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DOE OSTI2018

Combining Push-Forward Measures and Bayes' Rule to Construct Consistent Solutions to Stochastic Inverse Problems

We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data on quantities of interest. The solution, given as a probability measure, is derived using a Bayesian updating approach for measurable maps that finds a posterior probability measure, that when propagated through the deterministic model produces a push-forward measure that exactly matches the observed probability measure on the data. Our approach for finding such posterior measures, which we call consistent Bayesian inference or push-forward based inference, is simple and only requires the computation of the push-forward probability measure induced by the combination of a prior probability measure and the deterministic model. We establish existence and uniqueness of observation-consistent posteriors and present both stability and error analyses. We also discuss the relationships between consistent Bayesian inference, classical/statistical Bayesian inference, and a recently developed measure-theoretic approach for inference. Finally, analytical and numerical results are presented to highlight certain properties of the consistent Bayesian approach and the differences between this approach and the two aforementioned alternatives for inference.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Software Control Program For Transportable Microgrid State-of-charge Balancing And Frequency Stability Controls

A deterministic state-of-charge (SOC) balancing approach software control code is introduced as an integral secondary management to primary control layer of an islanded small microgrid or nanogrid system made up of multiple grid-forming inverter/battery/solar combination systems, where each set of batteries with each inverter are on independent DC buses (i.e. non-paralleled on the DC sides). A DERMS-level control approach, algorithm and automation controller program was developed to improve coordination and enable microgrid asset compliance and SOC balancing, enabling provision of a system-level power stability support architecture, load support, and asset scalability. The architecture is configured to treat each unit or micro/nano-grid as a node in a microgrid network, allowing for autonomous DERMS control regarding load and SOC balancing and power stability. As the network grows with the addition of units, greater coordination efforts may be required. The ideal small network microgrid ranges from 2-10 inverter/battery units before additional control parameters must be considered in the existing architecture. The control approach focuses on a deterministic state-of-charge analysis as the primary level control process followed by a secondary control loop using a forced frequency-watt droop strategy to conform off-the-shelf components into behaving under a leader-follower configuration. Adopting this control scheme has been shown to allow for a balanced, unit-coordinated microgrid network, enabling stable power flow. The deterministic state-of-charge approach is introduced as an integral primary control layer of an islanded small network microgrid. A standard strategy for SOC balancing is implementing a battery management system (BMS) to control SOC on the DC side. An alternative approach is to determine how to coordinate sending and receiving power on the AC side with multiple units. The latter approach assesses all the integrated units in the microgrid network. Once the individual units are identified, further system data is required to calculate each unit's total kWh, provided information about its capability to supply or consume kWh and availability. The secondary control layer in the multi-layered small network microgrid methodology uses the primary layer’s decision to initiate frequency setpoint changes, initializing the SOC balancing. The secondary control layer considers numerous system-dependent variables to enable a charging and discharging profile based on adjustable frequency setpoints. The combined architecture will result in stable, coordinated power flow enhancing an AC microgrid's functionalities.

Myers, KurtS [Idaho National Laboratory (INL), Ida↗

DOE OSTI2023

Robustness of the Stochastic Parameterization of Subgrid-Scale Wind Variability in Sea Surface Fluxes

Abstract High-resolution numerical models have been used to develop statistical models of the enhancement of sea surface fluxes resulting from spatial variability of sea surface wind. In particular, studies have shown that flux enhancement is not a deterministic function of the resolved state. Previous studies focused on single geographical areas or used a single high-resolution numerical model. This study extends the development of such statistical models by considering six different high-resolution models, four different geographical regions, and three different 10-day periods, allowing for a systematic investigation of the robustness of both the deterministic and stochastic parts of the data-driven parameterization. Results indicate that the deterministic part, based on regressing the unresolved normalized flux onto resolved-scale normalized flux and precipitation, is broadly robust across different models, regions, and time periods. The statistical features of the stochastic part of the model (spatial and temporal autocorrelation and parameters of a Gaussian process fit to the regression residual) are also found to be robust and not strongly sensitive to the underlying model, modeled geographical region, or time period studied. Best-fit Gaussian process parameters display robust spatial heterogeneity across models, indicating potential for improvements to the statistical model. These results illustrate the potential for the development of a generic, explicitly stochastic parameterization of sea surface flux enhancements dependent on wind variability.

