Search NASA⌕ Search

SEARCH · Search NASA

Results for “Probability”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records

Evaluating Probability of Containment Effectiveness at a GCS Sites using integrated assessment modeling approach with Bayesian decision Networks

Improved scientific and engineering understanding of the behavior of geologic CO2 storage together with established regulatory framework and incentive structures raise the prospects for accelerated, large-scale deployment of this greenhouse gas emissions reduction approach. Incentive structures call for the establishment of appropriate verification and accounting approaches to support claims of the integrity of a geologic storage complex and to justify taking credit for long-term storage. In this study, we present a framework for assessing the probability of containment effectiveness over the lifetime of a geologic carbon storage site (e.g., after 70 years of injection and post-injection site performance) using forward stochastic model realizations based on site characterization data and using a monitoring-informed Bayesian network based on hypothetical detectability from surface seismic surveys over the site injection and post-injection phases. The National Risk Assessment Partnership’s open-source Integrated Assessment Model (NRAP-Open-IAM) was utilized to develop an ensemble of 10,000 a priori stochastic forecasts of CO2 containment. Those simulations were used to train the Bayesian network model to estimate the prior probabilities of the CO2 leakage mass into overlying, monitorable aquifers considering the uncertainties in the reservoir properties, permeability of potentially leaky wells and the overlying aquifers. The conditional probabilities in the Bayesian network were either learned from the NRAP-Open-IAM simulations or derived from the predefined detection thresholds for the monitoring method. Observations obtained from monitoring, over time during the site operation phases were then used to generate updated posterior probabilities of containment (and any loss from containment) in the Bayesian network by propagating the prior probabilities through the conditional probabilities. We demonstrate how to construct and use the Bayesian network for verifying the long-term storage complex effectiveness informed by monitoring based on the NRAP-Open-IAM simulations previously developed for the FutureGen 2.0 site. This approach may have relevance for stake holders to demonstrate secure geologic storage, provide a defensible, probabilistic approach to claim credit for geologic storage, and to estimate the likelihood that any fraction of the claimed credit may need to be refunded to the creditor based on available monitoring information.

Bayesian network, Risk assessment, Monitoring, car↗

The FLOod Probability Interpolation Tool (FLOPIT): A Simple Tool to Improve Spatial Flood Probability Quantification and Communication

Understanding flood probabilities is essential to making sound decisions about flood-risk management. Many people rely on flood probability maps to inform decisions about purchasing flood insurance, buying or selling real-estate, flood-proofing a house, or managing floodplain development. Current flood probability maps typically use flood zones (for example the 1 in 100 or 1 in 500-year flood zones) to communicate flooding probabilities. However, this choice of communication format can miss important details and lead to biased risk assessments. Here we develop, test, and demonstrate the FLOod Probability Interpolation Tool (FLOPIT). FLOPIT interpolates flood probabilities between water surface elevation to produce continuous flood-probability maps. FLOPIT uses water surface elevation inundation maps for at least two return periods and creates Annual Exceedance Probability (AEP) as well as inundation maps for new return levels. Potential advantages of FLOPIT include being open-source, relatively easy to implement, capable of creating inundation maps from agencies other than FEMA, and applicable to locations where FEMA published flood inundation maps but not flood probability. Using publicly available data from the Federal Emergency Management Agency (FEMA) flood risk databases as well as state and national datasets, we produce continuous flood-probability maps at three example locations in the United States: Houston (TX), Muncy (PA), and Selinsgrove (PA). We find that the discrete flood zones generally communicate substantially lower flood probabilities than the continuous estimates.

