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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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At least 991 records · Page 55
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Hydrodynamic Stability of Multicomponent Droplet Gasification in Reduced Gravity

This investigation addresses the problem of hydrodynamic stability of a two-component droplet undergoing spherically-symmetrical gasification. The droplet components are assumed to have characteristic liquid species diffusion times that are large relative to characteristic droplet surface regression times. The problem is formulated as a linear stability analysis, with a goal of predicting when spherically-symmetric droplet gasification can be expected to be hydrodynamically unstable from surface-tension gradients acting along the surface of a droplet which result from perturbations. It is found that for the conditions assumed in this paper (quasisteady gas phase, no initial droplet temperature gradients, diffusion-dominated gasification), surface tension gradients do not play a role in the stability characteristics. In addition, all perturbations are predicted to decay such that droplets were hydrodynamically stable. Conditions are identified, however, that deserve more analysis as they may lead to hydrodynamic instabilities driven by capillary effects.

Aharon, I.↗
NASA NTRS1998

Analysis of a Rocket Based Combined Cycle Engine during Rocket Only Operation

The all rocket mode of operation is a critical factor in the overall performance of a rocket based combined cycle (RBCC) vehicle. However, outside of performing experiments or a full three dimensional analysis, there are no first order parametric models to estimate performance. As a result, an axisymmetric RBCC engine was used to analytically determine specific impulse efficiency values based upon both full flow and gas generator configurations. Design of experiments methodology was used to construct a test matrix and statistical regression analysis was used to build parametric models. The main parameters investigated in this study were: rocket chamber pressure, rocket exit area ratio, percent of injected secondary flow, mixer-ejector inlet area, mixer-ejector area ratio, and mixer-ejector length-to-inject diameter ratio. A perfect gas computational fluid dynamics analysis was performed to obtain values of vacuum specific impulse. Statistical regression analysis was performed based on both full flow and gas generator engine cycles. Results were also found to be dependent upon the entire cycle assumptions. The statistical regression analysis determined that there were five significant linear effects, six interactions, and one second-order effect. Two parametric models were created to provide performance assessments of an RBCC engine in the all rocket mode of operation.

Smith, T. D.↗
NASA NTRS2001

Ground-Based Correlates of Solar Irradiance Variation

Ground-based instruments cannot directly measure solar irradiance variability at the 0.1% level at which it occurs because of the earth's atmosphere. However, many forms of ground-based solar observations correlate well with solar irradiance variations, and this fact has been used to construct facular-sunspot models which can explain about 90% of the variance of total solar irradiance as observed by spacecraft radiometers. It is not yet clear whether remaining discrepancies are observational or require additional sources in the model. This paper is a selective review of the current status of the use of ground-based data to understand spacecraft observations of solar irradiance and to apply this understanding to periods before space-based measurements were available. New results from the extension of the histogram analysis of NASA/NSO spectromagnetograph observations (Jones et al., 2000, ApJ529, 1070) to the period from Nov. 1992 to Sep. 2000 are reported which confirm that strong mixed polarity magnetic regions (quiet network) are not significantly correlated with total solar irradiance and which show an unexplained linear trend in the residuals of a multiple regression.

Jones, Harrison P.↗
NASA NTRS2005

Optimal Prediction of Clocks from Finite Data

This talk is about optimal linear prediction of processes with stationary dth increments, which serve as a class of models for random clock disturbances. The predictor is obtained by orthogonal projection on the affine space of estimators whose errors are invariant to additive polynomials of degree < d. The projection conditions give a system of linear equations thatcan be solved straightforwardly for the regression coefficients. If the data are equally spaced, then the predictor can be obtained by an extension of Levinson's algorithm.

stationary increments↗
NASA NTRSDate not supplied

Efficient Parametric Uncertainty Analysis of an Earth Entry Vehicle Concept Using Least Angle Regression