Endo, Kota↗

DOE OSTI2014

FW-CADIS Method for Global and Regional Variance Reduction of Monte Carlo Radiation Transport Calculations

This paper presents a hybrid (Monte Carlo/deterministic) method for increasing the efficiency of Monte Carlo calculations of distributions, such as flux or dose rate distributions (e.g., mesh tallies), as well as responses at multiple localized detectors and spectra. This method, referred to as Forward-Weighted CADIS (FW-CADIS), is an extension of the Consistent Adjoint Driven Importance Sampling (CADIS) method, which has been used for more than a decade to very effectively improve the efficiency of Monte Carlo calculations of localized quantities (e.g., flux, dose, or reaction rate at a specific location). The basis of this method is the development of an importance function that represents the importance of particles to the objective of uniform Monte Carlo particle density in the desired tally regions. Implementation of this method utilizes the results from a forward deterministic calculation to develop a forward-weighted source for a deterministic adjoint calculation. The resulting adjoint function is then used to generate consistent space-and energy-dependent source biasing parameters and weight windows that are used in a forward Monte Carlo calculation to obtain more uniform statistical uncertainties in the desired tally regions. The FW-CADIS method has been implemented and demonstrated within the MAVRIC (Monaco with Automated Variance Reduction using Importance Calculations) sequence of SCALE and the ADVANTG (Automated Deterministic Variance Reduction Generator)/MCNP framework. Application of the method to representative real-world problems, including calculation of dose rate and energy-dependent flux throughout the problem space, dose rates in specific areas, and energy spectra at multiple detectors, is presented and discussed. Results of the FW-CADIS method and other recently developed global variance-reduction approaches are also compared, and the FW-CADIS method outperformed the other methods in all cases considered.

Wagner, John C↗

DOE OSTI2022

On-the-fly response function generation method for composite coarse mesh

The hybrid stochastic deterministic transport code COMET, based on the incident response expansion theory, is used to model reactor cores with high fidelity and formidable computational speed. COMET models a reactor core using a library of incident flux response expansion coefficients that are pre computed for all the unique lattice cells (e.g., fuel assemblies, reflector blocks, etc.) in the core. In order to further improve its computational efficiency in pre-calculating the response library a new response function generation method is developed to compute the response functions for the composite coarse meshes made of a smaller set of unique lattices on the fly within the COMET's deterministic transport core sweep. The efficiency is achieved by eliminating a number of unique lattices that can be made up from the reduced set of unique meshes on the fly. The numerical process consists of the following steps. First, the boundary condition on composite coarse mesh boundaries is projected onto the expansion basis to compute the incident flux moments on external surfaces of all the basic (reduced set of unique) coarse meshes. Secondly, the deterministic sweeping solver in COMET is used to converge on the outgoing/incoming flux expansion moments crossing interfaces between the basic coarse meshes. Thirdly, the response functions for the composite coarse meshes are constructed as a superposition on the fly. The new response function generation method was tested on 88 composite coarse meshes consisting of CANDU fuel bundles and moderator blocks. It was found that response functions generated by the new method agree very well with those generated by direct Monte Carlo calculations. The average and maximum relative differences in the surface-to-surface response coefficients computed by the two methods are 0.10% and 0.20%, respectively. Similarly, the average and maximum relative differences in the response fission densities are 0.13% and 0.43%, respectively. These discrepancies are within one standard deviation of the stochastic uncertainties. The new method is five times faster than the original direct Monte Carlo method. The size of the response function library for the new method is five times smaller than that for the original method, leading to significantly less requirement for the computer hard drive space and memory. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2011

Hybrid and Parallel Domain-Decomposition Methods Development to Enable Monte Carlo for Reactor Analyses