54 ENVIRONMENTAL SCIENCES↗

TRISO SiC Failure Probability for Reactivity Initiated Accidents in High-Temperature Gas-Cooled Reactors

This work analyzes the failure process of the silicon carbide (SiC) layer in tristructural isotropic (TRISO) during reactivity-initiated accident scenarios for a high-temperature gas-cooled reactor (HTGR) with BISON. Two cases are considered—a group control rod withdrawal (CRW) and a control rod ejection (CRE)—reproduced from a previous study. Failure probability is modeled using Weibull statistics, and worst-case scenario Weibull parameters are adopted to simulate the envelopes in BISON with a one-dimensional TRISO model. CRW scenario results are characterized by higher values of maximum energy deposition and final temperature and volumetric strain with respect to the CRE ones, but the latter have remarkably higher SiC failure probability, mainly due to the offset in strain rates between the two cases. This work also confirms the validity and conservatism of the performance envelopes produced in a previous work by replicating the envelope formulation using RELAP5-3D and RAVEN with a different sampling technique and obtaining consistent results. A sensitivity analysis using the Sobol variance decomposition method on SiC failure probability is then performed involving a set of inputs on both CRW and CRE. The two most important parameters are Weibull modulus and characteristic stress, and their relative importance depends on the specific case. The proposed interpretation of the results is that both energy deposition and strain rate influence the relative degree of importance of the failure parameters. Computation of 95% confidence intervals around worst-case scenario SiC failure probability values is also carried out for four different sets of Weibull parameters. Heren a new criterion for SiC TRISO quality classification built upon safety-based ranges of Weibull parameters is proposed to be integrated in future Fuel-Production Quality Assurance Plans.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

A New Probability Table Methodology with Covariances on Probability Tables

Through this work, we test a new methodology of evaluating probability tables informed by a combination of physics models and experimental data. This methodology uses generalized least squares to produce a joint mean and covariance for average cross sections and probability tables. This methodology has been tested and validated using total Monte Carlo. Attempts were made to parameterize the probability table using a formulation provided in. Although the normal inverse Gaussian fit was successful for the total cross section probability distribution, the rational-function fit to the capture, inelastic, and fission cross sections was unsuccessful due to time constraints.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Quasar Identification Using Multivariate Probability Density Estimated from Nonparametric Conditional Probabilities

Nonparametric estimation for a probability density function that describes multivariate data has typically been addressed by kernel density estimation (KDE). A novel density estimator recently developed by Farmer and Jacobs offers an alternative high-throughput automated approach to univariate nonparametric density estimation based on maximum entropy and order statistics, improving accuracy over univariate KDE. This article presents an extension of the single variable case to multiple variables. The univariate estimator is used to recursively calculate a product array of one-dimensional conditional probabilities. In combination with interpolation methods, a complete joint probability density estimate is generated for multiple variables. Good accuracy and speed performance in synthetic data are demonstrated by a numerical study using known distributions over a range of sample sizes from 100 to 10 6 for two to six variables. Performance in terms of speed and accuracy is compared to KDE. The multivariate density estimate developed here tends to perform better as the number of samples and/or variables increases. As an example application, measurements are analyzed over five filters of photometric data from the Sloan Digital Sky Survey Data Release 17. The multivariate estimation is used to form the basis for a binary classifier that distinguishes quasars from galaxies and stars with up to 94% accuracy.

79 ASTRONOMY AND ASTROPHYSICS↗

A Practical Approach to Wave Function Propagation, Hopping Probabilities, and Time Steps in Surface Hopping Calculations

We compare several established approaches for propagating wave functions and calculating hopping probabilities within the fewest switches surface hopping (FSSH) algorithm for difficult cases with many electronic states and many trivial crossings. If only a single time step (Δt c ) is employed, we find that no published approach can accurately capture the dynamics correctly unless Δt c → 0 (which is not computationally feasible). If multiple time steps are employed, for a fixed classical time step (Δt c ), a robust scheme can be found for dynamically choosing quantum time steps (δt q1 and δt q2 ) and calculating hopping probabilities so that one can systematically reduce all errors and achieve maximally efficient accuracy; scattering calculations confirm that one can choose a fairly large classical time step. Furthermore, the robust scheme presented here uses both the “local diabatic” and adiabatic interpolation and thus borrows elements from both the Granucci/Persico and Meek/Levine algorithms. Our findings should be broadly applicable in the future.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Case Study on Pathogen Transport, Deposition, Evaporation and Transmission: Linking High-Fidelity Computational Fluid Dynamics Simulations to Probability of Infection