The objective of this work was to outline and apply an efficient and accurate parametric un-certainty propagation approach to the analysis of convective heating on an Earth entry vehicle concept. The described approach was based on Least Angle Regression used to solve a sparse and underdetermined linear system in the point-collocation non-intrusive polynomial chaos surrogate method. This approach involved an iterative process to computing the non-zero terms of the underlying polynomial chaos model using only enough samples to converge uncertainty interval predictions and Sobol index values based global nonlinear sensitivity estimates. The Earth entry vehicle was analyzed at three points along a representative trajectory for a Mars return mission. 329 sources of uncertainty were identified in the computational fluid dynamics model used to predict the forebody convective heating. These included uncertainty in flow field chemical rates, collision integrals, heats of formation, surface finite rate char model reaction rates, wall roughness height, and the turbulent Schmidt number. Results from this study showed that convective heating uncertainty as high as 50% of the nominal was predicted with only about 50 evaluations of the computational model. This was far fewer than would be required for a sampling-based approach or a full basis polynomial chaos model, which would have required over 50,000 samples. Additionally, results showed that over 90% of the total convective heating uncertainty was due to uncertainty in the N2catalytic rate on the surface, while the remainder of the uncertainty was attributed to the turbulent Schmidt number and the wall roughness uncertainties.

Thomas K West IV↗
DOE OSTI2021

The updated ITPA global H-mode confinement database: description and analysis

The multi-machine ITPA Global H-mode Confinement Database has been upgraded with new data from JET with the ITER-like wall and ASDEX Upgrade with the full tungsten wall. This paper describes the new database and presents results of regression analysis to estimate the global energy confinement scaling in H-mode plasmas using a standard power law. Various subsets of the database are considered, focusing on type of wall and divertor materials, confinement regime (all H-modes, ELMy H or ELM-free) and ITER-like constraints. Apart from ordinary least squares, two other, robust regression techniques are applied, which take into account uncertainty on all variables. Regression on data from individual devices shows that, generally, the confinement dependence on density and the power degradation are weakest in the fully metallic devices. Using the multi-machine scalings, predictions are made of the confinement time in a standard ELMy H-mode scenario in ITER. The uncertainty on the scaling parameters is discussed with a view to practically useful error bars on the parameters and predictions. One of the derived scalings for ELMy H-modes on an ITER-like subset is studied in particular and compared to the IPB98(y,2) confinement scaling in engineering and dimensionless form. Transformation of this new scaling from engineering variables to dimensionless quantities is shown to result in large error bars on the dimensionless scaling. Regression analysis in the space of dimensionless variables is therefore proposed as an alternative, yielding acceptable estimates for the dimensionless scaling. The new scaling, which is dimensionally correct within the uncertainties, suggests that some dependencies of confinement in the multi- machine database can be reconciled with parameter scans in individual devices. This includes vanishingly small dependence of confinement on line-averaged density and normalized plasma pressure (β), as well as a noticeable, positive dependence on effective atomic mass and plasma triangularity. Extrapolation of this scaling to ITER yields a somewhat lower confinement time compared to the IPB98(y, 2) prediction, possibly related to the considerably weaker dependence on major radius in the new scaling (slightly above linear). Further studies are needed to compare more flexible regression models with the power law used here. In addition, data from more devices concerning possible ‘hidden variables’ could help to determine their influence on confinement, while adding data in sparsely populated areas of the parameter space may contribute to further disentangling some of the global confinement dependencies in tokamak plasmas.

