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NASA NTRSDate not supplied

Statistical Analysis of Fading Power Vectors for Real-Time Atmospheric Channel Emulation

The design and testing of a free-space optical communication system requires assessment of the impact of random fluctuations in received power from a laser beam transmitted over an atmospheric channel. A number of methods for generating fading power vectors for in-lab emulation of an atmospheric channel have previously been reported. These techniques include spectral shaping and filtering of a signal from a normally distributed pseudo-random number generator, full wave optics simulations with random phase screens, and pre-recorded measurements from experimental free-space links. In this work, a statistical analysis of atmospheric fading is presented with the goal of producing a practical engineering model for the fading channel suitable for generating synthetic fade vectors in real-time for long-duration receiver testing with channel interleaving. Specifically, a parametric model is developed for turbulence-induced fade on space-to-ground links with large-aperture receivers, including aperture-averaging and the effects of aperture size on the instantaneous coupling efficiency for mode-limited receivers. In particular, we analyze the probability density function and temporal power spectrum for fluctuations of the coupling efficiency for few-mode fibers in a range of turbulence conditions.

free-space optical communication↗
NASA NTRS1973

Multiple regression technique for Pth degree polynominals with and without linear cross products

A multiple regression technique was developed by which the nonlinear behavior of specified independent variables can be related to a given dependent variable. The polynomial expression can be of Pth degree and can incorporate N independent variables. Two cases are treated such that mathematical models can be studied both with and without linear cross products. The resulting surface fits can be used to summarize trends for a given phenomenon and provide a mathematical relationship for subsequent analysis. To implement this technique, separate computer programs were developed for the case without linear cross products and for the case incorporating such cross products which evaluate the various constants in the model regression equation. In addition, the significance of the estimated regression equation is considered and the standard deviation, the F statistic, the maximum absolute percent error, and the average of the absolute values of the percent of error evaluated. The computer programs and their manner of utilization are described. Sample problems are included to illustrate the use and capability of the technique which show the output formats and typical plots comparing computer results to each set of input data.

Davis, J. W.↗
NASA NTRS1976

Monte Carlo investigation of thrust imbalance of solid rocket motor pairs

The Monte Carlo method of statistical analysis is used to investigate the theoretical thrust imbalance of pairs of solid rocket motors (SRMs) firing in parallel. Sets of the significant variables are selected using a random sampling technique and the imbalance calculated for a large number of motor pairs using a simplified, but comprehensive, model of the internal ballistics. The treatment of burning surface geometry allows for the variations in the ovality and alignment of the motor case and mandrel as well as those arising from differences in the basic size dimensions and propellant properties. The analysis is used to predict the thrust-time characteristics of 130 randomly selected pairs of Titan IIIC SRMs. A statistical comparison of the results with test data for 20 pairs shows the theory underpredicts the standard deviation in maximum thrust imbalance by 20% with variability in burning times matched within 2%. The range in thrust imbalance of Space Shuttle type SRM pairs is also estimated using applicable tolerances and variabilities and a correction factor based on the Titan IIIC analysis.

Sforzini, R. H.↗
NASA NTRS2021

Automated Technique for the Detection of Step-Like Solar Wind Dynamic Pressure Changes: Application to the Response of the Transpolar Potential to Solar Wind Dynamic Pressure Fronts

The input from the solar wind (SW) and the accompanying Interplanetary Magnetic Field (IMF) is the defining feature of the solar wind-magnetosphere interactions. One of the most important SW drivers is the solar wind dynamic pressure, and most significantly its sharp changes known as pressure fronts. Sudden enhancements in solar wind dynamic pressure, SWP, have been shown to lead to intensification of the auroral electrojets (and Region 1 field-aligned currents), increase in auroral emissions, and significant enhancement in ionospheric convection and the transpolar potential. Case studies of the interaction between pressure fronts and the terrestrial space environment shed great light on their importance to the structure and dynamics of the system. However, thorough understanding of the interaction requires fully statistical investigations. These statistical studies require a large number of suitable pressure front events. In the past these have been obtained through laborious manual inspection of solar wind data. We present an automated procedure that identifies sudden step enhancements in SWP that satisfy a desired set of limiting step-like characteristics, such as magnitude of the change, sign of the change (positive/negative), and rate of change. The procedure yields a list of suitable events, along with their step features within minutes. The technique is tested for missed events and false positives by direct comparison to manual inspection of the data. Its utility is illustrated by application to the statistical effect of pressure fronts to the transpolar potential as measured by the Assimilative Mapping of Ionospheric Electrodynamics (AMIE) technique.

