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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 NTRS1989

The Fault Tree Compiler (FTC): Program and mathematics

The Fault Tree Compiler Program is a new reliability tool used to predict the top-event probability for a fault tree. Five different gate types are allowed in the fault tree: AND, OR, EXCLUSIVE OR, INVERT, AND m OF n gates. The high-level input language is easy to understand and use when describing the system tree. In addition, the use of the hierarchical fault tree capability can simplify the tree description and decrease program execution time. The current solution technique provides an answer precisely (within the limits of double precision floating point arithmetic) within a user specified number of digits accuracy. The user may vary one failure rate or failure probability over a range of values and plot the results for sensitivity analyses. The solution technique is implemented in FORTRAN; the remaining program code is implemented in Pascal. The program is written to run on a Digital Equipment Corporation (DEC) VAX computer with the VMS operation system.

Butler, Ricky W.↗
NASA NTRS1982

An automated approach to the design of decision tree classifiers

An automated technique is presented for designing effective decision tree classifiers predicated only on a priori class statistics. The procedure relies on linear feature extractions and Bayes table look-up decision rules. Associated error matrices are computed and utilized to provide an optimal design of the decision tree at each so-called 'node'. A by-product of this procedure is a simple algorithm for computing the global probability of correct classification assuming the statistical independence of the decision rules. Attention is given to a more precise definition of decision tree classification, the mathematical details on the technique for automated decision tree design, and an example of a simple application of the procedure using class statistics acquired from an actual Landsat scene.

Argentiero, P.↗
DOE OSTI2021

Deterministic symbolic regression with derivative information: General methodology and application to equations of state

Symbolic regression methods simultaneously determine the model functional form and the regression parameter values by generating expression trees. Symbolic regression can capture the complexity of real–world phenomena but the use of deterministic optimization for symbolic regression has been limited due to the complexity of the search space of existing formulations. Herein we present a novel deterministic mixed–integer nonlinear programming formulation for symbolic regression that incorporates derivative constraints through auxiliary expression trees. By applying the chain rule to mathematical operations, binary expression trees are capable of representing the calculation of first and second derivatives. We apply this formulation to illustrative examples using derivative information to show increased model discrimination capability. In addition, we perform a case study of a thermodynamic equation of state to gain insight on valid functional forms with thermodynamics–based constraints on the first and second derivatives.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Getting allometry right at the Oak Ridge free‐air CO 2 enrichment experiment: Old problems and new opportunities for global change experiments

Societal Impact Statement Free‐air CO 2 enrichment (FACE) experiments provide essential data on forest responses to increasing atmospheric CO 2 for evaluations of climate change impacts on humanity. Understanding and reducing the uncertainty in the experimental results is critical to ensure scientific and public confidence in the models and policy initiatives that derive therefrom. One source of uncertainty is the estimation of tree biomass using mathematical relationships between biomass and easily obtained and non‐destructive measurements (allometry). We evaluated the robustness of the allometric relationships established at the beginning of a FACE experiment and discuss the challenges and opportunities for the new generation of FACE experiments. Summary Long‐term field experiments to elucidate forest responses to rising atmospheric CO 2 concentration require allometric equations to estimate tree biomass from non‐destructive measurements of tree size. We analyzed whether the allometric equations established at the beginning of a free‐air CO 2 enrichment (FACE) experiment in a Liquidambar styraciflua plantation were still valid at the end of the 12 year experiment. Aboveground woody biomass was initially predicted by an equation that included bole diameter, taper, and height, assuming that including taper and height as predictors would accommodate changes in tree structure that might occur over time and in response to elevated CO 2 . At the conclusion of the FACE experiment, we harvested 23 trees, measured dimensions and dry mass of boles and branches, and extracted and measured the woody root mass of 10 trees. Although 10 of the harvested trees were larger than the trees used to establish the allometric relationship, measured aboveground woody biomass was well predicted by the original allometry. The initial linear equation between bole basal area and woody root biomass underestimated final root biomass by 28%, but root biomass was just 21% of total wood mass, and errors in aboveground and belowground estimates were offsetting. The allometry established at the beginning of the experiment provided valid predictions of tree biomass throughout the experiment. New allometric approaches using terrestrial laser scanning should reduce an important source of uncertainty in decade‐long forest experiments and in assessments of centuries‐long forest biomass accretion used in evaluating carbon offsets and climate mitigation.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

