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DOE OSTI2015

Kullback--Leibler Approximation for Probability Measures on Infinite Dimensional Spaces

In a variety of applications it is important to extract information from a probability measure μ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and (possibly conditioned) continuous time Markov processes. It may then be of interest to find a measure ν, from within a simple class of measures, which approximates μ. Here, this problem is studied in the case where the Kullback–Leibler divergence is employed to measure the quality of the approximation. A calculus of variations viewpoint is adopted, and the particular case where ν is chosen from the set of Gaussian measures is studied in detail. Basic existence and uniqueness theorems are established, together with properties of minimizing sequences. Furthermore, parameterization of the class of Gaussians through the mean and inverse covariance is introduced, the need for regularization is explained, and a regularized minimization is studied in detail. The calculus of variations framework resulting from this work provides the appropriate underpinning for computational algorithms.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Hydrogen Extremely Low Probability of Rupture Version 1

SAND2024-08511O The Hydrogen Extremely Low Probability of Rupture (HELPR) software toolkit provides probabilistic fracture assessments of natural gas infrastructure for transporting hydrogen. Using probabilistic sampling and sensitivity analysis—along with engineering fatigue and fracture mechanics— the software develops models that can predict structural integrity measures for natural gas pipelines under stress. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Schroeder, Benjamin↗

DOE OSTI2019

An Improved Double-Gaussian Closure for the Subgrid Vertical Velocity Probability Distribution Function

Abstract The vertical velocity probability distribution function (PDF) is analyzed throughout the depth of the lower atmosphere, including the subcloud and cloud layers, in four large-eddy simulation (LES) cases of shallow cumulus and stratocumulus. Double-Gaussian PDF closures are examined to test their ability to represent a wide range of turbulence statistics, from stratocumulus cloud layers characterized by Gaussian turbulence to shallow cumulus cloud layers displaying strongly non-Gaussian turbulence statistics. While the majority of the model closures are found to perform well in the former case, the latter presents a considerable challenge. A new model closure is suggested that accounts for high skewness and kurtosis seen in shallow cumulus cloud layers. The well-established parabolic relationship between skewness and kurtosis is examined, with results in agreement with previous studies for the subcloud layer. In cumulus cloud layers, however, a modified relationship is necessary to improve performance. The new closure significantly improves the estimation of the vertical velocity PDF for shallow cumulus cloud layers, in addition to performing well for stratocumulus. In particular, the long updraft tail representing the bulk of cloudy points is much better represented and higher-order moments diagnosed from the PDF are also greatly improved. However, some deficiencies remain owing to fundamental limitations of representing highly non-Gaussian turbulence statistics with a double-Gaussian PDF.

Fitch, A. C.↗

DOE OSTI2018

A Joint Probability Density–Based Decomposition of Turbulence in the Atmospheric Boundary Layer

Abstract In convective flows, vertical turbulent fluxes, covariances between vertical velocity and scalar thermodynamic variables, include contributions from local mixing and large-scale coherent motions, such as updrafts and downdrafts. The relative contribution of these motions to the covariance is important in turbulence parameterizations. However, the flux partition is challenging, especially in regions without convective cloud. A method to decompose the vertical flux based on the corresponding joint probability density function (JPD) is introduced. The JPD-based method partitions the full JPD into a joint Gaussian part and the complement, which represent the local mixing and the large-scale coherent motions, respectively. The coherent part can be further divided into updraft and downdraft parts based on the sign of vertical velocity. The flow decomposition is independent of water condensate (cloud) and can be applied in cloud-free convection, the subcloud layer, and stratiform cloud regions. The method is applied to large-eddy simulation model data of three boundary layers. The results are compared with traditional cloud and cloud-core decompositions and a decaying scalar conditional sampling method. The JPD-based method includes a single free parameter and sensitivity tests show weak dependence on the parameter values. The results of the JPD-based method are somewhat similar to the cloud-core and conditional sampling methods. However, differences in the relative magnitude of the flux decomposition terms suggest that an objective definition of the flow regions is subtle and diagnosed flow properties like updraft characteristics depend on the sampling method. Moreover, the flux decomposition depends on the thermodynamic variable and convection characteristics.