A. Boudouridis↗
DOE OSTI2020

Statistics of the NiCoCr medium-entropy alloy: Novel aspects of an old puzzle

Abstract We study the K -state phenomenon in the NiCoCr medium-entropy alloy using first-principles techniques jointly with the efficient Wang–Landau Monte Carlo and simulated annealing algorithms. Our theoretical results successfully explain the existence of the peak around 940 K in the experimental specific heat curve that characterizes the K -state phenomenon and give a fine picture of its atomic origin. The peak is caused by the maximum change of the local configurations characterized by the short-range-order (SRO) parameters at that temperature. The maximum change in SRO parameters is dominated by the nearest-neighbor interactions of atoms but substantially tuned by the many-body interactions. One surprising aspect revealed by the reciprocal-space SRO parameters is that the Ni–Co pair distribution is not random even above the ordering transition temperature, dramatically different from Ni–Cr and Co–Cr, indicating the system cannot be treated as a pseudo binary alloy. This prototypical example shows the complicated nature of multicomponent alloys, different from binary alloys. Our methods can be directly used to study the important K -state phenomenon observed in a number of other composition-concentrated alloys regardless of their number of components.

Pei, Zongrui (ORCID:0000000307484629)↗
DOE OSTI2022

Fiber Uncertainty Visualization for Bivariate Data With Parametric and Nonparametric Noise Models

Visualization and analysis of multivariate data and their uncertainty are top research challenges in data visualization. Constructing fiber surfaces is a popular technique for multivariate data visualization that generalizes the idea of level-set visualization for univariate data to multivariate data. Here, in this paper, we present a statistical framework to quantify positional probabilities of fibers extracted from uncertain bivariate fields. Specifically, we extend the state-of-the-art Gaussian models of uncertainty for bivariate data to other parametric distributions (e.g., uniform and Epanechnikov) and more general nonparametric probability distributions (e.g., histograms and kernel density estimation) and derive corresponding spatial probabilities of fibers. In our proposed framework, we leverage Green's theorem for closed-form computation of fiber probabilities when bivariate data are assumed to have independent parametric and nonparametric noise. Additionally, we present a nonparametric approach combined with numerical integration to study the positional probability of fibers when bivariate data are assumed to have correlated noise. For uncertainty analysis, we visualize the derived probability volumes for fibers via volume rendering and extracting level sets based on probability thresholds. We present the utility of our proposed techniques via experiments on synthetic and simulation datasets.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Effects of random forest modeling decisions on biogeochemical time series predictions

Abstract Random forests (RF) are an increasingly popular machine learning approach used to model biogeochemical processes in the Earth system. While RF models are robust to many assumptions that complicate deterministic models, there are several important parameterization decisions for appropriate use and optimal model fit. We explored the role that parameter decisions, including training/testing data splitting strategies, variable selection, and hyperparameters play on RF goodness‐of‐fit by constructing models using 1296 unique parameter combinations to predict concentrations of nitrate, a key nutrient for biogeochemical cycling in aquatic ecosystems. Models were built on long‐term, publicly available water quality and meteorology time series collected by the National Estuarine Research Reserve monitoring network for two contrasting ecosystems representing freshwater and brackish estuaries. We found that accounting for temporal dependence when splitting data into training and testing subsets was key for avoiding over‐estimation of model predictive power. In addition, variable selection, the ratio of training to testing data, and to a lesser degree, variables per split and number of trees, were significant parameters for optimizing RF goodness‐of‐fit. We also explored how model parameter decisions influenced interpretation of the relative importance of predictors to the model, and model predictor‐dependent variable relationships, with results suggesting that both data structure and model parameterization influence these factors. Because much of the current RF literature is written for the computational and statistical science communities, the primary goal of this study is to provide guidelines for aquatic scientists new to machine learning to apply RF techniques appropriately to aquatic biogeochemical datasets.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

A hybrid full-wave Markov chain approach to calculating radio-frequency wave scattering from scrape-off layer filaments

The interaction of radio-frequency (RF) waves with edge turbulence modifies the incident wave spectrum, and can significantly affect RF heating and current drive in tokamaks. Previous lower hybrid (LH) scattering models have either used the weak-turbulence approximation, or treated more realistic, filamentary turbulence in the ray tracing limit. In this study, a new model is introduced which retains full-wave effects of RF scattering in filamentary turbulence. First, a Mie-scattering technique models the interaction of an incident wave with a single Gaussian filament. Next, an effective differential scattering width is derived for a statistical ensemble of filaments. Lastly, a Markov chain solves for the transmitted wave spectrum in slab geometry. This model is applied to LH launching for current drive. The resulting wave spectrum is asymmetrically broadened in angular wavenumber space. This asymmetry is not accounted for in previous LH scattering models. The modified wave spectrum is coupled to a ray tracing/Fokker–Planck solver (GENRAY/CQL3D) to study its impact on current drive. The resulting current profile is greatly altered, and there is significant increase in the on-axis current and decrease in the off-axis peaks. This is attributed to a portion of the modified wave spectrum that is strongly dampened on-axis during the first pass.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Delensing the CMB with the cosmic infrared background: the impact of foregrounds