Quantum Markov States and Quantum Hidden Markov States

In a previous paper (Funct. Anal. Appl., 3 (2015), 205–209), we defined quantum Markov states. Here we recall this definition and present a proof of the results from that paper (which are given there without proofs). We give a definition of a quantum hidden Markov state generated by a function of a quantum Markov process and show how it is related to other definitions of such states. Our definitions work for quantum Markov fields on ℤ{sup N} and on graphs. We consider an example with the Cayley tree.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1986

Simplified Decoding of Convolutional Codes

Some complicated intermediate steps shortened or eliminated. Decoding of convolutional error-correcting digital codes simplified by new errortrellis syndrome technique. In new technique, syndrome vector not computed. Instead, advantage taken of newly-derived mathematical identities simplify decision tree, folding it back on itself into form called "error trellis." This trellis graph of all path solutions of syndrome equations. Each path through trellis corresponds to specific set of decisions as to received digits. Existing decoding algorithms combined with new mathematical identities reduce number of combinations of errors considered and enable computation of correction vector directly from data and check bits as received.

Truong, T. K.↗
DOE OSTI2022

Design of Digital Twin Sensing Strategies Via Predictive Modeling and Interpretable Machine Learning

This work develops a methodology for sensor placement and dynamic sensor scheduling decisions for digital twins. The digital twin data assimilation is posed as a classification problem, and predictive models are used to train optimal classification trees that represent the map from observed data to estimated digital twin states. In addition to providing a rapid digital twin updating capability, the resulting classification trees yield an interpretable mathematical representation that can be queried to inform sensor placement and sensor scheduling decisions. The proposed approach is demonstrated for a structural digital twin of a 12 ft wingspan unmanned aerial vehicle. Offline, training data are generated by simulating scenarios using predictive reduced-order models of the vehicle in a range of structural states. Furthermore, these training data can be further augmented using experimental or other historical data. In operation, the trained classifier is applied to observational data from the physical vehicle, enabling rapid adaptation of the digital twin in response to changes in structural health. Within this context, we study the performance of the optimal tree classifiers and demonstrate how they enable explainable structural assessments from sparse sensor measurements and also inform optimal sensor placement.

47 OTHER INSTRUMENTATION↗
NASA NTRS1993

Software For Fault-Tree Diagnosis Of A System

Fault Tree Diagnosis System (FTDS) computer program is automated-diagnostic-system program identifying likely causes of specified failure on basis of information represented in system-reliability mathematical models known as fault trees. Is modified implementation of failure-cause-identification phase of Narayanan's and Viswanadham's methodology for acquisition of knowledge and reasoning in analyzing failures of systems. Knowledge base of if/then rules replaced with object-oriented fault-tree representation. Enhancement yields more-efficient identification of causes of failures and enables dynamic updating of knowledge base. Written in C language, C++, and Common LISP.

Iverson, Dave↗
DOE OSTI2019

Visualizing Hierarchical Performance Profiles of Parallel Codes Using CallFlow

Calling context trees (CCTs) couple performance metrics with call paths, helping understand the execution and performance of parallel programs. To identify performance bottlenecks, programmers and performance analysts visually explore CCTs to form and validate hypotheses regarding degraded performance. However, due to the complexity of parallel programs, existing visual representations do not scale to applications running on a large number of processors. In this work, we present CallFlow, an interactive visual analysis tool that provides a high-level overview of CCTs together with semantic refinement operations to progressively explore CCTs. Using a flow-based metaphor, we visualize a CCT by treating execution time as a resource spent during the call chain, and demonstrate the effectiveness of our design with case studies on large-scale, production simulation codes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Learning epistatic polygenic phenotypes with Boolean interactions

