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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

The Use of the Integrated Medical Model for Forecasting and Mitigating Medical Risks for a Near-Earth Asteroid Mission

Introduction The Integrated Medical Model (IMM) is a decision support tool that is useful to space flight mission managers and medical system designers in assessing risks and optimizing medical systems. The IMM employs an evidence-based, probabilistic risk assessment (PRA) approach within the operational constraints of space flight. Methods Stochastic computational methods are used to forecast probability distributions of medical events, crew health metrics, medical resource utilization, and probability estimates of medical evacuation and loss of crew life. The IMM can also optimize medical kits within the constraints of mass and volume for specified missions. The IMM was used to forecast medical evacuation and loss of crew life probabilities, as well as crew health metrics for a near-earth asteroid (NEA) mission. An optimized medical kit for this mission was proposed based on the IMM simulation. Discussion The IMM can provide information to the space program regarding medical risks, including crew medical impairment, medical evacuation and loss of crew life. This information is valuable to mission managers and the space medicine community in assessing risk and developing mitigation strategies. Exploration missions such as NEA missions will have significant mass and volume constraints applied to the medical system. Appropriate allocation of medical resources will be critical to mission success. The IMM capability of optimizing medical systems based on specific crew and mission profiles will be advantageous to medical system designers. Conclusion The IMM is a decision support tool that can provide estimates of the impact of medical events on human space flight missions, such as crew impairment, evacuation, and loss of crew life. It can be used to support the development of mitigation strategies and to propose optimized medical systems for specified space flight missions. Learning Objectives The audience will learn how an evidence-based decision support tool can be used to help assess risk, develop mitigation strategies, and optimize medical systems for exploration space flight missions.

Kerstman, Eric↗
DOE OSTI2017

MEASURING RISK IMPORTANCE IN A DYNAMIC PRA FRAMEWORK

Risk importance measures are indexes that are used to rank systems, structures and components (SSCs) using risk-informed methods. The most used/known measures are: Risk Reduction Worth (RRW), Risk Achievement Worth (RAW), Birnbaum (B) and Fussell-Vesely (FV). Once obtained from classical Probabilistic Risk Analysis (PRA) analyses, these risk measures can be effectively employed to optimize component testing and maintenance. In contrast to classical PRA methods, Dynamic PRA methods couple stochastic methods with safety analysis codes to determine risk associate to complex systems such as nuclear plants. Compared to classical PRA methods, they can evaluate with higher resolution the safety impact of timing and sequencing of events on the accident progression. The objective of this paper is to present a series of algorithms that can be used to determine classical risk importance measures (RRW, RAW, B and FV) along with newly developed ones from a Dynamic PRA analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

RISK MONITORING CAPABILITES FROM DYNAMIC PRA DATA

Risk Monitors (RMs) are software tools that are employed in nuclear power plants to monitor the safety properties of the plant itself during operation. These safety properties are generated using classical PRA methods which are typically based on static Boolean structures such as Fault-Trees (FTs) and Event-Trees (ETs). The outcomes of these methods are Core Damage Frequency (CDF) and risk importance values of plant components (e.g., valves and pumps). Examples of Risk Importance Measures (RIMs) commonly used are: Risk Achievement Worth (RAW), Risk Reduction Worth (RRW), Birnbaum (B) and Fussell-Vesely (FV) [1,2]. In a RM these values are updated in real time once plant components status is updated (e.g., under maintenance, off-line, testing). In addition, RMs can be used to optimize maintenance schedules so those safety features of the plant are below plant standard values. This paper presents an approach to create temporal profiles of RIMs (i.e., RM capabilities) given a temporal change of the plant configuration. Instead of employing data generated by ETs and FTs, the proposed approach will employ data generated by Dynamic PRA methods. In contrast to classical PRA methods, Dynamic PRA methods couple stochastic methods with safety analysis codes to determine risk associate to complex systems such as nuclear plants. Compared to classical PRA methods, they can evaluate with higher resolution the safety impact of timing and sequencing of events on the accident progression. We will describe how classical RIMs can be generated by Dynamic PRA data and then we will show how the temporal profiles of the RIMs can be generated given a temporal profile of the system configuration.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

