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DOE OSTI2016

Estimation of neutron spectrum in the low-level gamma spectroscopy system using unfolding procedure

The radiation resulting from neutron interactions with Ge nuclei in active volume of HPGe detectors is one of the main concerns in low-level gamma spectroscopy measurements [1,2]. It is usually not possible to measure directly spectrum of neutrons which strike detector. This paper explore the possibility of estimation of neutron spectrum using measured activities of certain Ge(n,γ) and Ge(n,n’) reactions (obtained from low-level gamma measurements), available ENDF cross section data and unfolding procedures. In this work HPGe detector with passive shield made from commercial low background lead was used for the measurement. The most important objective of this study was to reconstruct muon induced neutron spectrum created in the shield of the HPGe detector. MAXED [3] and GRAVEL [4] algorithms for neutron spectra unfolding were used. The results of those two algorithms were compared and we analyzed the sensitivity of the unfolding procedure to the various input parameters.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Responses of two nonlinear microbial models to warming and increased carbon input

A number of nonlinear microbial models of soil carbon decomposition have been developed. Some of them have been applied globally but have yet to be shown to realistically represent soil carbon dynamics in the field. A thorough analysis of their key differences is needed to inform future model developments. In this paper, we compare two nonlinear microbial models of soil carbon decomposition: one based on reverse Michaelis–Menten kinetics (model A) and the other on regular Michaelis–Menten kinetics (model B). Using analytic approximations and numerical solutions, we find that the oscillatory responses of carbon pools to a small perturbation in their initial pool sizes dampen faster in model A than in model B. Soil warming always decreases carbon storage in model A, but in model B it predominantly decreases carbon storage in cool regions and increases carbon storage in warm regions. For both models, the CO 2 efflux from soil carbon decomposition reaches a maximum value some time after increased carbon input (as in priming experiments). This maximum CO 2 efflux (F max ) decreases with an increase in soil temperature in both models. However, the sensitivity of F max to the increased amount of carbon input increases with soil temperature in model A but decreases monotonically with an increase in soil temperature in model B. These differences in the responses to soil warming and carbon input between the two nonlinear models can be used to discern which model is more realistic when compared to results from field or laboratory experiments. Lastly, these insights will contribute to an improved understanding of the significance of soil microbial processes in soil carbon responses to future climate change.

58 GEOSCIENCES↗

NASA NTRS1991

CO fundamental bands in late-type stars. II - Spectrum simulations for F-K stars

The procedure of Ayres and Wiedemann (1989) was applied to a range of stellar-atmosphere models to study the CO Delta-v = 1 spectrum and to establish its use as a remote sensor of thermal conditions in late-type stars. Spectra were computed to examine the sensitivity of the CO Delta-v = 1 to fundamental stellar parameters and to assess the errors introduced into the spectrum intepretation by uncertain input parameters and non-LTE effects. Results of the sensitivity study demonstrate that CO fundamental spectra are useful probes for the temperature structure of the outer layers of cool stellar atmospheres, but that their value is limited by the uncertainties introduced by non-LTE effects. However, in stars with surface gravities of log g of about 1.5 and greater, the values of these uncertainties are reasonably small.

Wiedemann, Guenter↗

DOE OSTI2024

Steam Generator Model Design Parameter Sensitivity Study Using Advanced Optimization Tools

This study focuses on design parameter sensitivity studies pertaining to a steam generator (SG) model, using both Python and machine-learning tools. The SG model is a mathematical representation (including fluid flow and heat transfer equations/models/correlations) of a steam-generating unit in a pressurized water reactor (PWR)-type small modular reactor (SMR) system. Design studies involve changing the model’s input design parameters (e.g., temperature, pressure, mass flow rate) to observe the resulting effects on the output of the system (e.g., heat transfer coefficient [HTC], Nusselt number, heat transfer performance). Sensitivity studies analyze the degree to which system output and/or desired parameters (e.g., HTC or heat transfer performance) are sensitive to changes in input parameters. By using machine-learning tools such as the Risk Analysis Virtual Environment (RAVEN) developed at Idaho National Laboratory (INL), detailed design parametric sensitivity studies and model optimization were performed. Six input parameters—namely, the pressure, temperature, and mass flow rate for the inlet of the primary-side (hot fluid) and secondary-side (cold fluid) of the SG—were randomly perturbed via RAVEN’s Monte Carlo Sampler module, using uniform distributions (±1% relative changes). The analysis results give valuable insights into SG system performance and optimization, and provide justification for researching optimized sensor placement to effectively monitor and obtain experimental data.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2024

