding precise verification results for sufficiently resolved data sets, and appropriately expanding the uncertainty when the data set does not support a precise result. For stochastic responses, a credibility assessment is also performed to give the analyst an indication of the trustworthiness of the results. Furthermore, this approach is suitable for both code and solution verification, and is particularly useful for solution verification of high-consequence simulations..

97 MATHEMATICS AND COMPUTING↗