First-collision source treatment for ray effect mitigation in discrete-ordinate radiation transport solutions

Deterministic transport codes play a fundamental role in the modelling and simulation of neutron transport. One of the most common deterministic methods is the method of discrete ordinates, also known as the S method. While offering significant advantages over other deterministic methods or stochastic methods like Monte Carlo, the method of discrete ordinates suffers from non-physical artifacts in its local solution due to its discretization of angle. These artifacts, referred to as ray effects because of their ray-like appearance, tend to be worse in problems with small sources in areas with little scattering. Significant effort has gone into developing methods to mitigate ray effects, such as the first-collision source treatment, which separates the angular flux into the uncollided and collided fluxes and solving them using non-traditional techniques such as ray tracing. One such code capable of doing this is Lawrence Livermore National Laboratory's deterministic transport code ARDRA. Current ray tracing methods typically trace to a set of points inside a zone to compute an overall flux. However, this approach has significant drawbacks, such as a low order of convergence and not being conservative. Therefore, a new method has been developed that traces instead to a set of points on each of a zone's surfaces and computing the currents, before using these to obtain the flux. A comparison between these two ray tracing methods showed significant advantages to the new surface method, including inherent conservation, a higher convergence rate, and an increase in calculable information like leakage. This work performed under the auspices of the U.S. Department of Energy by Lawrence Liver- more National Laboratory under Contract DE-AC52-07NA27344. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2013

An iterative stochastic ensemble method for parameter estimation of subsurface flow models

Parameter estimation for subsurface flow models is an essential step for maximizing the value of numerical simulations for future prediction and the development of effective control strategies. We propose the iterative stochastic ensemble method (ISEM) as a general method for parameter estimation based on stochastic estimation of gradients using an ensemble of directional derivatives. ISEM eliminates the need for adjoint coding and deals with the numerical simulator as a blackbox. The proposed method employs directional derivatives within a Gauss–Newton iteration. The update equation in ISEM resembles the update step in ensemble Kalman filter, however the inverse of the output covariance matrix in ISEM is regularized using standard truncated singular value decomposition or Tikhonov regularization. We also investigate the performance of a set of shrinkage based covariance estimators within ISEM. The proposed method is successfully applied on several nonlinear parameter estimation problems for subsurface flow models. The efficiency of the proposed algorithm is demonstrated by the small size of utilized ensembles and in terms of error convergence rates.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

An integration factor method for stochastic and stiff reaction–diffusion systems

Stochastic effects are often present in the biochemical systems involving reactions and diffusions. When the reactions are stiff, existing numerical methods for stochastic reaction diffusion equations require either very small time steps for any explicit schemes or solving large nonlinear systems at each time step for the implicit schemes. Here we present a class of semi-implicit integration factor methods that treat the diffusion term exactly and reaction implicitly for a system of stochastic reaction–diffusion equations. Our linear stability analysis shows the advantage of such methods for both small and large amplitudes of noise. Direct use of the method to solving several linear and nonlinear stochastic reaction–diffusion equations demonstrates good accuracy, efficiency, and stability properties. This new class of methods, which are easy to implement, will have broader applications in solving stochastic reaction–diffusion equations arising from models in biology and physical sciences.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1972

On a stochastic control method for weakly coupled linear systems

The stochastic control of two weakly coupled linear systems with different controllers is considered. Each controller only makes measurements about his own system; no information about the other system is assumed to be available. Based on the noisy measurements, the controllers are to generate independently suitable control policies which minimize a quadratic cost functional. To account for the effects of weak coupling directly, an approximate model, which involves replacing the influence of one system on the other by a white noise process is proposed. Simple suboptimal control problem for calculating the covariances of these noises is solved using the matrix minimum principle. The overall system performance based on this scheme is analyzed as a function of the degree of intersystem coupling.