This paper describes code and methods development at the Oak Ridge National Laboratory focused on enabling high-fidelity, large-scale reactor analyses with Monte Carlo (MC). Current state-of-the-art tools and methods used to perform real commercial reactor analyses have several undesirable features, the most significant of which is the non-rigorous spatial decomposition scheme. Monte Carlo methods, which allow detailed and accurate modeling of the full geometry and are considered the gold standard for radiation transport solutions, are playing an ever-increasing role in correcting and/or verifying the deterministic, multi-level spatial decomposition methodology in current practice. However, the prohibitive computational requirements associated with obtaining fully converged, system-wide solutions restrict the role of MC to benchmarking deterministic results at a limited number of state-points for a limited number of relevant quantities. The goal of this research is to change this paradigm by enabling direct use of MC for full-core reactor analyses. The most significant of the many technical challenges that must be overcome are the slow, non-uniform convergence of system-wide MC estimates and the memory requirements associated with detailed solutions throughout a reactor (problems involving hundreds of millions of different material and tally regions due to fuel irradiation, temperature distributions, and the needs associated with multi-physics code coupling). To address these challenges, our research has focused on the development and implementation of (1) a novel hybrid deterministic/MC method for determining high-precision fluxes throughout the problem space in k-eigenvalue problems and (2) an efficient MC domain-decomposition (DD) algorithm that partitions the problem phase space onto multiple processors for massively parallel systems, with statistical uncertainty estimation. The hybrid method development is based on an extension of the FW-CADIS method, which attempts to achieve uniform statistical uncertainty throughout a designated problem space. The MC DD development is being implemented in conjunction with the Denovo deterministic radiation transport package to have direct access to the 3-D, massively parallel discrete-ordinates solver (to support the hybrid method) and the associated parallel routines and structure. This paper describes the hybrid method, its implementation, and initial testing results for a realistic 2-D quarter core pressurized-water reactor model and also describes the MC DD algorithm and its implementation.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2012

Notes on the Lumped Backward Master Equation for the Neutron Extinction/Survival Probability

The expected or mean neutron number (or density) provides an adequate characterization of the neutron population and its dynamical excursions in most neutronic applications, in particular power reactors. Fluctuations in the neutron number, originating from the inherent randomness of neutron interactions and fission neutron multiplicities, are relatively small and ignorable for operational purposes, although measurements of the variance and time correlations provide valuable diagnostic information on fundamental reactor physics parameters. However, it is well known that there exist situations of great interest and importance in which a strictly deterministic description, or even one supplemented with a knowledge of low order statistical averages (variance, correlation), provides an incomplete and very unsatisfactory description of the state of the neutron population. These situations are marked by persistent large fluctuations in the neutron number where the emergence of a deterministic phase is suppressed. Such situations are strongly stochastic and therefore unpredictable (i.e., the mean is not representative of the actual population), and can arise either by design or by accident. Examples where the stochastic behavior of neutron populations must be taken into account include: nuclear weapon single-point safety assessment; criticality excursions in spent fuel storage and in the handling of fissile solutions in fuel fabrication and reprocessing; approach to critical under suboptimal reactor start-up conditions; preinitiation in fast burst research reactors; and weak nuclear signatures in the passive detection of nuclear materials. What distinguishes strongly stochastic neutronic systems from strongly deterministic systems is that, in the former, neutron multiplication occurs in the presence of weak neutron sources, such as spontaneous fission and background (cosmic) radiation. Weak sources (in a sense that can be made quite precise) lead to well separated fission chains (a fission chain is defined as the initial source neutron and all its subsequent progeny) in which some chains are short lived while others propagate for unusually long times. Under these conditions, fission chains do not overlap strongly and this precludes the cancellation of neutron number fluctuations necessary for the mean to become established as the dominant measure of the neutron population. The fate of individual chains then plays a defining role in the evolution of the neutron population in strongly stochastic systems, and of particular interest and importance in supercritical systems is the extinction probability, defined as the probability that the neutron chain (initiating neutron and its progeny) will be extinguished at a particular time, or its complement, the time-dependent survival probability. The time-asymptotic limit of the latter, the probability of divergence, gives the probability that the neutron population will grow without bound, and is more commonly known as the probability of initiation or just POI. The ability to numerically compute these probabilities, with high accuracy and without overly restricting the underlying physics (e.g., fission neutron multiplicity, reactivity variation) is clearly essential in developing an understanding of the behavior of strongly stochastic systems.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2012