Chinita, Maria J.↗

DOE OSTI2023

Time-dependent probability density function analysis of H-mode transitions

Abstract The first application of time-dependent probability density function (PDF) analysis to the L-H transition in fusion plasmas is presented. PDFs are constructed using Doppler Backscattering data of perpendicular fluctuation velocity, , and turbulence from the edge region of the DIII-D tokamak. These raw time-series data are sliced into millisecond-long sliding time-windows to create PDFs. During the transition, the PDFs develop strong right tails, indicative of turbulence-suppressing localised flows in the plasma edge; such features and other subtle behaviours are explored using novel information geometry techniques. This letter examines the applicability of these techniques to predict L-H transitions and investigate predator-prey self-regulation theories between turbulence and perpendicular velocity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2014

Species-Level Deconvolution of Metagenome Assemblies with Hi-C–Based Contact Probability Maps

Microbial communities consist of mixed populations of organisms, including unknown species in unknown abundances. These communities are often studied through metagenomic shotgun sequencing, but standard library construction methods remove long-range contiguity information; thus, shotgun sequencing and de novo assembly of a metagenome typically yield a collection of contigs that cannot readily be grouped by species. Methods for generating chromatin-level contact probability maps, e.g., as generated by the Hi-C method, provide a signal of contiguity that is completely intracellular and contains both intrachromosomal and interchromosomal information. Here, we demonstrate how this signal can be exploited to reconstruct the individual genomes of microbial species present within a mixed sample. We apply this approach to two synthetic metagenome samples, successfully clustering the genome content of fungal, bacterial, and archaeal species with more than 99% agreement with published reference genomes. We also show that the Hi-C signal can secondarily be used to create scaffolded genome assemblies of individual eukaryotic species present within the microbial community, with higher levels of contiguity than some of the species’ published reference genomes.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

Reference data, predictors, and probability grids for forest degradation classes in three sites in the Brazilian Amazon

Forest degradation by fires and selective logging is widespread in the Amazon region. We implemented a gradient boosted classification modeling framework to classify intact, logged, and burned forests at three Amazonian sites: Feliz Natal Municipality and Xingu Indigenous Territory in Mato Grosso State, and Saracá-Taquera National Forest in Pará State. We used forest degradation history from Landsat time-series as reference data and textural metrics derived from PlanetScope images as predictors. Textural metrics were computed using the Gray-Level Co-Occurrence Matrix (GLCM) textural technique. Included in the attached zip file are ten files: - a shapefile containing the reference data (fire and selective logging polygons and year of event) for each site; - a multiband tif file containing the 8 GLCM metrics used as predictors (Mean, Variance, Homogeneity, Contrast, Dissimilarity, Entropy, Angular Second Moment, Correlation) at the original PlanetScope resolution (3.125m) for each site; - a multiband tif file containing the 72 aggregated GLCM metrics used as predictors (Mean, Variance, Homogeneity, Contrast, Dissimilarity, Entropy, Angular Second Moment, and Correlation aggregated using the mean, first quartile, third quartile, maximum, median, minimum, root mean square, standard deviation, and skewness statistics) at 562m resolution for each site; - a multiband tif file containing the 3 probability grids for either intact, logged, or burned forests at the aggregation resolution (562m) for each site.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2017

Calculating Probability Densities with Homotopy and Applications to Particle Filters

In this work, we explore a homotopy sampling procedure and its generalization, loosely based on importance sampling, known as annealed importance sampling. The procedure makes use of a known probability distribution to find, via homotopy, the unknown normalization of a target distribution, as well as samples of the target distribution. We propose a reformulation of the method that leads to a rejection sampling alternative. Estimates of the error as a function of homotopy stages and sample averages are derived for the algorithmic version of the method. These estimates are useful in making computational efficiency decisions on how the calculation should proceed, given a computer architecture. Consideration is given to how the procedure can be adapted to Bayesian stationary and nonstationary estimation problems. The connection between homotopy sampling and thermodynamic integration is made. Emphasis is placed on the non-stationary problems, and in particular, on a sequential estimation technique known as particle filtering. It is shown that a modification of the particle filter framework to include the homotopy process can improve the computational robustness of particle filters.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

3D Multiresolution Velocity Model Fusion with Probability Graphical Models

ABSTRACT The variability in spatial resolution of seismic velocity models obtained via tomographic methodologies is attributed to many factors, including inversion strategies, ray-path coverage, and data integrity. Integration of such models, with distinct resolutions, is crucial during the refinement of community models, thereby enhancing the precision of ground-motion simulations. Toward this goal, we introduce the probability graphical model (PGM), combining velocity models with heterogeneous resolutions and nonuniform data point distributions. The PGM integrates data relations across varying resolution subdomains, enhancing detail within low-resolution (LR) domains by utilizing information and prior knowledge from high-resolution (HR) subdomains through a maximum posterior problem. Assessment of efficacy, utilizing both 2D and 3D velocity models—consisting of synthetic checkerboard models and a fault-zone model from Ridgecrest, California—demonstrates noteworthy improvements in accuracy, compared to state-of-the-art fusion techniques. Specifically, we find reductions of 30% and 44% in computed travel-time residuals for 2D and 3D models, respectively, as compared to conventional smoothing techniques. Unlike conventional methods, the PGM’s adaptive weight selection facilitates preserving and learning details from complex, nonuniform HR models and applies the enhancements to the LR background domain.