Kwong, R. H.↗
DOE OSTI2015

Probabilistic Density Function Method for Stochastic ODEs of Power Systems with Uncertain Power Input

Wind and solar power generators are commonly described by a system of stochastic ordinary differential equations (SODEs) where random input parameters represent uncertainty in wind and solar energy. The existing methods for SODEs are mostly limited to delta-correlated random parameters (white noise). Here we use the Probability Density Function (PDF) method for deriving a closed-form deterministic partial differential equation (PDE) for the joint probability density function of the SODEs describing a power generator with time-correlated power input. The resulting PDE is solved numerically. A good agreement with Monte Carlo Simulations shows accuracy of the PDF method.

PDF method, stochastic differential equations, pow↗
NASA NTRS2003

Structural Reliability Using Probability Density Estimation Methods Within NESSUS

A reliability analysis studies a mathematical model of a physical system taking into account uncertainties of design variables and common results are estimations of a response density, which also implies estimations of its parameters. Some common density parameters include the mean value, the standard deviation, and specific percentile(s) of the response, which are measures of central tendency, variation, and probability regions, respectively. Reliability analyses are important since the results can lead to different designs by calculating the probability of observing safe responses in each of the proposed designs. All of this is done at the expense of added computational time as compared to a single deterministic analysis which will result in one value of the response out of many that make up the density of the response. Sampling methods, such as monte carlo (MC) and latin hypercube sampling (LHS), can be used to perform reliability analyses and can compute nonlinear response density parameters even if the response is dependent on many random variables. Hence, both methods are very robust; however, they are computationally expensive to use in the estimation of the response density parameters. Both methods are 2 of 13 stochastic methods that are contained within the Numerical Evaluation of Stochastic Structures Under Stress (NESSUS) program. NESSUS is a probabilistic finite element analysis (FEA) program that was developed through funding from NASA Glenn Research Center (GRC). It has the additional capability of being linked to other analysis programs; therefore, probabilistic fluid dynamics, fracture mechanics, and heat transfer are only a few of what is possible with this software. The LHS method is the newest addition to the stochastic methods within NESSUS. Part of this work was to enhance NESSUS with the LHS method. The new LHS module is complete, has been successfully integrated with NESSUS, and been used to study four different test cases that have been proposed by the Society of Automotive Engineers (SAE). The test cases compare different probabilistic methods within NESSUS because it is important that a user can have confidence that estimates of stochastic parameters of a response will be within an acceptable error limit. For each response, the mean, standard deviation, and 0.99 percentile, are repeatedly estimated which allows confidence statements to be made for each parameter estimated, and for each method. Thus, the ability of several stochastic methods to efficiently and accurately estimate density parameters is compared using four valid test cases. While all of the reliability methods used performed quite well, for the new LHS module within NESSUS it was found that it had a lower estimation error than MC when they were used to estimate the mean, standard deviation, and 0.99 percentile of the four different stochastic responses. Also, LHS required a smaller amount of calculations to obtain low error answers with a high amount of confidence than MC. It can therefore be stated that NESSUS is an important reliability tool that has a variety of sound probabilistic methods a user can employ and the newest LHS module is a valuable new enhancement of the program.

Chamis, Chrisos C.↗
DOE OSTI2013

Spatially Varying Embedded Stochastic Galerkin Methods for Steady-State PDEs

Existing discretizations for stochastic PDEs, based on a tensor product between the deter ministic basis and the stochastic basis, treat the required resolution of uncertainty as uniform across the physical domain. However, solutions to many PDEs of interest exhibit spatially localized features that may result in uncertainty being severely over or under-resolved by existing discretizations. In this report, we explore the mechanics and accuracy of using a spatially varying stochastic expansion. This is achieved through an adaptive refinement algorithm where simple error estimates are used to independently drive refinement of the stochastic basis at each point in the physical domain. Results are presented comparing the accuracy of the adaptive techinque to the accuracy achieved using uniform refinement.