Steam Generator Model Design Parameter Sensitivity Study Using Advanced Optimization Tools

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2015

Modern sensitivity analysis - 15651

Sensitivity analysis has been applied to complex models, such as performance assessment models, since at least the advent of computational tools to support such an approach to model evaluation. Initially, sensitivity analysis methods were applied to deterministic models and focused on changing one input variable at a time. Probabilistic modeling opened the door to evaluating changes in all input variables simultaneously. Standardized rank regression methods were primarily used in the last century to evaluate probabilistic models. These methods assume linearity in the rank response of the model to the inputs. At the very least this assumes monotonicity in the response, but for the most part the response needs to be near-linear. This is highly unlikely for performance assessment models that are based on differential equations, multiplication and division of variables that are usually not correlated, and conservatism that is not well understood. There are better statistical methods for evaluating highly non-linear and dynamic probabilistic models. Some of these methods were founded in the data mining industry. This century has seen a rapid development of the internet that led directly to the development of data mining techniques for massive databases. Although the goals were different, these techniques can be adapted to sensitivity analysis for complex probabilistic models, which, also, form large, or even massive, databases. These modern sensitivity analysis procedures assess the importance of every explanatory variable (input parameters) used in a probabilistic model. In practice, this means that for each endpoint of interest, every explanatory variable in the model is associated with a quantitative measure of importance. For a given explanatory variable, the importance value depends on the endpoint of interest. This global approach to sensitivity analysis allows all levels of interactions to be evaluated, so that the variation in the output can be measured at every level of possible interaction. The effects are collected together during sensitivity analysis processing, and then separated out to attribute the overall contribution of each input parameter to the model output. These global sensitivity analysis procedures have the ability to characterize non-linear and non-monotonic relationships between explanatory variables and endpoints of interest. This is critically important because of the need to characterize complex interactions among multiple explanatory variables in PA models that often have non-linear and non-monotonic effects. The options for sensitivity analysis are fully explored, including an evaluation of several methods when applying them to a well-known complex non-linear non-monotonic model. The results clearly demonstrate the relative benefit of using data mining methods over simple statistical approaches such as standardized rank regression. (authors)

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1992

Experience of the JPL Exploratory Data Analysis Team at validating HIRS2/MSU cloud parameters

Validation of the HIRS2/MSU cloud parameters began with the cloud/climate feedback problem. The derived effective cloud amount is less sensitive to surface temperature for higher clouds. This occurs because as the cloud elevation increases, the difference between surface temperature and cloud temperature increases, so only a small change in cloud amount is needed to effect a large change in radiance at the detector. By validating the cloud parameters it is meant 'developing a quantitative sense for the physical meaning of the measured parameters', by: (1) identifying the assumptions involved in deriving parameters from the measured radiances, (2) testing the input data and derived parameters for statistical error, sensitivity, and internal consistency, and (3) comparing with similar parameters obtained from other sources using other techniques.