Consistent Adjoint Driven Importance Sampling using Space, Energy and Angle

For challenging radiation transport problems, hybrid methods combine the accuracy of Monte Carlo methods with the global information present in deterministic methods. One of the most successful hybrid methods is CADIS Consistent Adjoint Driven Importance Sampling. This method uses a deterministic adjoint solution to construct a biased source distribution and consistent weight windows to optimize a specific tally in a Monte Carlo calculation. The method has been implemented into transport codes using just the spatial and energy information from the deterministic adjoint and has been used in many applications to compute tallies with much higher figures-of-merit than analog calculations. CADIS also outperforms user-supplied importance values, which usually take long periods of user time to develop. This work extends CADIS to develop weight windows that are a function of the position, energy, and direction of the Monte Carlo particle. Two types of consistent source biasing are presented: one method that biases the source in space and energy while preserving the original directional distribution and one method that biases the source in space, energy, and direction. Seven simple example problems are presented which compare the use of the standard space/energy CADIS with the new space/energy/angle treatments.

Peplow, Douglas E.↗

DOE OSTI2014

A Comprehensive Evaluation of Robust Unit Commitment

This report summarizes the procedure to compare the robust UC approach with the deterministic counterpart. The procedure involves solving the robust and deterministic UC problems under various scenario configurations, and then performing system dispatch simulations under each UC solution to generate economic and operational performance measures. The report describes the parallelization process for solving UC problems as well as for running system dispatch simulations. The report also summarizes the statistical model used for generating Monte Carlo simulation samples and forming forecast ranges used in the robust UC approach. Some key findings are discussed as well. In particular, the economic and operational performance of the robust and deterministic approaches is compared under different 1) conservatism levels or the sizes of forecast range, 2) the wind penetration levels, and 3) the mixture of load and wind behaviors.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2016

Systematic Evaluation of Stochastic Methods in Power System Scheduling and Dispatch with Renewable Energy

As more wind power and other renewable resources are being integrated into the electric power grid, the forecast uncertainty brings operational challenges for the power system operators. In this report, different operational strategies for uncertainty management are presented and evaluated. A comprehensive and consistent simulation framework is developed to analyze the performance of different reserve policies and scheduling techniques under uncertainty in wind power. Numerical simulations are conducted on a modified version of the IEEE 118-bus system with a 20% wind penetration level, comparing deterministic, interval, and stochastic unit commitment strategies. The results show that stochastic unit commitment provides a reliable schedule without large increases in operational costs. Moreover, decomposition techniques, such as load shift factor and Benders decomposition, can help in overcoming the computational obstacles to stochastic unit commitment and enable the use of a larger scenario set to represent forecast uncertainty. In contrast, deterministic and interval unit commitment tend to give higher system costs as more reserves are being scheduled to address forecast uncertainty. However, these approaches require a much lower computational effort Choosing a proper lower bound for the forecast uncertainty is important for balancing reliability and system operational cost in deterministic and interval unit commitment. Finally, we find that the introduction of zonal reserve requirements improves reliability, but at the expense of higher operational costs.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2019

(U) Differences in the Use of Isotopic $χ$ Vectors Demonstrated with an Analytic k ∞ Problem (And Verification of SENSMG and MCNP6’s KSEN)

Comparisons of responses and first-order sensitivities of responses to the neutron fission spectrum ( χ ) have been done using different transport methods. Kodeli and Slavič compared sensitivities from Monte Carlo, deterministic, and method of characteristics of k eff in the SNEAK-7 benchmark, and the agreement was reasonable. Yamamoto compared deterministic and Monte Carlo sensitivities of k - and α -eigenvalues to the fission χ , but only for material (i.e. single-isotope) values of the fission χ . Haeck et al. compared Monte Carlo and deterministic sensitivities of k eff to the fission χ of individual isotopes for several benchmarks, and the agreement was excellent (except, strangely, for U-236). Kiedrowski and Brown compared Monte Carlo and analytic sensitivities of k ∞ to the fission χ in analytic problems, but only for material values of the fission χ .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Command of active and responsive elastomers by topological defects and patterns

