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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 NTRS2004

Deriving Laws from Ordering Relations

The effect of Richard T. Cox's contribution to probability theory was to generalize Boolean implication among logical statements to degrees of implication, which are manipulated using rules derived from consistency with Boolean algebra. These rules are known as the sum rule, the product rule and Bayes Theorem, and the measure resulting from this generalization is probability. In this paper, I will describe how Cox s technique can be further generalized to include other algebras and hence other problems in science and mathematics. The result is a methodology that can be used to generalize an algebra to a calculus by relying on consistency with order theory to derive the laws of the calculus. My goals are to clear up the mysteries as to why the same basic structure found in probability theory appears in other contexts, to better understand the foundations of probability theory, and to extend these ideas to other areas by developing new mathematics and new physics. The relevance of this methodology will be demonstrated using examples from probability theory, number theory, geometry, information theory, and quantum mechanics.

Knuth, Kevin H.↗
DOE OSTI2019

Probabilistic limit of detection for ricin identification using a shotgun proteomics assay

Robust and highly specific methods for the detection of the protein toxin ricin are of interest to the law enforcement community. In previous studies, methods based on liquid chromatography-tandem mass spectrometry shotgun proteomics have been proposed. The successful implementation of this approach relies on specific data evaluation criteria addressing (1) the quality of the mass spectrometric data, (2) the confidence of peptide identifications (peptide-spectrum matches), and (3) the number and sequence specificity of peptides detected. We present such data evaluation criteria, and use a novel approach to establish the limit of detection for this ricin assay. Specifically, we use logistic regression to determine the probability of detection for individual ricin peptides at different concentrations. We then apply basic rules from probability theory, combining these individual peptide probabilities into an overall assay limit of detection. This procedure yields an assay limit of detection for ricin at 42.5 ng on column or 21.25 ng/µL for a 2-µL injection. We also show that, in spite of the conventional wisdom that detergents are deleterious to mass spectrometric analyses, the presence of Tween-20 did not prevent detection of ricin peptides, and indeed assays performed in buffers that included Tween-20 gave better results than assays performed using other buffer formulations with or without detergent removal.

Heller, Natalie C.↗
NASA NTRS1986

Probabilistic versus fuzzy reasoning

This paper shows how to solve problems using probability theory that the fuzzy approaches claim probability cannot solve. By using the view that probabilities are a measure of belief in a proposition in a particular context, limitations imposed by the frequncy interpretations of probability are avoided. The various fuzzy approaches (fuzzy sets, fuzzy logic, possibility theory and higher order generalizations) seem to fill the gap caused by the restricted frequency interpretation. Close examination shows that the fuzzy approaches have exactly the same representation as the corresponding probabilistc approach and include similar calculi. The probabilistic approach assumes less information when the calculi differ.

Cheeseman, Peter↗
DOE OSTI2022

Conditional probability density functional theory

Here we present conditional probability (CP) density functional theory (DFT) as a formally exact theory. In essence, CP-DFT determines the ground-state energy of a system by finding the CP density from a series of independent Kohn-Sham (KS) DFT calculations. By directly calculating CP densities, we bypass the need for an approximate XC energy functional. In this paper we discuss and derive several key properties of the CP density and corresponding CP-KS potential. Illustrative examples are used throughout to help guide the reader through the various concepts and theory presented. We explore a suitable CP-DFT approximation and discuss exact conditions, limitations, and results for selected examples.