Kahn, Ralph↗

NASA NTRSDate not supplied

System Modeling of a Lunar Molten Regolith Electrolysis Plant

Introduction: In-Situ Resource Utilization (ISRU) is the process of extracting local resources to produce commodities for propulsion, life support systems, and off-planet construction rather than transporting consumables from Earth. Molten Regolith Electrolysis (MRE) is a novel ISRU method of extracting oxygen gas and metal alloy from lunar regolith. The MRE process involves placing lunar regolith between two electrodes, through which current is passed, to melt the regolith and reduce the metal oxide constituents by direct electrolysis (e.g. FeO, SiO2, MgO, Al2O3) into oxygen gas and metal alloys. The oxygen is liquefied and used as propellant for landers, while the metals (e.g. Ferro-alloys) are further processed and used in structural building materials and parts manufacturing. A system model was developed that accounted for the major processes of an MRE plant (from excavation of raw materials to storage of products) to assess the feasibility of a lunar MRE plant. The System Engineering and Integration (SE&I) ISRU Modeling and Analysis (SIMA) team utilized its previously documented system sizing model, the Mission Analysis and Integration Tool (MAIT) [1] as framework of the system model. MAIT uses MATLAB/Simulink to integrate subsystem models into a complete system model of the MRE plant. Total mass, volume, and power requirements were computed for numerous iterations of a MRE plant. System Model: Figure 1: MRE Plant Block Diagram The regolith excavation model determines the mass and power needed to excavate sufficient regolith. The preheating auger initiates the regolith heating process before regolith enters the MRE re-actor to reduce the energy required to turn the solid into a molten liquid. The MRE reactor is modeled in COMSOL Multiphysics and based on the research by Dominguez, Sibille, and Schreiner [2, 3, 4]. This preliminary reactor model provides an accurate calculation of thermal equilibrium during electrochemical operation of the reactor system to assess the optimal mass and power required to process the inlet flow of regolith. The model also computes the outlet flowrates of oxygen and molten products. For this analysis, the primary components of the metal alloy considered were iron and silicon. The oxygen is then purified using an Yttrium Stabilized Zirconia (YSZ) electrode, followed by liquefaction using a 90K cryocooler to be stored as liquid oxygen in insulated cylindrical tanks. In future iterations of the system model, the molten metal tapped from the MRE reactor will undergo additional processing or refinement. However, downstream handling of metals is currently a technology gap that is missing a high TRL subsystem model. Therefore, for this analysis, the accumulated metal alloy stream terminates after leaving the MRE reactor. Study Goals: This analysis investigates multiple input variables to the system to determine the sensitivity of a (near) complete plant at full-scale. This preliminary investigation ran parametric sweeps on the MRE reactor geometry, electrical current supply, layers of multi-layer insulation (MLI) on the reactor, size of the electrodes in the oxygen purification model, and regolith composition (based on landing site location). Three production targets of oxygen (1,000, 10,000, and 50,000 kg/yr) were investigated for this analysis. The parametric sweeps conducted in this analysis provide valuable insight into the expected impact of the various model inputs on plant size. This information can be used to identify the most critical components of the plant and guide future decisions on allocating funding for research and development, providing subsystem developers with appropriate interfaces with downstream and upstream processes, and assessing the overall feasibility of MRE when compared to other ISRU plants. References: [1] Carlson, A. et al. (2024) ICES, ICES-2024-53. [2] Dominguez, D.A., and Sibille, L. (2011) AIAA, AIAA-2011-700. [3] Schreiner, S.S. (2015) MIT, Dissertation. [4] Schreiner, S.S. et al. (2016) ASR, 57(7), pp.1585-1603.

ISRU↗

NASA NTRS1990

Distributed parameter estimation for large beam-like structures for general inputs

In this paper, maximum likelihood estimation for distributed parameter models of large flexible structures has been formulated. Distributed parameter models involve far fewer unknown parameters than independent modal characteristics of finite element models. The closed-form solutions for the partial differential equations with general forced inputs have been derived. The closed-form expressions of the sensitivity functions lead to highly efficient algorithms for analyzing ground or on-orbit test results. Numerical simulations with impulse and step inputs to the NASA Mini-MAST trust have been demonstrated. The estimations of modal properties involve its longitudinal elongation modes, lateral bending modes and torsional modes. The results show that distributed parameter models are promising in the parameter estimation of large flexible structures.

Shen, Ji-Yao↗

DOE OSTI2021

An extended polynomial chaos expansion for PDF characterization and variation with aleatory and epistemic uncertainties

This paper presents an extended polynomial chaos formalism for epistemic uncertainties and a new framework for evaluating sensitivities and variations of output probability density functions (PDF) to uncertainty in probabilistic models of input variables. An ”extended” polynomial chaos expansion (PCE) approach is developed that accounts for both aleatory and epistemic uncertainties, modeled as random variables, thus allowing a unified treatment of both types of uncertainty. We explore in particular epistemic uncertainty associated with the choice of prior probabilistic models for input parameters. A PCE-based Kernel Density (KDE) construction provides a composite map from the PCE coefficients and germ to the PDF of quantities of interest (QoI). Here, the sensitivities of these PDF with respect to the input parameters are then evaluated. Input parameters of the probabilistic models are considered. By sampling over the epistemic random variable, a family of PDFs is generated and the failure probability is itself estimated as a random variable with its own PCE. Integrating epistemic uncertainties within the PCE framework results in a computationally efficient paradigm for propagation and sensitivity evaluation. Two typical illustrative examples are used to demonstrate the proposed approach.

