Search NASA⌕ Search

SEARCH · Search NASA

Results for “Statistical error”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

On the Choice of Variable for Atmospheric Moisture Analysis

The implications of using different control variables for the analysis of moisture observations in a global atmospheric data assimilation system are investigated. A moisture analysis based on either mixing ratio or specific humidity is prone to large extrapolation errors, due to the high variability in space and time of these parameters and to the difficulties in modeling their error covariances. Using the logarithm of specific humidity does not alleviate these problems, and has the further disadvantage that very dry background estimates cannot be effectively corrected by observations. Relative humidity is a better choice from a statistical point of view, because this field is spatially and temporally more coherent and error statistics are therefore easier to obtain. If, however, the analysis is designed to preserve relative humidity in the absence of moisture observations, then the analyzed specific humidity field depends entirely on analyzed temperature changes. If the model has a cool bias in the stratosphere this will lead to an unstable accumulation of excess moisture there. A pseudo-relative humidity can be defined by scaling the mixing ratio by the background saturation mixing ratio. A univariate pseudo-relative humidity analysis will preserve the specific humidity field in the absence of moisture observations. A pseudorelative humidity analysis is shown to be equivalent to a mixing ratio analysis with flow-dependent covariances. In the presence of multivariate (temperature-moisture) observations it produces analyzed relative humidity values that are nearly identical to those produced by a relative humidity analysis. Based on a time series analysis of radiosonde observed-minus-background differences it appears to be more justifiable to neglect specific humidity-temperature correlations (in a univariate pseudo-relative humidity analysis) than to neglect relative humidity-temperature correlations (in a univariate relative humidity analysis). A pseudo-relative humidity analysis is easily implemented in an existing moisture analysis system, by simply scaling observed-minus background moisture residuals prior to solving the analysis equation, and rescaling the analyzed increments afterward.

Dee, Dick P.↗
NASA NTRS1995

Gaussian statistics of the cosmic microwave background: Correlation of temperature extrema in the COBE DMR two-year sky maps

We use the two-point correlation function of the extrema points (peaks and valleys) in the Cosmic Background Explorer (COBE) Differential Microwave Radiometers (DMR) 2 year sky maps as a test for non-Gaussian temperature distribution in the cosmic microwave background anisotropy. A maximum-likelihood analysis compares the DMR data to n = 1 toy models whose random-phase spherical harmonic components a(sub lm) are drawn from either Gaussian, chi-square, or log-normal parent populations. The likelihood of the 53 GHz (A+B)/2 data is greatest for the exact Gaussian model. There is less than 10% chance that the non-Gaussian models tested describe the DMR data, limited primarily by type II errors in the statistical inference. The extrema correlation function is a stronger test for this class of non-Gaussian models than topological statistics such as the genus.

Kogut, A.↗
NASA NTRS2015

An Empirical State Error Covariance Matrix Orbit Determination Example

State estimation techniques serve effectively to provide mean state estimates. However, the state error covariance matrices provided as part of these techniques suffer from some degree of lack of confidence in their ability to adequately describe the uncertainty in the estimated states. A specific problem with the traditional form of state error covariance matrices is that they represent only a mapping of the assumed observation error characteristics into the state space. Any errors that arise from other sources (environment modeling, precision, etc.) are not directly represented in a traditional, theoretical state error covariance matrix. First, consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. Then it follows that a measurement residual (the difference between expected and observed measurements) contains all errors for that measurement. Therefore, a direct and appropriate inclusion of the actual measurement residuals in the state error covariance matrix of the estimate will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully include all of the errors in the state estimate. The empirical error covariance matrix is determined from a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm. It is a formally correct, empirical state error covariance matrix obtained through use of the average form of the weighted measurement residual variance performance index rather than the usual total weighted residual form. Based on its formulation, this matrix will contain the total uncertainty in the state estimate, regardless as to the source of the uncertainty and whether the source is anticipated or not. It is expected that the empirical error covariance matrix will give a better, statistical representation of the state error in poorly modeled systems or when sensor performance is suspect. In its most straight forward form, the technique only requires supplemental calculations to be added to existing batch estimation algorithms. In the current problem being studied a truth model making use of gravity with spherical, J2 and J4 terms plus a standard exponential type atmosphere with simple diurnal and random walk components is used. The ability of the empirical state error covariance matrix to account for errors is investigated under four scenarios during orbit estimation. These scenarios are: exact modeling under known measurement errors, exact modeling under corrupted measurement errors, inexact modeling under known measurement errors, and inexact modeling under corrupted measurement errors. For this problem a simple analog of a distributed space surveillance network is used. The sensors in this network make only range measurements and with simple normally distributed measurement errors. The sensors are assumed to have full horizon to horizon viewing at any azimuth. For definiteness, an orbit at the approximate altitude and inclination of the International Space Station is used for the study. The comparison analyses of the data involve only total vectors. No investigation of specific orbital elements is undertaken. The total vector analyses will look at the chisquare values of the error in the difference between the estimated state and the true modeled state using both the empirical and theoretical error covariance matrices for each of scenario.