ABSTRACT The most promising avenue for detecting primordial gravitational waves from cosmic inflation is through measurements of degree-scale cosmic microwave background (CMB) B-mode polarization. This approach must face the challenge posed by gravitational lensing of the CMB, which obscures the signal of interest. Fortunately, the lensing effects can be partially removed by combining high-resolution E-mode measurements with an estimate of the projected matter distribution. For near-future experiments, the best estimate of the latter will arise from co-adding internal reconstructions (derived from the CMB itself) with external tracers such as the cosmic infrared background (CIB). In this work, we characterize how foregrounds impact the delensing procedure when CIB intensity, I, is used as the matter tracer. We find that higher point functions of the CIB and Galactic dust such as 〈BEI〉c and 〈EIEI〉c can, in principle, bias the power spectrum of delensed B-modes. To quantify these, we first estimate the dust residuals in currently available CIB maps and upcoming, foreground-cleaned Simons Observatory CMB data. Then, using non-Gaussian simulations of Galactic dust – extrapolated to the relevant frequencies, assuming the spectral index of polarized dust emission to be fixed at the value determined by Planck – we show that the bias to any primordial signal is small compared to statistical errors for ground-based experiments, but might be significant for space-based experiments probing very large angular scales. However, mitigation techniques based on multifrequency cleaning appear to be very effective. We also show, by means of an analytical model, that the bias arising from the higher point functions of the CIB itself ought to be negligible.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Modelling the Lyman-α forest with Eulerian and SPH hydrodynamical methods

ABSTRACT We compare two state-of-the-art numerical codes to study the overall accuracy in modelling the intergalactic medium and reproducing Lyman-α forest observables for DESI and high-resolution data sets. The codes employ different approaches to solving both gravity and modelling the gas hydrodynamics. The first code, Nyx, solves the Poisson equation using the Particle-Mesh (PM) method and the Euler equations using a finite-volume method. The second code, CRK-HACC , uses a Tree-PM method to solve for gravity, and an improved Lagrangian smoothed particle hydrodynamics (SPH) technique, where fluid elements are modelled with particles, to treat the intergalactic gas. We compare the convergence behaviour of the codes in flux statistics as well as the degree to which the codes agree in the converged limit. We find good agreement overall with differences being less than observational uncertainties, and a particularly notable ≲1 per cent agreement in the 1D flux power spectrum. This agreement was achieved by applying a tessellation methodology for reconstructing the density in CRK-HACC instead of using an SPH kernel as is standard practice. We show that use of the SPH kernel can lead to significant and unnecessary biases in flux statistics; this is especially prominent at high redshifts, z ∼ 5, as the Lyman-α forest mostly comes from lower-density regions that are intrinsically poorly sampled by SPH particles.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Quantifying concordance of correlated cosmological data sets

We develop estimators of agreement and disagreement between correlated cosmological data sets. These account for data correlations when computing the significance of both tensions and excess confirmation while remaining statistically optimal. We discuss and thoroughly characterize different approaches commenting on the ones that have the best behavior in practical applications. We complement the calculation of their statistical distribution within the Gaussian model with one estimator that takes non-Gaussianities fully into account. To illustrate the use of our techniques, we apply these estimators to supernovae measurements of the distance-redshift relation, absolutely calibrated by the local distance ladder. The suite of best estimators that we discuss finds results that are in excellent agreement between estimators and find no indications of significant internal inconsistencies in this data set above the 1% probability threshold. Furthermore, this shows the robustness of local determinations of the Hubble constant to features in the distance-redshift relation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