Geochemistry & Geophysics↗

DOE OSTI2016

Attributing Historical Changes in Probabilities of Record-Breaking Daily Temperature and Precipitation Extreme Events

Here, we describe two unprecedented large (100-member), longterm (61-year) ensembles based on MRI-AGCM3.2, which were driven by historical and non-warming climate forcing. These ensembles comprise the "Database for Policy Decision making for Future climate change (d4PDF)". We compare these ensembles to large ensembles based on another climate model, as well as to observed data, to investigate the influence of anthropogenic activities on historical changes in the numbers of record-breaking events, including: the annual coldest daily minimum temperature (TNn), the annual warmest daily maximum temperature (TXx) and the annual most intense daily precipitation event (Rx1day). These two climate model ensembles indicate that human activity has already had statistically significant impacts on the number of record-breaking extreme events worldwide mainly in the Northern Hemisphere land. Specifically, human activities have altered the likelihood that a wider area globally would suffer record-breaking TNn, TXx and Rx1day events than that observed over the 2001- 2010 period by a factor of at least 0.6, 5.4 and 1.3, respectively. However, we also find that the estimated spatial patterns and amplitudes of anthropogenic impacts on the probabilities of record-breaking events are sensitive to the climate model and/or natural-world boundary conditions used in the attribution studies.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2014

A Probability-based Approach to Evaluating Security of Nuclear Fuel Cycles

The National Research Council has reviewed several studies of the security and proliferation resistance of nuclear fuel cycles. The study found several recurring weaknesses in the execution of a commonly used method, which they call predefined frameworks. The predefined framework studies reviewed were attempts to utilize multiattribute utility theory to score and rank alternative fuel cycles. This white paper indicates how some of these weaknesses in the pre-defined frameworks (MAU) evaluation process can be addressed using more rigorous MAU assessment methods and models. First, the paper suggests how the weaknesses in previous MAU-based assessments could be corrected in future studies. The remaining sections of this paper describe an alternative approach that is based upon both probability theory and a multiplicative form of a multiattribute utility function.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2014

Using L/E Oscillation Probability Distributions

This paper explores the use of L /E oscillation probability distributions to compare experimental measurements and to evaluate oscillation models. In this case, L is the distance of neutrino travel and E is a measure of the interacting neutrino’s energy. While comparisons using allowed and excluded regions for oscillation model parameters are likely the only rigorous method for these comparisons, the L /E distributions are shown to give qualitative information on the agreement of an experiment’s data with a simple two-neutrino oscillation model. In more detail, this paper also outlines how the L /E distributions can be best calculated and used for model comparisons. Specifically, the paper presents the L /E data points for the final MiniBooNE data samples and, in the Appendix, explains and corrects the mistaken analysis published by the ICARUS collaboration.

Aguilar-Arevalo, A. A.↗

DOE OSTI2015

Efficient Probability of Failure Calculations for QMU using Computational Geometry (LDRD 13-0144 Final Report)

This SAND report summarizes our work on the Sandia National Laboratory LDRD project titled "Efficient Probability of Failure Calculations for QMU using Computational Geometry" which was project #165617 and proposal #13-0144. This report merely summarizes our work. Those interested in the technical details are encouraged to read the full published results, and contact the report authors for the status of the software and follow-on projects.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Informing a Tidal Turbine Strike Probability Model through Characterization of Fish Behavioral Response using Multibeam Sonar Output

One of the most important biological questions facing the marine and hydrokinetic (MHK) energy industry is whether fish and marine mammals that encounter MHK devices are likely to be struck by moving components. For hydrokinetic (HK) devices, i.e., those that generate energy from flowing water, this concern is greatest for large organisms because their increased length increases the probability that they will be struck as they pass through the area of blade sweep and because their increased mass means that the force absorbed if struck is greater and potentially more damaging (Amaral et al. 2015). Key to answering this question is understanding whether aquatic organisms change their swimming behavior as they encounter a device in a way that decreases their likelihood of being struck and possibly injured by the device. Whether near-field or far-field behavior results in general avoidance of or attraction to HK devices is a significant factor in the possible risk of physical contact with rotating turbine blades (Cada and Bevelhimer 2011).

13 HYDRO ENERGY↗

DOE OSTI2017

Probability of Detection Study to Assess the Performance of Nondestructive Inspection Methods for Wind Turbine Blades.