Database↗
DOE OSTI2024

Sub-pilot-scale Production of High-Value Products from U.S. Coals

Investigators from the University of Utah, University of Wyoming and Marshall University pursued a program to study the conversion of raw coal to high-value products of carbon fiber and silicon carbide. Team members also developed an initial framework for a data portal that can incorporate laboratory data on coal processing and product quality, and also work with tools for machine learning for data analysis, data visualization and economic assessment. Experimental R&D efforts focused on the conversion of raw coal to coal tar and other byproducts, and the resulting tar intermediates were upgraded to form anisotropic and isotropic pitch materials. These pitch materials were produced from coal using both thermal (pyrolysis) and chemical (mild solvolysis liquefaction) decomposition of raw coal. Four different coals were studied: Utah bituminous coal (Sufco), Wyoming PRB coal (Black Thunder), Illinois bituminous coal (Illinois #6), and West Virginia bituminous coal (Flying Eagle). Both metallurgical-grade coking coals and lower-grade steam coals were investigated, and controlled secondary gas-phase reactions were used during a two-stage pyrolysis process to induce cracking and condensation reactions among the pyrolytic tar species. This approach successfully improved the performance of the lower grade coals for yielding pitch materials, with properties more consistent with a commercial-grade pitch that had previously demonstrated success for quality carbon fiber production. The use of waste plastic materials was also studied, to help improve physical and chemical characteristics of the intermediate tars and final pitch product; in particular, for lowering the pitch softening point to an acceptable level for melt spinning carbon fiber. Mild solvolysis liquefaction was also used as a method for producing pitch for carbon fiber production. As expected, significantly higher pitch yields were obtained using this approach, and waste plastic materials were also successfully used to reduce pitch softening point to an acceptable level. The plastic materials were also utilized to create a solvent for the mild solvolysis process, and this plastic-derived solvent was shown to provide results consistent with more expensive commercial chemical solvents, and could thus avoid the need for costly recovery and recycle of a liquefaction solvent. Additional experimental R&D focused on the production of silicon carbide (β-SiC) from the residual char byproduct from pitch production, and also on the production of carbon fiber from the anisotropic pitch. SiC was successfully synthesized using a mixture of residual char and sandstone at a ratio of 1:1. Reaction temperature and residence time were optimized and yielded a product purity of 81%. For carbon fiber production, the most successful pitch samples were obtained from the mild solvolysis liquefaction approach, combined with the use of a plastic (HDPE)-derived solvent. Fiber properties improved over time as laboratory fiber production methodologies improved, and final yields of carbon fiber were obtained with a diameter of 12.14 ± 1.10 um, Modulus of 173.73 ± 15.25 GPa, and Tensile Strength of 1.04 ± 0.10 GPa. A proof-of-concept Modern Community Research Data Portal (MCRDP) was developed and deployed for coal and coal-derived pitch characterization, with the full support of (i) remote web-based access, (ii) distributed analysis, (iii) interactive visualization and exploration, (iv) shared and long-term data access, (v) advanced query capabilities and (vi) real-time collaboration. The Coal to Products Data Portal “coaltoproducts.org” provides researchers with space to store and share data within a project, tools for analyzing and understanding data for scientific investigation, and the ability to publish data to the broader community for reproducibility. The portal leverages the Material Commons 2.0 (MC) platform developed by the Center for PRedictive Integrated Structural Materials Science (PRISMS) of the University of Michigan, to achieve long-term longevity of data collections and, more importantly, collaborative science. A number of data visualization tools were also assessed and implemented for interrogating the experimental and modeling data. The machine learning portion of this project analyzed datasets from two different coal conversion processes performed on a diverse set of coal samples from both the coal pyrolysis experiments and the solvent liquefaction experiments. The work was initiated by exploring standard regression models on the pyrolysis data, aiming to understand the impact of sample characteristics and processing conditions on key product metrics. Over the course of the project, the focus expanded to include a variety of machine learning tools, delving into both supervised and unsupervised learning methods. Models tested on the pyrolysis data included linear, ridge, lasso, elastic-net, Gaussian process, random forest regression, and AutoSklearn, and the approach was continually refined to enhance predictive accuracy and model interpretability. Similar techniques were applied to the liquefaction data with an additional focus on feature engineering. Along with mesophase content, additional outputs of interest were the pitch yield, softening point, and QI content. Insights derived from these analyses are crucial in determining the factors influencing the quality and yield of coal-derived products. As the work progressed, the research evolved from foundational model comparisons to analyses of random forests, decision paths, and feature importance scores. A thorough market analysis was performed to examine the prospects of coal-based carbon fibers. The best opportunities for coal come from its lower and more stable price relative to petroleum, particularly for subbituminous coals, which is the primary advantage that a coal refinery may have over a petroleum refinery. Before a commercial CTP production facility can be modeled, however, several things need to be understood regarding the nature of the would-be coal refinery. These include the technology to be deployed, the size of facility, the volume(s) of co-product(s), and the waste and emissions profile of the plant. The volume of co-products and waste may be substantial and will require separate market analysis to ensure viability. In the near-term, the importance of coal tar pitch, in the form of carbon pitch, to the aluminum and steel industries is likely to overshadow the alternative use of this material as an input for carbon fiber. The importance of steel and aluminum in building materials, and the need for carbon materials in their manufacturing, will ensure that demand for these products remains for the long run. In addition, carbon fiber may also be the best substitute for steel and aluminum well into the future. While society will eventually be able to shift production of much of its electricity needs to renewables, it will not be able to shift away from fossil fuels for production of high-strength construction and vehicular materials. Demand for carbon fiber is expected to increase quickly, but the volume of carbon fiber and the amount of coal that would be needed to produce even a sizeable share of this market may still be relatively small compared to current coal production. Thus, other coal-based products like graphene, graphite, carbon foams, resins, and carbon-based building products will play important roles in sustaining coal production as coal-fired power generation continues to decline.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2026