The project resulted in the development of stimuli-responsive elastomer coatings formed by photopolymerized liquid crystal molecules. The molecular orientation of the liquid crystal elastomers is coupled to rubber-like elasticity. The project developed an approach to produce complex patterns of molecular orientation in elastomers by employing photopatterning technique based on plasmonic metamasks that convert unpolarized incoming light into a transmitted light beam with spatially-varying linear polarization. The polarization-modulated light beam aligns the film of azodye molecules, which serves as the substrate for liquid crystal elastomer coating. The alignment of the azodye molecules follows the polarization pattern with a phase shift of the alignment direction by 90 degrees. The azodye substrate imposes orientation of molecules in the adjacent liquid crystal layer which is preserved after the monomers are polymerized into a liquid crystal elastomer. By using differently aligned substrates one could produce various patterns of molecular orientation in the elastomer, which dictate the mechanical properties of the elastomers and their response to external stimuli such as temperature, humidity, and ultraviolet irradiation. In particular, the predesigned molecular orientation produces deterministically defined topography response of the liquid crystal coatings, in which their free surface changes from flat to either locally elevated or locally compressed, depending on whether the pre-inscribed molecular orientation is predesigned with a splay or bend deformation. The research established that the mechanism of this deterministic relation between the dynamic topography and pre-inscribed molecular orientation is rooted in the change of the tensorial order parameter that characterizes the degree of orientational order, and in the contraction/expansion of polymer molecules in response to the order parameter changes. In particular, lowering the order causes contraction of polymer globules. The work demonstrated that the dynamic topography of elastomer coatings with three-dimensional pattern of orientational order includes up and down motion of the material (along the normal to the coating) and also shifts in lateral directions. We demonstrate that the deterministic relationship between the orientational patterns and variations of coatings’ profile is caused by forces that are mathematically equivalent to active forces in the system of “pullers” or “pushers” in active matter, demonstrating universality of the out-of-equilibrium behavior. The project resulted in theoretical models that predictively describe the dynamic response of coatings. The topography of liquid crystal elastomers is sensitive to stimuli such as temperature, ultraviolet irradiation, and humidity. The applicability of the patterned approach to produce dynamic coatings was expanded from nematic elastomers to their smectic counterparts. The project combined a battery of imaging techniques to unveil the dynamic properties of the coatings, ranging from the state-of-the-art dynamic holographic microscopy to fluorescent confocal polarizing microscopy and polscope microscopy. The research uncovered potential applications of dynamic elastomer coatings, such as control placement of colloidal particles, engineering of living tissues with alignment patterns of cells that follow the orientational order of elastomer coatings. The approach developed in the project can be used to design programmable dynamic coatings with functionalities that mimic biological tissues such as skin.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Wind Turbine Rotor Design Optimization Using Importance Sampling: Preprint

Probabilistic methods are commonly adopted to estimate both ultimate and fatigue loads in wind turbines, and multiple papers have presented a variety of approaches. In contrast, system-level, integrated design optimization methods for wind turbines have so far relied on deterministic methods to estimate loads and deflections. This work aims at addressing this gap by adopting importance sampling to estimate ultimate blade deflection for use within a rotor design optimization. A comparison between the results of this approach against traditional approaches using deterministic load evaluations show that the probabilistic approach is more conservative and that the solutions found with deterministic approaches violate the probabilistic constraint on tip deflection between 13% and 17%. This highlights the importance of accurate load and deflection estimates and demonstrates that probabilistic approaches can be successfully integrated within a wind turbine design process despite the higher computational costs.

17 WIND ENERGY↗

DOE OSTI2016

Application of Hybrid Genetic Algorithm Routine in Optimizing Food and Bioengineering Processes

Optimization is a crucial step in the analysis of experimental results. Deterministic methods only converge on local optimums and require exponentially more time as dimensionality increases. Stochastic algorithms are capable of efficiently searching the domain space, however convergence is not guaranteed. This article demonstrates the novelty of hybrid genetic algorithm which combines both stochastic and deterministic routine for improved optimization results. A new hybrid genetic algorithm developed is applied to the Ackley benchmark function as well as case studies in foods, biofuels, and biotechnology processes. For each case study the hybrid genetic algorithm found a better optimum candidate than reported by the sources. In the case of food processing the hybrid genetic predicted 5% higher anthocyanin yield. Optimization of bio-oil production using HGA resulted in a 4.73 % higher yield. In enzyme production process HGA predicted 2.18 IU/gds of higher xylanase yield. In conclusion, hybridization of genetic algorithm with a deterministic algorithm resulted in maximum optimum compared to the statistical methods.