Detecting epistatic drivers of human phenotypes is a considerable challenge. Traditional approaches use regression to sequentially test multiplicative interaction terms involving pairs of genetic variants. For higher-order interactions and genome-wide large-scale data, this strategy is computationally intractable. Moreover, multiplicative terms used in regression modeling may not capture the form of biological interactions. Building on the Predictability, Computability, Stability (PCS) framework, we introduce the epiTree pipeline to extract higher-order interactions from genomic data using tree-based models. The epiTree pipeline first selects a set of variants derived from tissue-specific estimates of gene expression. Next, it uses iterative random forests (iRF) to search training data for candidate Boolean interactions (pairwise and higher-order). We derive significance tests for interactions, based on a stabilized likelihood ratio test, by simulating Boolean tree-structured null (no epistasis) and alternative (epistasis) distributions on hold-out test data. Finally, our pipeline computes PCS epistasis p-values that probabilisticly quantify improvement in prediction accuracy via bootstrap sampling on the test set. We validate the epiTree pipeline in two case studies using data from the UK Biobank: predicting red hair and multiple sclerosis (MS). In the case of predicting red hair, epiTree recovers known epistatic interactions surrounding MC1R and novel interactions, representing non-linearities not captured by logistic regression models. In the case of predicting MS, a more complex phenotype than red hair, epiTree rankings prioritize novel interactions surrounding HLA-DRB1 , a variant previously associated with MS in several populations. Taken together, these results highlight the potential for epiTree rankings to help reduce the design space for follow up experiments.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS2005

Faults Discovery By Using Mined Data

Fault discovery in the complex systems consist of model based reasoning, fault tree analysis, rule based inference methods, and other approaches. Model based reasoning builds models for the systems either by mathematic formulations or by experiment model. Fault Tree Analysis shows the possible causes of a system malfunction by enumerating the suspect components and their respective failure modes that may have induced the problem. The rule based inference build the model based on the expert knowledge. Those models and methods have one thing in common; they have presumed some prior-conditions. Complex systems often use fault trees to analyze the faults. Fault diagnosis, when error occurs, is performed by engineers and analysts performing extensive examination of all data gathered during the mission. International Space Station (ISS) control center operates on the data feedback from the system and decisions are made based on threshold values by using fault trees. Since those decision-making tasks are safety critical and must be done promptly, the engineers who manually analyze the data are facing time challenge. To automate this process, this paper present an approach that uses decision trees to discover fault from data in real-time and capture the contents of fault trees as the initial state of the trees.

Lee, Charles↗
DOE OSTI2025

From Feynman diagrams to the amplituhedron: a gentle review

In this article we review, for a mathematical audience, the computation of (tree-level) scattering amplitudes in Yang-Mills theory in detail. In particular we demonstrate explicitly how the same formulas for six-particle NMHV helicity amplitudes are obtained from summing Feynman diagrams and from computing the canonical form of the n=6, k=1, m=4 amplituhedron.

Feynman diagrams↗
NASA NTRS2013

Method and system for dynamic probabilistic risk assessment

The DEFT methodology, system and computer readable medium extends the applicability of the PRA (Probabilistic Risk Assessment) methodology to computer-based systems, by allowing DFT (Dynamic Fault Tree) nodes as pivot nodes in the Event Tree (ET) model. DEFT includes a mathematical model and solution algorithm, supports all common PRA analysis functions and cutsets. Additional capabilities enabled by the DFT include modularization, phased mission analysis, sequence dependencies, and imperfect coverage.

Dugan, Joanne Bechta↗
DOE OSTI2023

Learning Symbolic Expressions: Mixed-Integer Formulations, Cuts, and Heuristics

Here, in this paper, we consider the problem of learning a regression function without assuming its functional form. This problem is referred to as symbolic regression. An expression tree is typically used to represent a solution function, which is determined by assigning operators and operands to the nodes. Cozad and Sahinidis propose a nonconvex mixed-integer nonlinear program (MINLP), in which binary variables are used to assign operators and nonlinear expressions are used to propagate data values through nonlinear operators, such as square, square root, and exponential. We extend this formulation by adding new cuts that improve the solution of this challenging MINLP. We also propose a heuristic that iteratively builds an expression tree by solving a restricted MINLP. We perform computational experiments and compare our approach with a mixed-integer program–based method and a neural network–based method from the literature.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2011