A high-fidelity, low-Mach computational fluid dynamics simulation tool that includes evaporating droplets and variable-density turbulent flow coupling is well-suited to ascertain transmission probability and supports risk mitigation methods development for airborne infectious diseases such as COVID-19. A multi-physics large-eddy simulation-based paradigm is used to explore droplet and aerosol pathogen transport from a synthetic cough emanating from a kneeling humanoid. For an outdoor configuration that mimics the recent open-space social distance strategy of San Francisco, maximum primary droplet deposition distances are shown to approach 8.1 m in a moderate wind configuration with the aerosol plume transported in excess of 15 m. In quiescent conditions, the aerosol plume extends to approximately 4 m before the emanating pulsed jet becomes neutrally buoyant. A dose–response model, which is based on previous SARS coronavirus (SARS-CoV) data, is exercised on the high-fidelity aerosol transport database to establish relative risk at eighteen virtual receptor probe locations.

59 BASIC BIOLOGICAL SCIENCES↗

Precipitation Probability and Its Future Changes From a Global Cloud-Resolving Model and CMIP6 Simulations

This study investigates precipitation probability and its future changes using simulations from the Non-hydrostatic Icosahedral Atmospheric Model (NICAM), a global cloud-resolving model, and Coupled Model Intercomparison Project Phase 6 (CMIP6) models. For the precipitation probability comparison between models and Tropical Rainfall Measuring Mission (TRMM) during 1998–2008, the difference is greatly reduced by regridding to a common coarser resolution, but the difference signs largely remain. Both NICAM and CMIP6 model ensemble mean show less global-mean nonprecipitation fractions than observations, but NICAM agrees better with observations. For global-mean light precipitation probability, NICAM (CMIP6 model ensemble mean) is smaller (larger) than TRMM. NICAM shows higher heavy precipitation probability than TRMM in native resolutions, but it is close to TRMM and falls in the CMIP6 model range after regridding. For the precipitation probability changes from 1979–2008 to 2075–2104, NICAM predicts an increase in nonprecipitation and extreme heavy (>100 mm/day) precipitation probability but a slight decrease in the probability for precipitation <100 mm/day. After regridding to 2.5°, the precipitation intensity where the probability starts to increase becomes ~20 mm/day and the relative increases in nonprecipitation and heavy precipitation probability become much larger. Future heavy precipitation probability relative increases from CMIP6 models are much larger than NICAM at their native resolutions, but NICAM falls in the CMIP6 model range after regridding, indicating robust future increase (decrease) in heavy (light) precipitation probability regardless of underlying convection treatments. Discrepancy, however, exists in the projected nonprecipitation fraction changes: NICAM shows that nonprecipitation probability will increase over most of low and middle latitudes where CMIP6 models show less increases and even decreases.

54 ENVIRONMENTAL SCIENCES↗

Divide and conquer: separating the two probabilities in seismic phase picking

There are two fundamental probabilities in the seismic phase picking process—the probability of the existence of a seismic phase (detection probability) and the probability associated with the phase arrival time estimation (timing probability). The nearly ubiquitous approach in developing deep learning phase picking models is to use a kernel, such as a truncated Gaussian, to mask the labelled phase arrival time and train a segmentation model. Once a model is trained, the times of the peaks in the output are taken as phase arrival times (picks), and the height of the peaks are taken as ‘probability’ of the picks. Here, we show that this ‘probability’ represents neither the detection nor the timing probability because this approach forces the output to follow the shape of the kernel. We introduce an approach using two models to estimate these two distinct probabilities. We use a binary classifier with a calibrated confidence to address the detection probability and a multiclass classifier to obtain a probability mass function to address the timing probability. This new approach can make the deep learning-based phase picking process more interpretable and provide options to logically control seismic monitoring workflows.