09 BIOMASS FUELS↗

DOE OSTI2016

STOCHASTIC OPTICS: A SCATTERING MITIGATION FRAMEWORK FOR RADIO INTERFEROMETRIC IMAGING

Just as turbulence in the Earth’s atmosphere can severely limit the angular resolution of optical telescopes, turbulence in the ionized interstellar medium fundamentally limits the resolution of radio telescopes. We present a scattering mitigation framework for radio imaging with very long baseline interferometry (VLBI) that partially overcomes this limitation. Our framework, “stochastic optics,” derives from a simplification of strong interstellar scattering to separate small-scale (“diffractive”) effects from large-scale (“refractive”) effects, thereby separating deterministic and random contributions to the scattering. Stochastic optics extends traditional synthesis imaging by simultaneously reconstructing an unscattered image and its refractive perturbations. Its advantages over direct imaging come from utilizing the many deterministic properties of the scattering—such as the time-averaged “blurring,” polarization independence, and the deterministic evolution in frequency and time—while still accounting for the stochastic image distortions on large scales. These distortions are identified in the image reconstructions through regularization by their time-averaged power spectrum. Using synthetic data, we show that this framework effectively removes the blurring from diffractive scattering while reducing the spurious image features from refractive scattering. Stochastic optics can provide significant improvements over existing scattering mitigation strategies and is especially promising for imaging the Galactic Center supermassive black hole, Sagittarius A*, with the Global mm-VLBI Array and with the Event Horizon Telescope.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Neutrino Transport with Monte Carlo Method. I. Toward Fully Consistent Implementation of Nucleon Recoils in Core-collapse Supernova Simulations

The small energy exchange via nucleon recoils in neutrino–nucleon scattering is now supposed to be one of the important factors for successful explosions of core-collapse supernovae (CCSNe), as they can change neutrino spectra through accumulation of a large number of scatterings. In deterministic methods employed for neutrino transport in CCSN simulations, we normally cannot afford to deploy a large enough number of energy bins needed to resolve this small energy exchange, and subgrid techniques are employed one way or another. In this paper, we study quantitatively with the Monte Carlo (MC) method how well such a treatment performs. We first investigate the effects of nucleon recoils on the neutrino spectra and confirm that the average energy is reduced by ~15% for heavy-lepton neutrinos and much smaller amounts for other types of neutrinos in a typical postbounce situation. It is also observed that the nucleon scattering dominates the electron scattering in the thermalization of neutrino spectra in all flavors. We then study possible artifacts that the coarse energy grid may produce in the deterministic methods. In order to mimic the latter calculation, we redistribute MC particles in each energy bin after a certain interval in a couple of ways and study how the results are affected, depending on the energy resolution. We also discuss the possible implications of our results for the deterministic methods.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2012

Methods for Detector Placement and Analysis of Criticality Accident Alarm Systems