Mass Spectrometer Transient Analysis

This software implements a complete preprocessing pipeline for transient mass spectrometry (MS) data collected during TAP (Temporal Analysis of Products) experiments. It is designed to extract chemically meaningful fluxes from overlapping ion signals by applying a calibrated defragmentation matrix and solving the resulting linear system using non-negative least squares (NNLS) regression. The core script, preprocess_mass_spec.py, performs the following operations: Gain correction: Applies amplifier gain scalars derived from inert-packed calibration pulses to normalize signal intensities across AMUs and acquisition settings. Background subtraction: Removes experiment baselines using user-defined time windows, ensuring compatibility with slow-diffusing species and preventing negative values that would interfere with NNLS. Options to subtract before and after defragmentation. Defragmentation: Constructs a fragmentation matrix A from zeroth moments of calibration pulses (equal molar gas:inert mixtures) and solves Ax=b at each time point, where b is the raw MS signal and x is the estimated species flux. The matrix is normalized to inert signals and accounts for instrument-specific fragmentation behavior. Pulse-mode handling: Supports both averaged and individual pulse modes, enabling statistical treatment of fluxes and calculation of standard deviations. Integration and output: Computes zeroth moments (integrated fluxes) and exports time-resolved and integrated data in CSV format, suitable for downstream kinetic modeling. The software is validated using both virtual TAP simulations (VTAP) and experimental data from propane dehydrogenation (PDH) on CrOx/Al2O3 catalysts. It preserves temporal resolution by applying NNLS point-by-point across the pulse duration (typically 6,000+ time slices per pulse), leveraging the linear superposition principle to reconstruct full flux profiles. The defragmented outputs are compatible with kinetic extraction methods such as the G and Y procedures, which are used to derive rate–concentration relationships from TAP data. The details of these validations are discussed in detail in the supporting manuscript and supporting information. Example data and output files are also included. The methodology is robust to experimental noise and drift, with calibration protocols that account for pulse size effects, MS aging, and inert gas normalization. The software is modular, reproducible, and tailored for high-throughput TAP-MS workflows in catalysis research.