58 GEOSCIENCES↗

Quantifying conditional probabilities of fish-turbine encounters and impacts

Tidal turbines are one source of marine renewable energy but development of tidal power is hampered by uncertainties in fish-turbine interaction impacts. Current knowledge gaps exist in efforts to quantify risks, as empirical data and modeling studies have characterized components of fish approach and interaction with turbines, but a comprehensive model that quantifies conditional occurrence probabilities of fish approaching and then interacting with a turbine in sequential steps is lacking. We combined empirical acoustic density measurements of Pacific herring ( Clupea pallasii ) and when data limited, published probabilities in an impact probability model that includes approach, entrainment, interactions, and avoidance of fish with axial or cross-flow tidal turbines. Interaction impacts include fish collisions with stationary turbine components, blade strikes by rotating blades, and/or a collision followed by a blade strike. Impact probabilities for collision followed by a blade strike were lowest with estimates ranging from 0.0000242 to 0.0678, and highest for blade strike ranging from 0.000261 to 0.40. Maximum probabilities occurred for a cross-flow turbine at night with no active or passive avoidance. Estimates were lowest when probabilities were conditional on sequential events, and when active and passive avoidance was included for an axial-flow turbine during the day. As expected, conditional probabilities were typically lower than analogous independent events and literature values. Estimating impact probabilities for Pacific herring in Admiralty Inlet, Washington, United States for two device types illustrates utilization of existing data and simultaneously identifies data gaps needed to fully calculate empirical-based probabilities for any site-species combination.

collision risk↗

Structural Aspects of Neutron Survival Probabilities

The neutron survival probability (and related quantities including probabilities of extinction and initiation) is a central element of the broader stochastic theory of neutron populations and finds application in fields including reactor start-up, analysis of reactor power bursts and criticality accidents, and safeguards. In a full neutron transport formulation, the equation governing the single-neutron survival probability is a backward or adjoint-like integro-partial differential equation with the added complexity of being highly nonlinear. Analogous formulations of this equation exist in the context of many approximate theories of neutron transport, with the point kinetics formulation having received significant theoretical attention since the 1940s. This work continues this tradition by providing a novel analysis of the single-neutron survival probability equation using the tools of boundary layer theory. The analysis reveals that the “fully dynamic” solution of the single-neutron survival probability equation—and some key probability distributions derived from it—may be cast as a singular perturbation around the underlying quasi-static single-neutron probability of initiation. In this perturbation solution, the expansion parameter is the ratio of the neutron generation time to a macroscopic time scale characterizing the overall system evolution; this interpretation illuminates some of the fundamental structural aspects of neutron survival phenomena.

97 MATHEMATICS AND COMPUTING↗

Conservative Estimation of Tail Probabilities from Limited Sample Data

Several sparse-sample uncertainty quantification (UQ) methods are compared for conservative but not overly conservative estimation of small tail probabilities involving responses that lay beyond specified thresholds in the tails of probability distributions. Sixteen very differently shaped distributions (or probability density functions, PDFs) and tail probability magnitudes ranging from 10 -5 to 10 -1 are considered in order for the study to be relevant to a wide range of risk analysis and quantification of margins and uncertainty (QMU) problems. The emphasis of the study is on limited data regimes ranging from N = 2 to 20 samples, reflective of most experimental and some expensive computational situations. Relatively simple sparse-sample UQ methods tested for this regime involve statistical tolerance interval "Equivalent Normal and related "Ensemble of Normals" and "Superdistribution (SD) approaches. (The independently derived SD is effectively equivalent to the Bayesian posterior predictive distribution given the assumptions of the derivation.) The performance of the methods was generally improved for N ≥ 5 samples with a generalized Jackknife resampling technique, which determines a tail probability estimate by averaging estimates from smaller sub-samples. Several quantitative metrics for method conservatism and accuracy of tail probability estimation are used to assess and rank the methods' performance over many random trials for each test PDF and probability magnitude. A variant of Bootstrap resampling was also tried, but did not significantly improve tail probability estimates in most cases. Detailed results are presented from over 100-million tests over the above factors that provide useful granular information on which methods or combination of methods perform best in various areas of the factor space.