Aleatory uncertainty↗

DOE OSTI2015

SENSITIVITY EVALUATION OF THE DAILY THERMAL PREDICTIONS OF THE AGR-2 EXPERIMENT IN THE ADVANCED TEST REACTOR

A temperature sensitivity evaluation has been performed for the AGR-2 fuel experiment on an individual capsule. A series of cases were compared to a base case by varying different input parameters into the ABAQUS finite element thermal model. These input parameters were varied by ±10% to show the temperature sensitivity to each parameter. The most sensitive parameters are the outer control gap distance, heat rate in the fuel compacts, and neon gas fraction. Thermal conductivity of the fuel compacts and thermal conductivity of the graphite holder were in the middle of the list for sensitivity. The smallest effects were for the emissivities of the stainless steel and graphite, along with gamma heat rate in the non-fueled components. Sensitivity calculations were also performed varying with fast neutron fluence, showing a general temperature rise with an increase in fast neutron fluence. This is a result of the control gas gap becoming larger due to the graphite holder shrinkage with neutron damage. A smaller sensitivity is due to the thermal conductivity of the fuel compacts and graphite holder decreasing with fast neutron fluence.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS1974

On the design of optimal input signals in system identification

The problem of designing optimal inputs in the identification of multi-input multi-output linear systems with unknown time-varying parameters is considered using a Bayesian approach. A sensitivity index gives a measure of performance for the closed-loop system inputs. The computation of the optimal closed-loop mappings is shown to be a nontrivial exercise in stochastic control with no analytic solution, but optimal open-loop and affine laws yield much more tractable problems. For time-invariant systems, the sensitivity index considered is shown to be equivalent to the trace of the (strictly positive definite) information matrix associated with the system. Numerical examples are given. A Kalman filter is used to estimate the parameters. A necessary condition for the Kalman filter not to diverge when applying linear feedback is also given.

Lopez-Toledo, A. A.↗

NASA NTRS1985

Dual control and prevention of the turn-off phenomenon in a class of mimo systems

A recently developed methodology of adaptive dual control based upon sensitivity functions is applied here to a multivariable input-output model. The plant has constant but unknown parameters. It represents a simplified linear version of the relationship between the vibration output and the higher harmonic control input for a helicopter. The cautious and the new dual controller are examined. In many instances, the cautious controller is seen to turn off. The new dual controller modifies the cautious control design by numerator and denominator correction terms which depend upon the sensitivity functions of the expected future cost and avoids the turn-off and burst phenomena. Monte Carlo simulations and statistical tests of significance indicate the superiority of the dual controller over the cautious and the heuristic certainity equivalence controllers.

Mookerjee, P.↗

DOE OSTI2022

Uncertainty Quantification of Monolithic Tungsten Target Block Fatigue

The current STS spallation target design consists of 21 water cooled, tantalum clad, monolithic tungsten blocks. The target wheel assembly rotates such that each target block receives a direct proton pulse every 1.4 seconds (21 blocks / 15 Hz pulses). The quasi-steady heating induced by the repetitive beam pulses creates a significant mean stress distribution in the target. On top of this, the rapid energy deposition from a proton pulse induces dynamic stress waves that are of the same order of magnitude as the mean stresses. Over the design goal of 5,000 operational hours per year for a decade, each target must withstand over 130 million repetitions of these dynamic stress events. The fatigue life prediction of the target blocks is a complex sequence of simulations that depend upon a set of input parameters. For the tungsten block, the end goal is the fatigue factor-of-safety (FOS). This study documents a new structural analysis routine using software available to U.S. national laboratories (e.g. CUBIT, Sierra Multiphysics, Dakota) that enables more rapid target fatigue analysis. The increased throughput is amenable to parameter sensitivity and uncertainty quantification (UQ) studies. A set of input parameters (ultimate strength, fatigue strength, density, elastic modulus, Poisson’s ratio, thermal conductivity, coefficient of thermal expansion, specific heat, flow rate) with expected ranges are documented based on literature data, recent experimental testing, and engineering judgement. UQ bounds the resulting fatigue FOS at [0.5, 3.4] using epistemic interval analysis. These bounds are expected to be wider due to model effects (discretization) and beam effects (focus, offset) that were not included. Parameter sensitivity underscores the importance of ultimate strength and fatigue strength of irradiated tungsten on the fatigue calculations.

43 PARTICLE ACCELERATORS↗

DOE OSTI2022

Thermal modeling of three lakes within the continuous permafrost zone in Alaska using the LAKE 2.0 model