Kristy, Stephen [Idaho National Laboratory (INL), ↗
NASA NTRS1992

Components of interannual ozone change based on Nimbus 7 TOMS data

A multiple regression statistical model is applied to estimate the latitude and seasonal dependences of the solar cycle, quasi-biennial oscillation (QBO), and anthropogenic trend components of stratospheric total ozone change using 13.2 years of Nimbus 7 TOMS data. The characteristics of the linear trend component are in agreement with earlier studies. The QBO regression coefficient is significantly different from zero at high southern latitudes in the Austral spring supporting earlier evidence that the Antarctic ozone depletion is modulated by the QBO. The existence of a solar cycle component is indicated by empirical studies of model residuals and by the approximate agreement of the derived global mean solar coefficient amplitude with photochemical calculations. Initial estimates for the latitude dependence of the solar coefficient suggest higher amplitudes with increasing latitude, especially in the Southern Hemisphere in spring. The statistical model predicts a return to more rapid ozone depletions during the next 4 years as solar minimum is approached.

Hood, Lon L.↗
DOE OSTI2024

A Provably Accurate Randomized Sampling Algorithm for Logistic Regression

In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we present a simple, randomized sampling-based algorithm for logistic regression problem that guarantees high-quality approximations to both the estimated probabilities and the overall discrepancy of the model. Our analysis builds upon two simple structural conditions that boil down to randomized matrix multiplication, a fundamental and well-understood primitive of randomized numerical linear algebra. We analyze the properties of estimated probabilities of logistic regression when leverage scores are used to sample observations, and prove that accurate approximations can be achieved with a sample whose size is much smaller than the total number of observations. To further validate our theoretical findings, we conduct comprehensive empirical evaluations. Overall, our work sheds light on the potential of using randomized sampling approaches to efficiently approximate the estimated probabilities in logistic regression, offering a practical and computationally efficient solution for large-scale datasets.

Chowdhury, Agniva↗
NASA NTRS1995

Geostatistical Approaches for Spatial Estimation of Vegetation Quantities Using Ground and Image Data

A major challenge in the study of the earth system is the mapping of vegetation quantities over large regions. Geostatistical methods, such as cokriging and stochastic simulation, have the potential to exploit more fully both remotely sensed data and ground information and improve the spatial estimation of vegetation variables over traditional regression methods. A synthetic example constructed from imaging spectrometer data allows a useful comparison among regression, cokriging and a simple probability-field method. A range of linear relationships between direct (sampled) and ancillary images is used. The lowest root-mean-square-error is achieved with cokriging until the correlation between direct and ancillary data exceeds .89, at which point regression is the superior estimator. Probability-field simulation gives a range of possible realizations, most more precise than those from regression. The relationship between ground measurements and image data is thus demonstrated to be one of the critical factors in the choice of a spatial estimation method.

Dungan, Jennifer L.↗
DOE OSTI2022

Predicting battery capacity from impedance at varying temperature and state of charge using machine learning

Prediction of battery health from electrochemical impedance spectroscopy (EIS) data can enable rapid measurement of battery state in real-world applications without using additional sensors or time-consuming performance measurements. However, deconvoluting the effect of capacity, state of charge, and temperature on EIS response is complicated analytically. Here, various machine-learning models, such as linear, Gaussian process, random forest, and artificial neural network regression, are utilized to predict capacity from EIS using hundreds of capacity, direct current (DC) resistance, and EIS measurements recorded under varying conditions of health, temperature, and state of charge (SOC). Several feature extraction and selection methods from traditional electrochemical analysis and statistical modeling are explored using machine-learning pipelines. EIS data from just two frequencies can accurately predict capacity, and interrogation shows that the optimal set of frequencies is not usually intuitive. Best results are achieved with an ensemble model, which predicts battery capacity with a mean absolute error of 1.9% on data from unobserved cells.