97 MATHEMATICS AND COMPUTING↗

Computing the Instantaneous Collision Probability between Satellites using Characteristic Function Inversion

The probability that two satellites overlap in space at a specified instant of time is called their instantaneous collision probability. Assuming Gaussian uncertainties and spherical satellites, this probability is the integral of a Gaussian distribution over a sphere. This paper shows how to compute the probability using an established numerical procedure called characteristic function inversion. The collision probability in the short-term encounter scenario is also evaluated with this approach, where the instant at which the probability is computed is the time of closest approach between the objects. Python and R code is provided to evaluate the probability in practice. Overall, the approach has been established for over fifty years, is implemented in existing software, does not rely on analytical approximations, and can be used to evaluate two and three dimensional collision probabilities.

79 ASTRONOMY AND ASTROPHYSICS↗

A Sparse-Grid Probabilistic Scheme for Approximation of the Runaway Probability of Electrons in Fusion Tokamak Simulation

Runaway electrons (RE) generated during magnetic disruptions present a major threat to the safe operation of plasma nuclear fusion reactors. A critical aspect of understanding RE dynamics is to calculate the runaway probability, i.e., the probability that an electron in the phase space will runaway on, or before, a prescribed time. Such probability can be obtained by solving the adjoint equation of the underlying Fokker-Planck equation that controls the electron dynamics. In this effort, we present a sparse-grid probabilistic scheme for computing the runaway probability. The key ingredient of our approach is to represent the solution of the adjoint equation as a conditional expectation, such that discretizing the differential operator reduces to the approximation of a set of integrals. Adaptive sparse grid interpolation is utilized to approximate the map from the phase space to the runaway probability. The main novelties of this effort are the integration of the sparse-grid method into the probabilistic numerical scheme for computing escape probability, and the application of the proposed method in computing RE probabilities. Two numerical examples are given to illustrate that the proposed method can achieve O(Δt) convergence, and that the local anisotropic adaptive refinement strategy (M. Stoyanov, Adaptive sparse grid construction in a context of local anisotropy and multiple hierarchical parents. In: Sparse Grids and Applications-Miami 2016, Springer, Berlin, 2018, pp. 175–199) can effectively handle the sharp transition layer between the runaway and non-runaway regions.

Yang, Minglei↗

Sensitivity analysis applied to SiC failure probability in TRISO modeled with BISON

Here, a sensitivity analysis on the failure probability of the Silicon Carbide (SiC) layer in tristructural isotropic (TRISO) nuclear fuel during transient conditions predicted by the BISON fuel performance code is performed. The principal goal of the analysis is to understand the most important parameters dictating SiC failure behavior in BISON during Reactivity Initiated Accidents (RIAs). SiC brittle fracture probability is modeled using Weibull statistics. A total of seven inputs related to SiC failure has been selected for the analysis, including the Weibull statistics parameters, elastic moduli for SiC and Pyrolitic Carbon (PyC) and SiC stress-free temperature. A 1D TRISO BISON model has been established for various reactivity insertions performed at the Nuclear Safety Research Reactor (NSRR). The principal advantage associated with the 1D TRISO model developed in this work is its computational efficiency. The Sobol variance decomposition method is used, and the sensitivity indices are presented for eight different values of the energy deposition. The results show that the two most important parameters impacting the predicted SiC failure probability are the Weibull modulus and the characteristic stress, and a co-variance amongst these parameters is obtained for low reactivity insertions. An additional new finding of this work is that the relative importance of Weibull parameters depends on the energy deposition, and thus reactivity, regime. For low energy depositions, two parameters are of influence on SiC failure probability, while for high energy depositions only one parameter impacts failure probability results. Moreover, optimization of the Weibull modulus and characteristic stress is performed by minimizing the RMSE between BISON failure probability predictions and experimental failure fractions for each energy deposition. This work also demonstrates the validity of the NSRR tests BISON simulations and of the respective sensitivity analysis results as conservative, yet indicative for slower transients characterized by lower deposited energies. Such verification is achieved through the partial extension of the analysis to a group Control Rod Withdrawal reproduced from a previous study. Another novel result of this analysis is that no single set of Weibull parameters can reproduce all reactivity insertion experimental failure results, which is related to the intrinsic nature of SiC failure properties, and a new range for the parameters is proposed to produce a failure probability envelope that encompasses the experimental fractions. Additionaly, this work proposes a new approach for future failure analysis with BISON, consisting in the use of Weibull parameters ranges, rather than fixed sets, along with failure envelopes generation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