Frisbee, Joseph H., Jr.↗
NASA NTRS1978

A parametric multiclass Bayes error estimator for the multispectral scanner spatial model performance evaluation

The author has identified the following significant results. The probability of correct classification of various populations in data was defined as the primary performance index. The multispectral data being of multiclass nature as well, required a Bayes error estimation procedure that was dependent on a set of class statistics alone. The classification error was expressed in terms of an N dimensional integral, where N was the dimensionality of the feature space. The multispectral scanner spatial model was represented by a linear shift, invariant multiple, port system where the N spectral bands comprised the input processes. The scanner characteristic function, the relationship governing the transformation of the input spatial, and hence, spectral correlation matrices through the systems, was developed.

Mobasseri, B. G.↗
DOE OSTI2025

Bayesian model-data comparison incorporating theoretical uncertainties

Accurate comparisons between theoretical models and experimental data are critical for scientific progress. However, inferred physical model parameters can vary significantly with the chosen physics model, highlighting the importance of properly accounting for theoretical uncertainties. In this Letter, we present a Bayesian framework that explicitly quantifies these uncertainties by statistically modeling theory errors, guided by qualitative knowledge of a theory’s varying reliability across the input domain. We demonstrate the effectiveness of this approach using two systems: a simple ball drop experiment and multi-stage heavy-ion simulations. In both cases incorporating model discrepancy leads to improved parameter estimates, with systematic improvements observed as additional experimental observables are integrated.

Bayesian methods↗
NASA NTRS2014

Combined Uncertainty and A-Posteriori Error Bound Estimates for General CFD Calculations: Theory and Software Implementation

This workshop presentation discusses the design and implementation of numerical methods for the quantification of statistical uncertainty, including a-posteriori error bounds, for output quantities computed using CFD methods. Hydrodynamic realizations often contain numerical error arising from finite-dimensional approximation (e.g. numerical methods using grids, basis functions, particles) and statistical uncertainty arising from incomplete information and/or statistical characterization of model parameters and random fields. The first task at hand is to derive formal error bounds for statistics given realizations containing finite-dimensional numerical error [1]. The error in computed output statistics contains contributions from both realization error and the error resulting from the calculation of statistics integrals using a numerical method. A second task is to devise computable a-posteriori error bounds by numerically approximating all terms arising in the error bound estimates. For the same reason that CFD calculations including error bounds but omitting uncertainty modeling are only of limited value, CFD calculations including uncertainty modeling but omitting error bounds are only of limited value. To gain maximum value from CFD calculations, a general software package for uncertainty quantification with quantified error bounds has been developed at NASA. The package provides implementations for a suite of numerical methods used in uncertainty quantification: Dense tensorization basis methods [3] and a subscale recovery variant [1] for non-smooth data, Sparse tensorization methods[2] utilizing node-nested hierarchies, Sampling methods[4] for high-dimensional random variable spaces.

CFD↗
DOE OSTI2024

Designing ITER motional Stark effect line shift (MSE-LS) spectrometers

As a part of ITER beam aided diagnostics, the design of Motional Stark Effect (MSE) diagnostic observing the emission from the Balmer-α line is underway. The physics of Stark splitting shows that the Stark manifold is polarization dependent, and the energy splitting results in a line shift proportional to the electric field. Due to the challenges of maintaining the calibration of the plasma facing mirrors in ITER, the conventional MSE polarimetry measurement technique is replaced with a spectral approach that is deemed more favorable in the ITER environment. The MSE line shift (LS) diagnostic is designed to quantify the Lorentz electric field magnitude by measuring the Stark manifold using visible spectroscopy. In the presence of large magnetic fields and high energy heating beams of 1 MeV, the expected Stark splitting is much larger than in typical devices. The MSE-LS design has unique challenges requiring careful consideration and modeling of its viewing geometry and photon budget. The MSE-LS approach on ITER is promising but has stringent demands on the allowable errors for the statistical and systematic fitting uncertainties. In this study, a full system model and numerical simulations of data for each sightline are completed. For a range of optical transmission fractions, photon noise analysis is conducted to determine the statistical uncertainties. This provides guidance on the spectrometer throughput, dispersion at the detector, optics, and other design choices. A conceptual design of a high throughput spectrometer with a volume phase transmission grating is presented.