Cyr, Eric C.↗
DOE OSTI2020

Combining model-based and model-free methods for stochastic control of distributed energy resources

Modern distribution systems are experiencing a fast transformation with the growing penetration of distributed energy resources (DERs). Along with the economic and environmental benefits of DERs, challenges arise to address the uncertainties caused by their inherent volatility. If properly coordinated, however, DERs have the potential to provide the controllability that grid operators need. Here, we propose a hierarchical control framework that combines the model-based and model-free methods for stochastic DER control in distribution systems. The upper-level scheduler considers a chance-constrained optimal power flow problem (model-based) that schedules DER setpoints to minimize the operational cost and maintain the operating reserve. The lower-level distributed DER controllers absorb real-time disturbances and uncertainties using the extremum seeking control (model-free) to achieve grid objectives. The combination of model-based and model-free methods allows us to take the advantages of both methods to effectively manage the uncertainty in distribution systems. The proposed work is demonstrated on the IEEE 13-node feeder.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2016

SU-F-T-182: A Stochastic Approach to Daily QA Tolerances On Spot Properties for Proton Pencil Beam Scanning

Purpose: Proton pencil beam scanning is used clinically across the United States. There are no current guidelines on tolerances for daily QA specific to pencil beam scanning, specifically related to the individual spot properties (spot width). Using a stochastic method to determine tolerances has the potential to optimize tolerances on individual spots and decrease the number of false positive failures in daily QA. Individual and global spot tolerances were evaluated. Methods: As part of daily QA for proton pencil beam scanning, a field of 16 spots (corresponding to 8 energies) is measured using an array of ion chambers (Matrixx, IBA). Each individual spot is fit to two Gaussian functions (x,y). The spot width (σ) in × and y are recorded (32 parameters). Results from the daily QA were retrospectively analyzed for 100 days of data. The deviations of the spot widths were histogrammed and fit to a Gaussian function. The stochastic spot tolerance was taken to be the mean ± 3σ. Using these results, tolerances were developed and tested against known deviations in spot width. Results: The individual spot tolerances derived with the stochastic method decreased in 30/32 instances. Using the previous tolerances (± 20% width), the daily QA would have detected 0/20 days of the deviation. Using a tolerance of any 6 spots failing the stochastic tolerance, 18/20 days of the deviation would have been detected. Conclusion: Using a stochastic method we have been able to decrease daily tolerances on the spot widths for 30/32 spot widths measured. The stochastic tolerances can lead to detection of deviations that previously would have been picked up on monthly QA and missed by daily QA. This method could be easily extended for evaluation of other QA parameters in proton spot scanning.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

Error Convergence Characterization for Stochastic Transport Methods

There has been increased interest in reliably and efficiently solving engineering systems involving uncertainty in recent years. Characterization of the convergence of errors within the problem, including statistical and bias errors, increases confidence that chosen solution methods are appropriate for a particular problem and quantity of interest (QoI), that implementation errors have not been made, and can aid users or algorithms in solving problems within a tolerance efficiently. We demonstrate a method for characterizing error convergence in a simple stochastic transport problem. Though the approach is applicable to problems with more complicated physics, our simple problem enables analytic QoI solutions so that error convergence behavior and the identification of limiting errors can be presented with high precision. A one-dimensional, two-material, neutral-particle, and absorption-only transport problem involving uniformly distributed uncertain total cross sections is presented. Random sampling (RS) and stochastic collocation (SC) are used as stochastic solvers which sample from the uncertain space and Monte Carlo (MC) transport is employed to solve transport results on the resulting realizations. Probability density functions (PDFs) are created using either RS solutions or samples taken from a polynomial chaos expansion (PCE) constructed with SC solutions. The convergence of each solver is characterized with respect to the QoI against analytic solutions, convergence behavior is used to efficiently solve a QoI within a tolerance, and convergence plots are used to identify dominant solution errors.

42 ENGINEERING↗
DOE OSTI2014

A domain decomposition method of stochastic PDEs: An iterative solution techniques using a two-level scalable preconditioner

Recent advances in high performance computing systems and sensing technologies motivate computational simulations with extremely high resolution models with capabilities to quantify uncertainties for credible numerical predictions. A two-level domain decomposition method is reported in this investigation to devise a linear solver for the large-scale system in the Galerkin spectral stochastic finite element method (SSFEM). In particular, a two-level scalable preconditioner is introduced in order to iteratively solve the large-scale linear system in the intrusive SSFEM using an iterative substructuring based domain decomposition solver. The implementation of the algorithm involves solving a local problem on each subdomain that constructs the local part of the preconditioner and a coarse problem that propagates information globally among the subdomains. The numerical and parallel scalabilities of the two-level preconditioner are contrasted with the previously developed one-level preconditioner for two-dimensional flow through porous media and elasticity problems with spatially varying non-Gaussian material properties. A distributed implementation of the parallel algorithm is carried out using MPI and PETSc parallel libraries. The scalabilities of the algorithm are investigated in a Linux cluster.