25 ENERGY STORAGE↗
DOE OSTI2024

Development of Modified Perturbation Solutions to the One-Phase Stefan Problems With a Convective Boundary

The classical Stefan problem is used to track the moving solid-liquid interface during the freezing process. Perturbation theory has often been applied to find an approximate analytical solution due to the nonlinearity of the moving interface. However, the Stefan number (i.e., the sensible over latent heat) must be small and usually less than 0.01 to assume the perturbation expansion, which in turn limits the thermal engineering applications. In this study, a modified perturbation solution is developed by adding a correction term after the leading-order solution to be valid for a much wider range of Stefan numbers (i.e., 0.01 less than or equal to Ste less than or equal to 1). Specifically, a one-phase Stefan problem is first formulated subjected to a convective boundary in the Cartesian, cylindrical, and spherical coordinate systems for inward solidification. The leading-order solution is calculated based on the regular perturbation theory, while the correction term is obtained using the Monte-Carlo method and a multi-variant regression. Results show that the correction term has a linear relationship with the Stefan number and is not significantly influenced by the Biot number. The proposed modified perturbation solution can accurately and rapidly predict the nonlinear moving interface motion for the freezing process.

DIRECT ENERGY CONVERSION,MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Leveraging Artificial Intelligence to Predict Novel Eutectic Alloys

The goal of this project was to train an artificial neural network (ANN) to predict the fractional composition and melting point of eutectic alloys using fundamental atomic properties as inputs. The fundamental properties considered include atomic number, atomic weight, atomic radius, valence electron concentration, electronegativity, and electron affinity. The project involved several phases, starting with data preparation, where phase diagram data was harvested from the ASM International database. Approximately 1300 binary eutectics were collected and cleaned to ensure relevance and accuracy. A regression model was selected for training, utilizing a rectified linear unit as the activation function. Various model configurations were evaluated for predictive accuracy, with validation techniques employed to ensure robustness. The model demonstrated predictive capabilities above random guessing and was able to achieve up to 11% accuracy under certain conditions. An ablative test identified atomic radius and valence electron concentration as critical inputs for model performance. Incorporating the melting point of atomic constituents improved accuracy significantly, although ultimately the model’s predictive capability still fell short of the 80% target. This report details the methodology, results, and implications of the research, contributing to the understanding of employing artificial intelligence to predict the phase transition behavior of eutectic alloys.

36 MATERIALS SCIENCE↗
NASA NTRS1980

Image-analysis library

MATHPAC image-analysis library is collection of general-purpose mathematical and statistical routines and special-purpose data-analysis and pattern-recognition routines for image analysis. MATHPAC library consists of Linear Algebra, Optimization, Statistical-Summary, Densities and Distribution, Regression, and Statistical-Test packages.

Source record↗
NASA NTRSDate not supplied

Developing Rationale for Experimental Designs Employed During Forthcoming NASA Quesst Mission Community Noise Campaigns

Since the publication of R.A. Fisher’s “The Arrangement of Field Experiments” in 1926, the enumerated principles that contributed to the improvement of agricultural field experiments in the early 20th century (randomization, replication, blocking, and appropriate variation of factors) remain hallmarks of all well-designed clinical trials and scientific endeavors in the 21st century. Beginning in 2026, NASA will conduct community noise campaigns with the first-of-kind X-59 experimental aircraft to 1) demonstrate the possibility of quiet supersonic flight over land and 2) to collect live data about annoyance (a categorical response) in relation to estimated noise levels (an experimental factor) produced by the new noise phenomenon, a low-noise “sonic thump”. The resulting predicted relationship between perceptual response and estimated noise level, e.g., mixed logistic regression or related models in the class of generalized linear (mixed) models, is believed to be a useful policy tool that domestic and international regulators can use when deciding whether existing prohibitions of supersonic flight over land can be replaced with a noise-based limit. The X-59 is engineered with the expectation that annoyance in the tested ranges should be a rare outcome, and, consequently, NASA convened an interdisciplinary team to examine and refine the rationale underlying the experimental design for future community campaigns. In this presentation, we review relevant literature on experiments with rare binary outcomes, relate the deliberations of the NASA team to tenets of good experimental design, and highlight several challenges and operational realities of this ambitious campaign.