Determining the optimum placement to minimize the number of detectors for a criticality accident alarm system (CAAS) in a large manufacturing facility is a complex problem. There is typically a target for the number of detectors that can be used over a given zone of the facility. A study to optimize detector placement typically begins with some initial guess at the placement of the detectors and is followed by either predictive calculations of accidents at specific locations or adjoint calculations based on preferred detector locations. Within an area of a facility, there may be a large number of potential criticality accident sites. For any given placement of the detectors, the list of accident sites can be reduced to a smaller number of locations at which accidents may be difficult for detectors to detect. Developing the initial detector placement and determining the list of difficult accident locations are both based on the practitioner's experience. Simulations following fission particles released from an accident location are called 'forward calculations.' These calculations can be used to answer the question 'where would an alarm be triggered?' by an accident at a specified location. Conversely, 'adjoint calculations' start at a detector site using the detector response function as a source and essentially run in reverse. These calculations can be used to answer the question 'where would an accident be detected?' by a specified detector location. If the number of accidents, P, is much less than the number of detectors, Q, then forward simulations may be more convenient and less time-consuming. If Q is large or the detectors are not placed yet, then a mesh tally of dose observed by a detector at any location must be computed over the entire zone. If Q is much less than P, then adjoint calculations may be more efficient. Adjoint calculations employing a mesh tally can be even more advantageous because they do not rely on a list of specific difficult-to-detect accident sites, which may not have included every possible accident location. Analog calculations (no biasing) simply follow particles naturally. For sparse buildings and line-of-sight calculations, analog Monte Carlo (MC) may be adequate. For buildings with internal walls or large amounts of heavy equipment (dense geometry), variance reduction may be required. Calculations employing the CADIS method use a deterministic calculation to create an importance map and a matching biased source distribution that optimize the final MC to quickly calculate one specific tally. Calculations employing the FW-CADIS method use two deterministic calculations (one forward and one adjoint) to create an importance map and a matching biased source distribution that are designed to make the MC calculate a mesh tally with more uniform uncertainties in both high-dose and low-dose areas. Depending on the geometry of the problem, the number of detectors, and the number of accident sites, different approaches to CAAS placement studies can be taken. These are summarized in Table I. SCALE 6.1 contains the MAVRIC sequence, which can be used to perform any of the forward-based approaches outlined in Table I. For analog calculations, MAVRIC simply calls the Monaco MC code. For CADIS and FW-CADIS, MAVRIC uses the Denovo discrete ordinates (SN) deterministic code to generate the importance map and biased source used by Monaco. An adjoint capability is currently being added to Monaco and should be available in the next release of SCALE. An adjoint-based approach could be performed with Denovo alone - although fine meshes, large amounts of memory, and long computation times may be required to obtain accurate solutions. Coarse-mesh SN simulations could be employed for adjoint-based scoping studies until the adjoint capability in Monaco is complete. CAAS placement studies, especially those dealing with mesh tallies, require some extra utilities to aid in the analysis. Detectors must receive a minimum dose rate in order to alarm; therefore, a simple yes/no plot could be more useful to the analyst than a standard dose rate contour plot. Alarm systems that require several detectors to alarm simultaneously for a given accident would need to combine several yes/no plots in order to show accident sites where multiple detectors would be triggered. This could require a plot of 'areas of coverage' that is mapped over the building geometry. Several new utilities (which will be part of SCALE 6.2) were created to help with CAAS analysis.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2012

Analysis Of Ductile Crack Growth In Pipe Test In STYLE Project

The Oak Ridge National Laboratory (ORNL) is conducting structural analyses, both deterministic and probabilistic, to simulate a large scale mock-up experiment planned within the European Network for Structural Integrity for Lifetime Management non-RPV Components (STYLE). The paper summarizes current ORNL analyses of STYLE s Mock-up3 experiment to simulate/evaluate ductile crack growth in a cladded ferritic pipe. Deterministic analyses of the large-scale bending test of ferritic surge pipe, with an internal circumferential crack, are simulated with a number of local micromechanical approaches, such as Gurson-Tvergaard-Needleman (GTN) model and cohesive-zone model. Both WARP 3D and ABAQUS general purpose finite element programs are being used to predict the failure load and the failure mode, i.e. ductile tearing or net-section collapse, as part of the pre-test phase of the project. Companion probabilistic analyses of the experiment are utilizing the ORNL developed open-source Structural Integrity Assessment Modular - Probabilistic Fracture Mechanics (SIAM-PFM) framework. SIAM-PFM contains engineering assessment methodology such as the tearing instability (J-T analysis) module developed for inner surface cracks under bending load. The driving force J-integral estimations are based on the SC.ENG1 or SC.ENG2 models. The J-A2 methodology is used to transfer (constraint-adjust) J-R curve material data from standard test specimens to the Mock-up3 experiment configuration. The probabilistic results of the Mock-Up3 experiment obtained from SIAM-PFM will be compared to those generated using the deterministic finite element modeling approach. The objective of the probabilistic analysis is to provide uncertainty bounds that will assist in assessing the more detailed 3D finite-element solutions and to also assess the level of confidence that can be placed in the best-estimate finite-element solutions.

99 GENERAL AND MISCELLANEOUS↗