42 ENGINEERING↗
DOE OSTI2014

A stochastic Galerkin method for the Euler equations with Roe variable transformation

The Euler equations subject to uncertainty in the initial and boundary conditions are investigated via the stochastic Galerkin approach. We present a new fully intrusive method based on a variable transformation of the continuous equations. Roe variables are employed to get quadratic dependence in the flux function and a well-defined Roe average matrix that can be determined without matrix inversion. In previous formulations based on generalized polynomial chaos expansion of the physical variables, the need to introduce stochastic expansions of inverse quantities, or square roots of stochastic quantities of interest, adds to the number of possible different ways to approximate the original stochastic problem. We present a method where the square roots occur in the choice of variables, resulting in an unambiguous problem formulation. The Roe formulation saves computational cost compared to the formulation based on expansion of conservative variables. Moreover, the Roe formulation is more robust and can handle cases of supersonic flow, for which the conservative variable formulation fails to produce a bounded solution. For certain stochastic basis functions, the proposed method can be made more effective and well-conditioned. This leads to increased robustness for both choices of variables. We use a multi-wavelet basis that can be chosen to include a large number of resolution levels to handle more extreme cases (e.g. strong discontinuities) in a robust way. For smooth cases, the order of the polynomial representation can be increased for increased accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

An asymptotic-preserving stochastic Galerkin method for the radiative heat transfer equations with random inputs and diffusive scalings

In this paper, we develop an Asymptotic-Preserving (AP) stochastic Galerkin scheme for the radiative heat transfer equations with random inputs and diffusive scalings. In this problem the random inputs arise due to uncertainties in cross section, initial data or boundary data. We use the generalized polynomial chaos based stochastic Galerkin (gPC-SG) method, which is combined with the micro–macro decomposition based deterministic AP framework in order to handle efficiently the diffusive regime. For linearized problem we prove the regularity of the solution in the random space and consequently the spectral accuracy of the gPC-SG method. We also prove the uniform (in the mean free path) linear stability for the space-time discretizations. Several numerical tests are presented to show the efficiency and accuracy of proposed scheme, especially in the diffusive regime.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Multi-fidelity stochastic collocation method for computation of statistical moments

We present an efficient numerical algorithm to approximate the statistical moments of stochastic problems, in the presence of models with different fidelities. The method extends the multi-fidelity approximation method developed in . By combining the efficiency of low-fidelity models and the accuracy of high-fidelity models, our method exhibits fast convergence with a limited number of high-fidelity simulations. We establish an error bound of the method and present several numerical examples to demonstrate the efficiency and applicability of the multi-fidelity algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Data Analysis Approaches for the Risk-Informed Safety Margins Characterization Toolkit

In the past decades, several numerical simulation codes have been employed to simulate accident dynamics (e.g., RELAP5-3D, RELAP-7, MELCOR, MAAP). In order to evaluate the impact of uncertainties into accident dynamics, several stochastic methodologies have been coupled with these codes. These stochastic methods range from classical Monte-Carlo and Latin Hypercube sampling to stochastic polynomial methods. Similar approaches have been introduced into the risk and safety community where stochastic methods (such as RAVEN, ADAPT, MCDET, ADS) have been coupled with safety analysis codes in order to evaluate the safety impact of timing and sequencing of events. These approaches are usually called Dynamic PRA or simulation-based PRA methods. These uncertainties and safety methods usually generate a large number of simulation runs (database storage may be on the order of gigabytes or higher). The scope of this paper is to present a broad overview of methods and algorithms that can be used to analyze and extract information from large data sets containing time dependent data. In this context, “extracting information” means constructing input-output correlations, finding commonalities, and identifying outliers. Some of the algorithms presented here have been developed or are under development within the RAVEN statistical framework.

97 MATHEMATICS AND COMPUTING↗