36 MATERIALS SCIENCE↗
NASA NTRSDate not supplied

Multiclass Flight Anomaly Detection Using Sensor Fusion Based on Dempster-Shafer Theory

As aviation systems in commercial operations continue to grow in complexity, the anomalies exhibited by these systems become more elaborate and difficult to detect. To address the challenge of detecting these complex anomalies, deep learning models have been used extensively in aviation anomaly detection studies, at the expense of end-user interpretability. Aiming to maintain the same level of interpretability as traditional threshold-exceedance methods, we continue our development of prediction models using ordinal patterns and their distributions throughout the flight. Specifically, this study extends our work into multiclass anomaly detection using sensor fusion based on Dempster-Shafer theory (DST), a second-order probability theory used to combine information from different sources of evidence. Our approach uses DST to reduce the uncertainty in the class predictions of an ensemble of classifiers. These classifiers rely on the similarity between flight data and class templates to make a prediction of the state of the aircraft. Our approach aims to take advantage of simple models trained on interpretable features (ordinal patterns) to correctly predict an anomaly and identify the flight dynamics linked to the anomaly. Our results show an improvement when using DST-based sensor fusion over simple majority voting. Additionally, our results provide insight into aircraft states linked to rare high-risk anomalies.

Risk detection↗
NASA NTRSDate not supplied

Multiclass Flight Anomaly Detection Using Sensor Fusion Based on Dempster-Shafer Theory

As aviation systems in commercial operations continue to grow in complexity, the anomalies exhibited by these systems become more elaborate and difficult to detect. To address the challenge of detecting these complex anomalies, deep learning models have been used extensively in aviation anomaly detection studies, at the expense of end-user interpretability. Aiming to maintain the same level of interpretability as traditional threshold-exceedance methods, we continue our development of prediction models using ordinal patterns and their distributions throughout the flight. Specifically, this study extends our work into multiclass anomaly detection using sensor fusion based on Dempster-Shafer theory (DST), a second-order probability theory used to combine information from different sources of evidence. Our approach uses DST toreduce the uncertainty in the class predictions of an ensemble of classifiers. These classifiers rely on the similarity between flight data and class templates to make a prediction of the state of the aircraft. Our approach aims to take advantage of simple models trained on interpretable features (ordinal patterns) to correctly predict an anomaly and identify the flight dynamics linked to the anomaly. Our results show an improvement when using DST-based sensor fusion over simple majority voting. Additionally, our results provide insight into aircraft states linked to rare high-risk anomalies.

Risk detection↗
DOE OSTI2025

Statistical evaluation of microscale stress conditions leading to void nucleation in the weak shock regime

Here, we investigate the heterogeneity of the stress state driven by anisotropic deformation response at the single crystal level through five statistical volume element (SVE) calculations of polycrystalline BCC tantalum. This work focuses on grain boundaries as a prominent material defect type prone to void nucleation based upon experimental observations of predominantly intergranular void nucleation in this material. The SVEs are constructed to be statistically representative of larger volumes of material and are meshed such that mean and standard deviation of grain size and orientation information is reconstructed. The computational meshes feature hexahedral (brick) elements and smooth conformal grain boundaries where significant stress concentration is known to occur, a tail effect of interest in the extreme events process of dynamic ductile damage. An existing micromechanical crystallographic plasticity model shown to capture the single crystal behavior of BCC tantalum well is used to perform the polycrystal calculations. The model includes representation of the non-Schmid effect of non-planar screw dislocation kinetics in tantalum. A three-dimensional stress state time profile predicted by damage modeling of a flyer plate impact experiment is applied as boundary conditions to each SVE. Resulting grain boundary stress state statistics are strongly non-Gaussian. Significant structural evolution is observed within the compressive hold before unloading into tension in the stress profile. Strong angular dependence of grain boundary traction magnitude with shock direction is observed. Non-Schmid effects continue to suggest their influence on propensity of microstructural defect types to nucleate voids. A general void nucleation criterion is proposed using probability theory. The general framework is specified to polycrystalline BCC tantalum in the weak shock regime to include the SVE calculations and literature molecular dynamics calculations of grain boundary void nucleation strength. Probability density functions (PDFs) are used to describe the interaction between the local stress state heterogeneity and the distributed grain boundary void nucleation strength state. A causation entropy maximization procedure removes the requirement for ad hoc selection of a PDF functional form and provides a rigorous procedure for data-based PDF determination. The resulting physically informed PDF describes the spatial appearance frequency of nucleated voids as a function of applied macroscale pressure. Lower length scale physics are thus packaged in a precise and computationally efficient way to provide computational plasticity insight to macroscale dynamic ductile damage models.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A comparative analysis of YOLOv8 and U-Net image segmentation approaches for transmission electron micrographs of polycrystalline thin films