Abstract. Lakes in the Arctic are important reservoirs of heat with much lower albedo in summer and greater absorption of solar radiation than surrounding tundra vegetation. In the winter, lakes that do not freeze to their bed have a mean annual bed temperature >0 ∘C in an otherwise frozen landscape. Under climate warming scenarios, we expect Arctic lakes to accelerate thawing of underlying permafrost due to warming water temperatures in the summer and winter. Previous studies of Arctic lakes have focused on ice cover and thickness, the ice decay process, catchment hydrology, lake water balance, and eddy covariance measurements, but little work has been done in the Arctic to model lake heat balance. We applied the LAKE 2.0 model to simulate water temperatures in three Arctic lakes in northern Alaska over several years and tested the sensitivity of the model to several perturbations of input meteorological variables (precipitation, shortwave radiation, and air temperature) and several model parameters (water vertical resolution, sediment vertical resolution, depth of soil column, and temporal resolution). The LAKE 2.0 model is a one-dimensional model that explicitly solves vertical profiles of water state variables on a grid. We used a combination of meteorological data from local and remote weather stations, as well as data derived from remote sensing, to drive the model. We validated modeled water temperatures with data of observed lake water temperatures at several depths over several years for each lake. Our validation of the LAKE 2.0 model is a necessary step toward modeling changes in Arctic lake ice regimes, lake heat balance, and thermal interactions with permafrost. The sensitivity analysis shows us that lake water temperature is not highly sensitive to small changes in air temperature or precipitation, while changes in shortwave radiation and large changes in precipitation produced larger effects. Snow depth and lake ice strongly affect water temperatures during the frozen season, which dominates the annual thermal regime of Arctic lakes. These findings suggest that reductions in lake ice thickness and duration could lead to more heat storage by lakes and enhanced permafrost degradation.

Clark, Jason A. (ORCID:0000000248105261)↗

DOE OSTI2025

Implementation of Perturbation Theory and Sensitivity Capabilities in Griffin

Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor Multiphysics analysis application, jointly developed by Argonne and Idaho National Laboratories under the DOE-NE NEAMS program. This fiscal year, capabilities for reactivity and sensitivity evaluation using perturbation methods were implemented and verified. The First Order Perturbation Method (FOPT) was employed to compute reactivity worth resulting from small perturbations in input parameters, while the Generalized Perturbation Theory (GPT) was used to evaluate sensitivities of a range of response types, including reaction rate ratio, k-eigenvalue, neutron generation time, and effective delayed neutron fraction. These perturbation methods enable users to quantify how response quantities change due to a perturbation in a input parameter without explicitly performing an additional transport simulation for each perturbed state. In particular, the GPT formulation accounts for indirect effects arising from flux changes by solving generalized inhomogeneous equations, for which a Neumann series-based iterative solution method was developed and implemented in Griffin. The implemented reactivity and sensitivity evaluation capabilities were verified using two test problems: an infinite homogeneous system and a two-dimensional hexagonal core. The results showed excellent agreement with reference solutions obtained by a direct method based on finite difference approximation as well as GPT-based results from the PERSENT code, confirming the accuracy of both reactivity and sensitivity evaluations. Additionally, preliminary uncertainty quantification (UQ) results were obtained by combining the sensitivity values computed using GPT and external covariance data, demonstrating that the implemented sensitivity results can be reliably used for uncertainty calculations. To further demonstrate the generality and practical strength of the implementation, the sensitivity evaluation capability was successfully applied to the Empire microreactor with a geometrically complex design that poses significant modeling challenges. The results confirm that Griffin enables sensitivity evaluations even for irregular and highly heterogeneous reactor configurations, thereby establishing a foundation for UQ applications in advanced reactor designs and analyses.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1987

Vibrations and structureborne noise in space station

Analytical models were developed to predict vibrations and structureborne noise generation of cylindrical and rectangular acoustic enclosures. These models are then used to determine structural vibration levels and interior noise to random point input forces. The guidelines developed could provide preliminary information on acoustical and vibrational environments in space station habitability modules under orbital operations. The structural models include single wall monocoque shell, double wall shell, stiffened orthotropic shell, descretely stiffened flat panels, and a coupled system composed of a cantilever beam structure and a stiffened sidewall. Aluminum and fiber reinforced composite materials are considered for single and double wall shells. The end caps of the cylindrical enclosures are modeled either as single or double wall circular plates. Sound generation in the interior space is calculated by coupling the structural vibrations to the acoustic field in the enclosure. Modal methods and transfer matrix techniques are used to obtain structural vibrations. Parametric studies are performed to determine the sensitivity of interior noise environment to changes in input, geometric and structural conditions.

Vaicaitis, R.↗

DOE OSTI2021

LABS: Los Alamos Benchmark Suite - Current status and planning [Slides]

The LABS repository now has over 500 verified and revised input files with about 600 input files left to get up to speed with what we currently use. After that there are many, many more to go. We're in the process of building code infrastructure, moving to template output files, automating input file generation, outputting file data mining for calculation results, and benchmarking selection on sensitivity and other benchmark characteristics. We intend to open source LABS. We'll most likely release the input files sooner rather than later. The associated tool will probably be open sourced later.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