Instruments & Instrumentation↗
DOE OSTI2025

Validation of the DESI DR2 measurements of baryon acoustic oscillations from galaxies and quasars

The Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2) galaxy and quasar clustering data represents a significant expansion of data from Data Release 1 (DR1), providing improved statistical precision in baryon acoustic oscillation (BAO) constraints across multiple tracers, including bright galaxies, luminous red galaxies, emission line galaxies, and quasars. In this paper, we validate the BAO analysis of DR2. We present the results of robustness tests on the blinded DR2 data and, after unblinding, consistency checks on the unblinded DR2 data. All results are compared with those obtained from a suite of mock catalogs that replicate the selection and clustering properties of the DR2 sample. We confirm the consistency of DR2 BAO measurements with DR1 while achieving a reduction in statistical uncertainties due to the increased survey volume and completeness. The combined BAO precision, including both statistical and systematic errors, improves from ∼0.52% in DR1 to 0.30% in DR2—a factor of 1.7 gain. We assess the impact of analysis choices, including different data vectors (correlation function vs power spectrum), modeling approaches and systematics treatments, and an assumption of the Gaussian likelihood, finding that our BAO constraints are stable across these variations and assumptions with a few minor refinements to the baseline setup of the DR1 BAO analysis. We summarize a series of pre-unblinding tests that confirmed the readiness of our analysis pipeline, the final systematic errors, and the DR2 BAO analysis baseline. The successful completion of these tests led to the unblinding of the DR2 BAO measurements, ultimately leading to the DESI DR2 cosmological analysis, with their implications for the expansion history of the Universe and the nature of dark energy presented in the DESI key paper (companion paper).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

On the use of Graphs for Test Sequence Selection

This report demonstrates that applying graph theory techniques provides a way to obtain sufficient statistics in finding errors when testing complex state machines. It discusses how to define the tests, then demonstrates how to automatically generate test suites that diversify test cases, subject to constraints. If included within a continuous integration approach, these constructs provide an unbiased means to systematically check for errors within the latest controller software release.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Partnership Center for High-Fidelity Boundary Plasma Simulation (Final Report)

Within the Partnership Center for High-Fidelity Boundary Plasma Simulation (HBPS), work at UT-Austin was aimed at improved verification, validation, and uncertainty quantification (VVUQ) for edge plasma simulations and on performing gyrokinetics simulations of pedestal instabilities and turbulence in order to expand foundational understanding of pedestal transport. Regarding VVUQ, the accomplishments can be summarized as follows. First, it was shown that the Moment Preserving Constrained Resampling technique, when applied periodically in particle-in-cell simulations in the XGC code, can dramatically improve the accuracy of the simulation at essentially equivalent computational cost. Second, a technique for estimating model correlations, which are required to solve the model selection and sample allocation problem in multifidelity UQ techniques, without sampling the highest fidelity, most computationally expensive model, was developed and demonstrated. Third, previously developed methods for estimating statistical and discretization errors were applied to numerical methods relevant to edge plasma simulations, namely in particle-in-cell-based approaches, and shown to work. Finally, benchmark studies for comparing gyrokinetic codes were developed and performed, leading to reasonable agreement between four commonly used codes. Regarding physics studies, gyrokinetic simulations to investigate microtearing modes in the DIII-D pedestal were performed using the GENE code.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1965

Prediction analysis and management decisions.

Prediction analysis techniques /PAT/ using statistical methods, computers, error analysis, etc, for system weight, performance and other parameter predictions in Apollo program

PROGRAM MANAGEMENT↗
NASA NTRS1972

Digital simulation of hybrid loop operation in RFI backgrounds.