Design of Experiments; blocking; randomization; co↗
NASA NTRS1994

Understanding software faults and their role in software reliability modeling

This study is a direct result of an on-going project to model the reliability of a large real-time control avionics system. In previous modeling efforts with this system, hardware reliability models were applied in modeling the reliability behavior of this system. In an attempt to enhance the performance of the adapted reliability models, certain software attributes were introduced in these models to control for differences between programs and also sequential executions of the same program. As the basic nature of the software attributes that affect software reliability become better understood in the modeling process, this information begins to have important implications on the software development process. A significant problem arises when raw attribute measures are to be used in statistical models as predictors, for example, of measures of software quality. This is because many of the metrics are highly correlated. Consider the two attributes: lines of code, LOC, and number of program statements, Stmts. In this case, it is quite obvious that a program with a high value of LOC probably will also have a relatively high value of Stmts. In the case of low level languages, such as assembly language programs, there might be a one-to-one relationship between the statement count and the lines of code. When there is a complete absence of linear relationship among the metrics, they are said to be orthogonal or uncorrelated. Usually the lack of orthogonality is not serious enough to affect a statistical analysis. However, for the purposes of some statistical analysis such as multiple regression, the software metrics are so strongly interrelated that the regression results may be ambiguous and possibly even misleading. Typically, it is difficult to estimate the unique effects of individual software metrics in the regression equation. The estimated values of the coefficients are very sensitive to slight changes in the data and to the addition or deletion of variables in the regression equation. Since most of the existing metrics have common elements and are linear combinations of these common elements, it seems reasonable to investigate the structure of the underlying common factors or components that make up the raw metrics. The technique we have chosen to use to explore this structure is a procedure called principal components analysis. Principal components analysis is a decomposition technique that may be used to detect and analyze collinearity in software metrics. When confronted with a large number of metrics measuring a single construct, it may be desirable to represent the set by some smaller number of variables that convey all, or most, of the information in the original set. Principal components are linear transformations of a set of random variables that summarize the information contained in the variables. The transformations are chosen so that the first component accounts for the maximal amount of variation of the measures of any possible linear transform; the second component accounts for the maximal amount of residual variation; and so on. The principal components are constructed so that they represent transformed scores on dimensions that are orthogonal. Through the use of principal components analysis, it is possible to have a set of highly related software attributes mapped into a small number of uncorrelated attribute domains. This definitively solves the problem of multi-collinearity in subsequent regression analysis. There are many software metrics in the literature, but principal component analysis reveals that there are few distinct sources of variation, i.e. dimensions, in this set of metrics. It would appear perfectly reasonable to characterize the measurable attributes of a program with a simple function of a small number of orthogonal metrics each of which represents a distinct software attribute domain.

Munson, John C.↗
DOE OSTI2024

Gradient Coding With Iterative Block Leverage Score Sampling

Gradient coding is a method for mitigating straggling servers in a centralized computing network that uses erasure-coding techniques to distributively carry out first-order optimization methods. Randomized numerical linear algebra uses randomization to develop improved algorithms for large-scale linear algebra computations. In this study, we propose a method for distributed optimization that combines gradient coding and randomized numerical linear algebra. The proposed method uses a randomized ℓ 2 -subspace embedding and a gradient coding technique to distribute blocks of data to the computational nodes of a centralized network, and at each iteration the central server only requires a small number of computations to obtain the steepest descent update. The novelty of our approach is that the data is replicated according to importance scores, called block leverage scores, in contrast to most gradient coding approaches that uniformly replicate the data blocks. Furthermore, we do not require a decoding step at each iteration, avoiding a bottleneck in previous gradient coding schemes. We show that our approach results in a valid ℓ 2 -subspace embedding, and that our resulting approximation converges to the optimal solution.

97 MATHEMATICS AND COMPUTING↗