Metallic thin films offer a platform to experimentally study the dynamics of microstructural evolution, but the required transmission electron microscopy (TEM)-based imaging generates complex images that are challenging to segment and quantify. This work provides a comparative analysis of a new YOLOv8 model and an established U-Net model for bright-field TEM images of polycrystals, employing a framework leveraging physical observables to evaluate performance against two hand-traced benchmark datasets. This methodology obviates the comparison of large, diversely structured, and manually labeled datasets that are required to assess performance on a per-image/per-pixel basis. It is found that the YOLOv8 model, adapted for real-time instance segmentation, has up to 43× faster inferencing (NVIDIA GeForce RTX 4090) compared to U-Net and reconstructs hand-traced grain size distributions (GSDs) with excellent fidelity, finding mean diameter within 3% for grains near an optimal magnification; for grains that deviate from the optimal pixel-diameter, the size of small- (large)-diameter grains is systematically over- (under)-estimated. This is partially mitigated by including scale-aware augmentations during training. Moreover, when the bias is corrected post-inference by a rigid shift in distribution, the YOLOv8 model reproduces ground truth GSDs with exceptional fidelity, with statistical tests indicating <5% probability that the distributions are distinct. Based on ground truth data, calibration curves pertaining to this shift can be constructed for a given model. This issue is not present in the U-Net model’s results, indicating that for quantitative measurements where the true size of objects is of interest, special procedures must be implemented for YOLO-based models.

36 MATERIALS SCIENCE↗
NASA NTRS1972

Bias and spread in extreme value theory measurements of probability of error

Extreme value theory is examined to explain the cause of the bias and spread in performance of communications systems characterized by low bit rates and high data reliability requirements, for cases in which underlying noise is Gaussian or perturbed Gaussian. Experimental verification is presented and procedures that minimize these effects are suggested. Even under these conditions, however, extreme value theory test results are not particularly more significant than bit error rate tests.

Smith, J. G.↗
NASA NTRS2009

Reliability Analysis of Systems Subject to First-Passage Failure

An obvious goal of reliability analysis is the avoidance of system failure. However, it is generally recognized that it is often not feasible to design a practical or useful system for which failure is impossible. Thus it is necessary to use techniques that estimate the likelihood of failure based on modeling the uncertainty about such items as the demands on and capacities of various elements in the system. This usually involves the use of probability theory, and a design is considered acceptable if it has a sufficiently small probability of failure. This report contains findings of analyses of systems subject to first-passage failure.

Lutes, Loren D.↗
DOE OSTI2023

Further development of finite-temperature density functional theory (Technical Report on FG02-08ER46496)

The final year of funding was spent supporting research into extending conditional probability theory to generate the thermal dependence of PBE. The necessary background work led to a paper being published on the uniform electron gas (Dennis Perchak, Ryan J. McCarty, and Kieron Burke, Phys. Rev. B 105, 165143 (2022).). The graduate student John Kozlowski also contributed to a mathematical paper about DFT (Steven Crisostomo, Ryan Pederson, John Kozlowski, Bhupalee Kalita, Antonio C. Cancio, Kiril Datchev, Adam Wasserman, Suhwan Song, and Kieron Burke, Letters in Mathematical Physics 113, 42 (2023).).