A digital computer model for Monte-Carlo simulation of an imperfect second-order hybrid phase-locked loop (PLL) operating in radio-frequency interference (RFI) and Gaussian noise backgrounds has been developed. Characterization of hybrid loop performance in terms of cycle slipping statistics and phase error variance, through computer simulation, indicates that the hybrid loop has desirable performance characteristics in RFI backgrounds over the conventional PLL or the costas loop.

Ziemer, R. E.↗
NASA NTRS1975

A system for multichannel recording and automatic reading of information

A system for the recording and processing of telescope data is considered for measurements of EW asymmetry. The information is recorded by 45 channels on a continuously moving 35-mm film. The dead time of the recorder is about 0.1 sec. A sorting electronic circuit is used to reduce the errors when the statistical time distribution of the pulses is recorded. The recorded information is read out by means of photoresistors. The phototransmitter signals are fed either to the mechanical recorder unit for preliminary processing, or to a logical circuit which controls the operation of the punching device. The punched tape is processed by an electronic computer.

Bogomolov, E. A.↗
NASA NTRS1975

Mission Analysis Program for Solar Electric Propulsion (MAPSEP). Volume 2: User's manual for earth orbital MAPSEP

The trajectory simulation mode (SIMSEP) requires the namelist SIMSEP to follow TRAJ. The SIMSEP contains parameters which describe the scope of the simulation, expected dynamic errors, and cumulative statistics from previous SIMSEP runs. Following SIMSEP are a set of GUID namelists, one for each guidance correction maneuver. The GUID describes the strategy, knowledge or estimation uncertainties and cumulative statistics for that particular maneuver. The trajectory display mode (REFSEP) requires only the namelist TRAJ followed by scheduling cards, similar to those used in GODSEP. The fixed field schedule cards define: types of data displayed, span of interest, and frequency of printout. For those users who can vary the amount of blank common storage in their runs, a guideline to estimate the total MAPSEP core requirements is given. Blank common length is related directly to the dimension of the dynamic state (NDIM) used in transition matrix (STM) computation, and, the total augmented (knowledge) state (NAUG). The values of program and blank common must be added to compute the total decimal core for a CDC 6500. Other operating systems must scale these requirements appropriately.

Source record↗
NASA NTRS1982

Atmospheric turbulence parameters for modeling wind turbine dynamics

A model which can be used to predict the response of wind turbines to atmospheric turbulence is given. The model was developed using linearized aerodynamics for a three-bladed rotor and accounts for three turbulent velocity components as well as velocity gradients across the rotor disk. Typical response power spectral densities are shown. The system response depends critically on three wind and turbulence parameters, and models are presented to predict desired response statistics. An equation error method, which can be used to estimate the required parameters from field data, is also presented.

Holley, W. E.↗
NASA NTRS1984

Analysis of the quality of image data acquired by the LANDSAT-4 thematic mapper and multispectral scanners

A seven step procedure developed for evaluating the geometric properties of MSS and TM film produces is being implemented. Some 476 control points were selected of which 238 are being tested and edited for digitization and scaling errors. Tables show statistics established for assessing the spectral characteristics and variability, as well as the spatial resolution and radiometric sensitivity of TM data for a forest environment in an effort to determine the extent to which major forest cover type can be detected and identified on TM digital and image products. Results thus far show that the high quality obtained are more than sufficient for meeting most of the inventory objectives of the renewable resource specialist. The TM data should be extremely valuable for: (1) estimating forest cover types; (2) updating land use survey maps; and (3) determining the size and shape and location of individual forest clearings and water resources.

Colwell, R. N.↗
NASA NTRS1984

Research Relative to High Spatial Resolution Passive Microwave Sounding Systems

Methods to obtain high resolution passive microwave weather observations, and understanding of their probable impact on numerical weather prediction accuracy were investigated. The development of synthetic aperture concepts for geosynchronous passive microwave sounders were studied. The effects of clouds, precipitation, surface phenomena, and atmospheric thermal fine structure on a scale of several kilometers were examined. High resolution passive microwave sounders (e.g., AMSU) with an increased number of channels will produce initialization data for numerical weather prediction (NWP) models with both increased spatial resolution and coverage. The development of statistical models for error growth in high resolution primitive equation NWP models which permit the consequences of various observing system alternatives, including sensors and assimilation times and procedures is discussed. A high resolution three dimensional primitive equation NWP model to determine parameters in an error growth model similar to that formulated by Lorenz, but with more degrees of freedom is utilized.

Staelin, D. H.↗