The Dark Energy Spectrographic Instrument (DESI) Guide-Focus Assembly

The specific research of the DESI project is to study in detail the expansion history of the Universe over the past 10 billion years. In order to do this, the project designed, fabricated, tested and commissioned the DESI instrument which has been deployed at the Mayall Telescope at the Kitt Peak National Observatory near Tucson, Arizona. The DESI project was conducted by approximately 30 US and foreign national laboratories. Our CRADA with the The Institut de Física d’Altes Energies (IFAE) in Barcelona (Spain) involved both research planning for eventual observing on the DESI telescope; and in providing hardware jointly designed by LBNL and IFAE; ten guide and focus sensor systems (GFAs) that either provide feedback to the Mayall telescope tracking system or provide focus position information to the DESI corrector hexapod. The key major goals of this CRADA were achieved.For survey planning, Drs. Fernandez, Fosalba, Garcia-Bellido, and Gaztañaga were all important contributors to the working groups to which they were assigned. Their application of redshift techniques, development of simulations to support target selection, exploration of the use of alternative observables to extract cosmological information like AP and void statistics, and the use of PAU data to assist in the optimization of targeting selections have been vital in the early planning for targets during commissioning. The major role in the project involved Drs. Castander, Miquel, Padilla, and Sànchez. They were all directly involved with the development of the Guide-Focus Assembly (GFA) hardware, software and filter validation. In order to accomplish the goals of the DESI Project, the Mayall telescope must track DESI targeted galaxies for up to 15 minutes and the DESI corrector must be repositioned on its hexapod system for different telescope orientations. The guide and focus assemblies (GFA) provide in this information. There are ten GFA modules on the focal plane, six providing tracking information and four providing focus information. A common GFA design supports both functions by a simple switching of its operating mode. IFAE designed, fabricated, tested and delivered twelve GFAs. Once received at LBNL, the GFAs were integrated with the focal plane. This was an iterative process as the GFA’s were delivered as they were made. Our working relationship with the IFAE scientists and engineers was remarkable given the distance and time zone issues. The GFAs have performed extremely well during the commissioning phase of the instrument.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Characterizing PuO 2 Powder at Oak Ridge National Laboratory for the Multi-Lab Plutonium Process Signatures Campaign FY 2022

This report highlights the development of advanced analytical capabilities at Oak Ridge National Laboratory to characterize PuO 2 powder to support the Multi-Lab Plutonium Process Signatures Campaign in FY 2022. Two samples from a batch of 76 statistical precipitation runs were packaged and shipped from Pacific Northwest National Laboratory to Oak Ridge National Laboratory at the beginning of FY 2022. Techniques were used to characterize the sample, including powder X-ray diffraction, Raman spectroscopy, and diffuse reflectance spectroscopy. A brief description of each technique, the results and discussion, and future work are described in this report. Opportunities to expand current capabilities and include additional analytical capabilities for the next campaign will also be discussed.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1963

Mathematical Optimization Techniques

The papers collected in this volume were presented at the Symposium on Mathematical Optimization Techniques held in the Santa Monica Civic Auditorium, Santa Monica, California, on October 18-20, 1960. The objective of the symposium was to bring together, for the purpose of mutual education, mathematicians, scientists, and engineers interested in modern optimization techniques. Some 250 persons attended. The techniques discussed included recent developments in linear, integer, convex, and dynamic programming as well as the variational processes surrounding optimal guidance, flight trajectories, statistical decisions, structural configurations, and adaptive control systems. The symposium was sponsored jointly by the University of California, with assistance from the National Science Foundation, the Office of Naval Research, the National Aeronautics and Space Administration, and The RAND Corporation, through Air Force Project RAND.

Bellman, R.↗
NASA NTRS1973

Round-off errors in cutting plane algorithms based on the revised simplex procedure

This report statistically analyzes computational round-off errors associated with the cutting plane approach to solving linear integer programming problems. Cutting plane methods require that the inverse of a sequence of matrices be computed. The problem basically reduces to one of minimizing round-off errors in the sequence of inverses. Two procedures for minimizing this problem are presented, and their influence on error accumulation is statistically analyzed. One procedure employs a very small tolerance factor to round computed values to zero. The other procedure is a numerical analysis technique for reinverting or improving the approximate inverse of a matrix. The results indicated that round-off accumulation can be effectively minimized by employing a tolerance factor which reflects the number of significant digits carried for each calculation and by applying the reinversion procedure once to each computed inverse. If 18 significant digits plus an exponent are carried for each variable during computations, then a tolerance value of 0.1 x 10 to the minus 12th power is reasonable.

Moore, J. E.↗
NASA NTRS1979

Feature selection via entropy minimization: An example using LANDSAT satellite data

The author has identified the following significant results. The minimum entropy model may provide several useful advantages over traditional techniques for processing LANDSAT data. Total computer time to conduct a complete pattern recognition process is reduced. Subjective (transformed image), as well as statistically derived information is made available to the analyst/user much earlier in the analysis process. A rapid feedback loop in which numerous training set combinations can be tested for difference and representativeness is available. Additional tests of LANDSAT data processing using the minimum entropy model are clearly justified.

Zandonella, A.↗
NASA NTRS1980

Digital simulation of dynamic processes in radiometer systems

The development and application of several computer programs for simulating different classes of microwave radiometers are described. The programs are dynamic in nature, and they may be used to determine the instantaneous behavior of system variables as a function of time. Some of the programs employ random variable models in the simulations so that the statistical nature of the results may be investigated. The programs have been developed to utilize either the Continuous System Modeling Program or the Advanced Continuous System Language. The validity of most of the programs was investigated using statistical tests, and the results show excellent correlation with theoretical predictions. The programs are currently being used in the investigation of new design techniques for microwave radiometers.

Stanley, W. D.↗