Graph Theory Roots of Spatial Operators for Kinematics and Dynamics

Spatial operators have been used to analyze the dynamics of robotic multibody systems and to develop novel computational dynamics algorithms. Mass matrix factorization, inversion, diagonalization, and linearization are among several new insights obtained using such operators. While initially developed for serial rigid body manipulators, the spatial operators and the related mathematical analysis have been shown to extend very broadly including to tree and closed topology systems, to systems with flexible joints, links, etc. This work uses concepts from graph theory to explore the mathematical foundations of spatial operators. The goal is to study and characterize the properties of the spatial operators at an abstract level so that they can be applied to a broader range of dynamics problems. The rich mathematical properties of the kinematics and dynamics of robotic multibody systems has been an area of strong research interest for several decades. These properties are important to understand the inherent physical behavior of systems, for stability and control analysis, for the development of computational algorithms, and for model development of faithful models. Recurring patterns in spatial operators leads one to ask the more abstract question about the properties and characteristics of spatial operators that make them so broadly applicable. The idea is to step back from the specific application systems, and understand more deeply the generic requirements and properties of spatial operators, so that the insights and techniques are readily available across different kinematics and dynamics problems. In this work, techniques from graph theory were used to explore the abstract basis for the spatial operators. The close relationship between the mathematical properties of adjacency matrices for graphs and those of spatial operators and their kernels were established. The connections hold across very basic requirements on the system topology, the nature of the component bodies, the indexing schemes, etc. The relationship of the underlying structure is intimately connected with efficient, recursive computational algorithms. The results provide the foundational groundwork for a much broader look at the key problems in kinematics and dynamics. The properties of general graphs and trees of nodes and edge were examined, as well as the properties of adjacency matrices that are used to describe graph connectivity. The nilpotency property of such matrices for directed trees was reviewed, and the adjacency matrices were generalized to the notion of block weighted adjacency matrices that support block matrix elements. This leads us to the development of the notion of Spatial Kernel Operator SKO kernels. These kernels provide the basis for the development of SKO resolvent operators.

Jain, Abhinandan↗
DOE OSTI2021

Physics-Infused AI/ML Based Digital-Twin Framework for Flow-Induced-Vibration Damage Prediction in a Nuclear Reactor Heat Exchanger

This report summarizes some of the ongoing work related to the development of an expert-elicitation-digital-twin framework for real time damage state prediction in heat exchanger components of a nuclear reactor. The framework is targeted towards predicting damage associated with coupled low cycle fatigue (associated with regular heat-up, cool-down and power operation transients) and high cycle fatigue (associated with flow induced vibration transients). The overall framework will be based on a NoSQL based database, physics-infused-geometry-dependent virtual-sensor data, different AI/ML techniques-based data-driven-predictive-model applications (Apps) and real-time plant sensor measurements available through few existing sensors. Towards this overall goal, this report updates some of the ongoing work, such as on implementation of a NoSQL Database (such as MongoDB), FE based heat transfer analysis of a heat exchanger (e.g. of a PWR steam generator) for generating geometry-dependent virtual sensor data and evaluation of various AI/ML models such as based on multivariate linear regression, ensembled decision-tree based Random-Forest and Gradient-Boosting regression and high-dimensional-kernel-function-transformation based Support-Vector-Machine regression models. The AI/ML models were evaluated for predicting multi-time-series thermal states at thousands of 3D point-clouds

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Computing a Stable Distance on Merge Trees

Distances on merge trees facilitate visual comparison of collections of scalar fields. Two desirable properties for these distances to exhibit are 1) the ability to discern between scalar fields which other, less complex topological summaries cannot and 2) to still be robust to perturbations in the dataset. The combination of these two properties, known respectively as stability and discriminativity, has led to theoretical distances which are either thought to be or shown to be computationally complex and thus their implementations have been scarce. In order to design similarity measures on merge trees which are computationally feasible for more complex merge trees, many researchers have elected to loosen the restrictions on at least one of these two properties. The question still remains, however, if there are practical situations where trading these desirable properties is necessary. Here we construct a distance between merge trees which is designed to retain both discriminativity and stability. While our approach can be expensive for large merge trees, we illustrate its use in a setting where the number of nodes is small. This setting can be made more practical since we also provide a proof that persistence simplification increases the outputted distance by at most half of the simplified value. As a result, we demonstrate our distance measure on applications in shape comparison and on detection of periodicity in the von Kármán vortex street.

97 MATHEMATICS AND COMPUTING↗