Wind turbine blades pose a unique set of inspection challenges that span from very thick and attentive spar cap structures to porous bond lines, varying core material and a multitude of manufacturing defects of interest. The need for viable, accurate nondestructive inspection (NDI) technology becomes more important as the cost per blade, and lost revenue from downtime, grows. NDI methods must not only be able to contend with the challenges associated with inspecting extremely thick composite laminates and subsurface bond lines, but must also address new inspection requirements stemming from the growing understanding of blade structural aging phenomena. Under its Blade Reliability Collaborative program, Sandia Labs quantitatively assessed the performance of a wide range of NDI methods that are candidates for wind blade inspections. Custom wind turbine blade test specimens, containing engineered defects, were used to determine critical aspects of NDI performance including sensitivity, accuracy, repeatability, speed of inspection coverage, and ease of equipment deployment. The detection of fabrication defects helps enhance plant reliability and increase blade life while improved inspection of operating blades can result in efficient blade maintenance, facilitate repairs before critical damage levels are reached and minimize turbine downtime. The Sandia Wind Blade Flaw Detection Experiment was completed to evaluate different NDI methods that have demonstrated promise for interrogating wind blades for manufacturing flaws or in-service damage. These tests provided the Probability of Detection information needed to generate industry-wide performance curves that quantify: 1) how well current inspection techniques are able to reliably find flaws in wind turbine blades (industry baseline) and 2) the degree of improvements possible through integrating more advanced NDI techniques and procedures. _____________ S a n d i a N a t i o n a l L a b o r a t o r i e s i s a m u l t i m i s s i o n l a b o r a t o r y m a n a g e d a n d o p e r a t e d b y N a t i o n a l T e c h n o l o g y a n d E n g i n e e r i n g S o l u t i o n s o f S a n d i a , L L C , a w h o l l y o w n e d s u b s i d i a r y o f H o n e y w e l l I n t e r n a t i o n a l , I n c . , f o r t h e U . S . D e p a r t m e n t o f E n e r g y ' s N a t i o n a l N u c l e a r S e c u r i t y A d m i n i s t r a t i o n u n d e r c o n t r a c t D E - N A 0 0 0 3 5 2 5 .

17 WIND ENERGY↗

DOE OSTI2017

Probability density of tunneled carrier states near heterojunctions calculated numerically by the scattering method.

The energy-dependent probability density of tunneled carrier states for arbitrarily specified longitudinal potential-energy profiles in planar bipolar devices is numerically computed using the scattering method. Results agree accurately with a previous treatment based on solution of the localized eigenvalue problem, where computation times are much greater. These developments enable quantitative treatment of tunneling-assisted recombination in irradiated heterojunction bipolar transistors, where band offsets may enhance the tunneling effect by orders of magnitude. The calculations also reveal the density of non-tunneled carrier states in spatially varying potentials, and thereby test the common approximation of uniform- bulk values for such densities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Probability of Loss of Assured Safety in Systems with Multiple Time-Dependent Failure Modes: Incorporation of Delayed Link Failure in the Presence of Aleatory Uncertainty.

Probability of loss of assured safety (PLOAS) is modeled for weak link (WL)/strong link (SL) systems in which one or more WLs or SLs could potentially degrade into a precursor condition to link failure that will be followed by an actual failure after some amount of elapsed time. The following topics are considered: (i) Definition of precursor occurrence time cumulative distribution functions (CDFs) for individual WLs and SLs, (ii) Formal representation of PLOAS with constant delay times, (iii) Approximation and illustration of PLOAS with constant delay times, (iv) Formal representation of PLOAS with aleatory uncertainty in delay times, (v) Approximation and illustration of PLOAS with aleatory uncertainty in delay times, (vi) Formal representation of PLOAS with delay times defined by functions of link properties at occurrence times for failure precursors, (vii) Approximation and illustration of PLOAS with delay times defined by functions of link properties at occurrence times for failure precursors, and (viii) Procedures for the verification of PLOAS calculations for the three indicated definitions of delayed link failure.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Probability of Encounter Between Ports of Entry (PrEP): Aversion Force-Field “Early Validation” Report

To enhance detection and interdiction of radiological or nuclear material trafficking between primary POEs into the US, The Department of Homeland Security is faced with highly variable smuggling pathways through expansive geographic regions. The goal of this project is to test an approach to estimating likely pathways, as well as the probability of encounter along any given route. Our goal is to test the feasibility of a novel approach based on assessing the adversary’s perception of discovery likelihood over a broad geographic region, and using that result to estimate an “aversion force field” over the same region. The aversion force field is derived from analogies based on the physics of electric charges. Combining the aversion force with the intention of an adversary to reach their destination, generates a route that is consistent with both the adversary’s intention and their aversion to deterrent measures. Phase I is exploratory. Its goal to demonstrate the feasibility of the approach. This report describes progress in an essential part of the approach, specifically, to implement and couple two principle model components: (1) the Bayesian network model of an adversary’s perception of discovery likelihood; and (2) the physics-inspired aversion field model. The objective is to show that the field produced from the two components is plausible and consistent with the assumptions and the data. Figure 1 illustrates the workflow of this phase to the present stage. After collecting preliminary data and implementing each of the two model components, they were separately evaluated. Following this step, the output from the Bayesian network was input to the aversion field solver, and the combined results evaluated as reported here.

97 MATHEMATICS AND COMPUTING↗