O · , H · , and · OH radical etching probability of polystyrene obtained for a radio frequency driven atmospheric pressure plasma jet

Atmospheric pressure plasma jets have great potential for the surface modification of polymers. In this work, the authors report on polystyrene etching by a radio frequency driven atmospheric pressure plasma jet with a focus on the role of H · , O · , and · OH radicals in this process. The absolute flux of H · , O · , and · OH radicals reaching the surface of the polymer was determined by a COMSOL MULTIPHYSICS reacting fluid dynamics model incorporating detailed transport phenomena in the boundary layer near the substrate. The simulated results of H · and · OH densities in the jet effluent were experimentally verified by two-photon absorption laser induced fluorescence and laser induced fluorescence, respectively. The carbon atom removal flux from the polystyrene surface was taken from previously reported measurements using the same plasma source. The authors show that the boundary layer effects in the interfacial region above the substrate can have a significant impact on the calculated etching probabilities. The reaction probability (β) has a significant uncertainty although a variation of 2 orders of magnitude in β leads to uncertainties of approximately 1 order of magnitude variation in the determined etching probability. The etching probability of polystyrene by · OH radicals was confirmed to be at least an order of magnitude larger than the polystyrene etching probability by O · radicals. The authors also confirmed the weak polystyrene etching probability by H · radicals. The model suggests that the presence of a 30 ppm O 2 impurity can lead to the production of · OH radicals in the far effluent of the Ar + 1% H 2 plasma jet close to the substrate at sufficient densities to enable effective etching.

36 MATERIALS SCIENCE↗

Probability of Hydrogen Ignition: A Landscape Review and Gaps Assessment

The primary hazard of a leak from a hydrogen system is due to the immediate or delayed ignition of the fuel leading to a jet flame or explosion. Therefore, understanding the hydrogen ignition probability is critical for analyzing the risk of hydrogen systems. This report reviews the current understanding of hydrogen ignition mechanisms and methods for modeling their probability. The stoichiometry, ignition strength, and ignition source temperature are all important characteristics that can affect both the probability of ignition and the outcome of the subsequent combustion event. A brief review of diffusion ignition demonstrates that ignition probability models must account for seemingly spontaneous ignition of hydrogen in addition to scenarios where the ignition source is readily identified. State-of-the art models for both immediate and delayed ignition probabilities are presented, including different physical aspects of the scenarios (e.g., flow rate, ignition source characteristics) that are considered in the different modeling approaches. Current models often fail to account for the unique properties of hydrogen compared to other fuels, and most lack rigorous validation with hydrogen as a fuel. A fault tree framework is proposed to systematically evaluate the probability of ignition by integrating various ignition mechanisms and their uncertainties. Furthermore, this type of framework could enable additional insights into the most important mechanisms and would enable uncertainty quantification in risk assessment modeling. Recommendations for future research include the need for experimental validation of ignition models and the development of comprehensive methodologies that incorporate the specifics of hydrogen behavior in real-world scenarios.

hydrogen↗