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2022

A Survey of Mathematical Structures for Lunar Networks

To sustain the current and increasing accessibility of space, a scalable communications infrastructure (i.e. the Solar System Internet, SSI) is necessary. The goal of this paper is to begin the discovery of the fundamental underlying mathematical structure of space networks to help the research community harness these structures for algorithm development and optimization. To ensure the applicability of the research, the approaches are considered through the lens of simulated scenarios inspired by the Artemis Back-to-the-Moon mission set for 2024. We note that any approach to an SSI must fit under the umbrella of Delay Tolerant Networking (DTN), due to celestial mobility, high link latencies, high variance in link latencies, disconnections, lack of end-to-end paths, and so on. These difficulties are exacerbated by the fact that the underlying structure of a space network is a time-evolving network and may experience multiple discontinuities in its topology. In this paper we propose several novel approaches to a mathematical foundation for Delay Tolerant Networking Theory that fall outside the traditional scope of temporal network theory. These techniques include methods from Topological Data Analysis, Dynamic Graph Analysis, Applied Algebraic Geometry, Probability Theory, and Game Theory. Some of these methods include tools adapted to the study of dynamic metric spaces, such as zigzag persistent homology and their higher parameter analogs. We find that several of these methods target desired engineering outcomes such as discovery and automatic sub-netting. While each approach is theoretical, they are also algorithmic in nature and offer immediate practical applications. The paper concludes with comparisons of the various methods along with suggestions for future work.

Delay tolerant networking↗
DOE OSTI2021

GeoMicro3D: A novel numerical model for simulating the reaction process and microstructure formation of alkali-activated slag

Highlights: • The GeoMicro3D model was innovatively developed for simulating the reaction process and microstructure formation of AAS. • In GeoMicro3D, the dissolution of slag and reactions of aqueous ions are fundamentally described in the local lattice cell. • A novel approach is proposed to speed up the nucleation simulations. • GeoMicro3D was implemented and verified with the relevant experimental data and thermodynamic calculation results. For the first time, this study developed a novel model, named GeoMicro3D, to simulate the reaction process and microstructure formation of alkali-activated slag. The GeoMicro3D model consists of four modules that are designed to simulate, respectively: (i) the initial spatial distribution of real-shape slag particles in alkaline activator, (ii) the dissolution of slag and diffusion of ions via the transition state theory and lattice Boltzmann method, respectively, (iii) the spatial distribution of reaction products using a nucleation probability theory, and (iv) the chemical reactions with thermodynamic modelling. Afterwards the GeoMicro3D model was implemented and verified. The simulation results were discussed and compared with the relevant experimental data and thermodynamic calculation results using GEMS. A good agreement was found in the comparisons, showing the strong simulation capability of GeoMicro3D.

36 MATERIALS SCIENCE↗
DOE OSTI2017

A risk map methodology to assess the spatial and temporal distribution of leakage into groundwater from Geologic Carbon Storage

The risks to potable aquifers due to brine leakage through plugged and abandoned (P&A) wells is highly uncertain and a potentially significant contributor to the risk profile in Geologic Carbon Storage (GCS). This uncertainty stems from the unknown location of wells and the large variance of P&A wellbore permeability, making the spatial assessment of P&A brine leakage risk challenging. A new methodology is presented to generate “risk maps”, or spatial distributions of brine leakage risk to groundwater resources as defined with no-impact or Maximum Contaminant Level (MCL) thresholds. The methodology utilizes probability theory, thereby avoiding the use of computationally expensive Monte Carlo simulations while maintaining flexibility in modeling techniques. These maps provide quantitative probabilities of risk as a function of time to inform site selection and monitoring during and post-injection, conducive to the US EPA's permitting of class-VI wells and the so-called “area of review”, AoR. As a demonstration of the methodology, a numerical model of a hypothetical fully-coupled system spanning from the injection reservoir to the USDW is used to assess the evolution of brine leakage through P&A wells. Risk maps of CO 2 leakage can also be generated with this methodology for a comprehensive assessment of GCS leakage risk.

58 GEOSCIENCES↗