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Results for “Bias and Uncertainty”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

An additional source of uncertainty and bias in digital spectral estimates near the Nyquist frequency

An additional source of bias and uncertainty in digital spectral estimates near the Nyquist frequency is discovered which is produced by the fact that the finite width main lobe of the spectral window is periodic with period of 2(omega sub c), equal to 4pi times the Nyquist frequency. For estimates near omega sub c, contributions from frequencies near -(omega sub c) are found to appear even for a sufficiently sampled bandlimited time history. In real-world applications, this source should be significant if the number of data points is small, and it should be of even more importance if the signal is not strictly bandlimited.

Hardin, J. C.↗
NASA NTRS1999

Uncertainty Analysis of Instrument Calibration and Application

Experimental aerodynamic researchers require estimated precision and bias uncertainties of measured physical quantities, typically at 95 percent confidence levels. Uncertainties of final computed aerodynamic parameters are obtained by propagation of individual measurement uncertainties through the defining functional expressions. In this paper, rigorous mathematical techniques are extended to determine precision and bias uncertainties of any instrument-sensor system. Through this analysis, instrument uncertainties determined through calibration are now expressed as functions of the corresponding measurement for linear and nonlinear univariate and multivariate processes. Treatment of correlated measurement precision error is developed. During laboratory calibration, calibration standard uncertainties are assumed to be an order of magnitude less than those of the instrument being calibrated. Often calibration standards do not satisfy this assumption. This paper applies rigorous statistical methods for inclusion of calibration standard uncertainty and covariance due to the order of their application. The effects of mathematical modeling error on calibration bias uncertainty are quantified. The effects of experimental design on uncertainty are analyzed. The importance of replication is emphasized, techniques for estimation of both bias and precision uncertainties using replication are developed. Statistical tests for stationarity of calibration parameters over time are obtained.

Tripp, John S.↗
NASA NTRS1995

Impact of uncertainty on modeling and testing

A thorough understanding of the uncertainties associated with the modeling and testing of the Space Shuttle Main Engine (SSME) Engine will greatly aid decisions concerning hardware performance and future development efforts. This report will describe the determination of the uncertainties in the modeling and testing of the Space Shuttle Main Engine test program at the Technology Test Bed facility at Marshall Space Flight Center. Section 2 will present a summary of the uncertainty analysis methodology used and discuss the specific applications to the TTB SSME test program. Section 3 will discuss the application of the uncertainty analysis to the test program and the results obtained. Section 4 presents the results of the analysis of the SSME modeling effort from an uncertainty analysis point of view. The appendices at the end of the report contain a significant amount of information relative to the analysis, including discussions of venturi flowmeter data reduction and uncertainty propagation, bias uncertainty documentations, technical papers published, the computer code generated to determine the venturi uncertainties, and the venturi data and results used in the analysis.

Coleman, Hugh W.↗
NASA NTRS1990

Bias and uncertainty in the absorption emission measurement of atomic sodium density in the SSME exit plane

The measurement of atomic sodium concentration in the TTB 019 firing of April 1990 is significant in that it represents the first measurement of density at the exit plane of the space shuttle main engine. The knowledge of the sodium density, combined with the certainty that the exit plane of the plume is optically thin at the sodium D-line wavelengths, provides essential information for evaluation of diagnostic techniques using sodium atoms, such as resonant Doppler velocimetry for temperature, pressure, and velocity through high resolution fluorescent lineshape analysis. The technique used for the sodium atom line transmission (SALT) measurements is that of resonant absorption emission using a hollow cathode lamp as the reference source. Through the use of two-dimensional kinetic (TDK) predictions of temperature and density for the flight engine case and radiative transfer calculations, this line-of-sight spectrally integrated transmission indicates a sodium atom concentration, i.e., mole fraction, of 0.91e-10. The subject of this paper is the assumptions and measurement uncertainties tied into the calculation. Because of the narrow shape of the source emission, the uncertainties in the absorption profile could introduce considerable bias in the measurement. The following were investigated: (1) the inclusion of hyperfine splitting of the D-lines in the calculation; (2) the use of the flight engine predictions of plume temperature and density versus those for the large throat engine; (3) the assumption of a Gaussian, i.e., Doppler, distribution for the source radiance with a temperature of 400 K; (4) the use of atomic collisional shift and width values for the work by Jongerius; and (5) a Doppler shift for a 7 degree outward velocity vector at the plume edge. Also included in the study was the bias introduced by an uncertainty in the measurement of the D1/D2 line ratio in the source.

Bauman, Leslie E.↗
NASA NTRS1999

Uncertainty Analysis of Inertial Model Attitude Sensor Calibration and Application with a Recommended New Calibration Method

Statistical tools, previously developed for nonlinear least-squares estimation of multivariate sensor calibration parameters and the associated calibration uncertainty analysis, have been applied to single- and multiple-axis inertial model attitude sensors used in wind tunnel testing to measure angle of attack and roll angle. The analysis provides confidence and prediction intervals of calibrated sensor measurement uncertainty as functions of applied input pitch and roll angles. A comparative performance study of various experimental designs for inertial sensor calibration is presented along with corroborating experimental data. The importance of replicated calibrations over extended time periods has been emphasized; replication provides independent estimates of calibration precision and bias uncertainties, statistical tests for calibration or modeling bias uncertainty, and statistical tests for sensor parameter drift over time. A set of recommendations for a new standardized model attitude sensor calibration method and usage procedures is included. The statistical information provided by these procedures is necessary for the uncertainty analysis of aerospace test results now required by users of industrial wind tunnel test facilities.

Tripp, John S.↗
NASA NTRS2023

A Framework for Estimating Global River Discharge From the Surface Water and Ocean Topography Satellite Mission

The Surface Water and Ocean Topography (SWOT) mission will vastly expand measurements of global rivers, providing critical new data sets for both gaged and ungaged basins. SWOT discharge products (available approximately 1 year after launch) will provide discharge for all river that reaches wider than 100 m. In this paper, we describe how SWOT discharge produced and archived by the US and French space agencies will be computed from measurements of river water surface elevation, width, and slope and ancillary data, along with expected discharge accuracy. We present for the first time a complete estimate of the SWOT discharge uncertainty budget, with separate terms for random (standard error) and systematic (bias) uncertainty components in river discharge time series. We expect that discharge uncertainty will be less than 30% for two-thirds of global reaches and will be dominated by bias. Separate river discharge estimates will combine both SWOT and in situ data; these “gage-constrained” discharge estimates can be expected to have lower systematic uncertainty. Temporal variations in river discharge time series will be dominated by random error and are expected to be estimated within 15% for nearly all reaches, allowing accurate inference of event flow dynamics globally, including in ungaged basins. We believe this level of accuracy lays the groundwork for SWOT to enable breakthroughs in global hydrologic science.

Michael Durand↗
NASA NTRS1990

Attitude determination error analysis - General model and specific application

This paper presents a comprehensive approach to filter and dynamics modeling for attitude determination error analysis. The discussion includes models for both batch least-squares and sequential estimators, a specific dynamic model for attitude determination error analysis of a three-axis stabilized spacecraft equipped with strapdown gyros, and the incorporation of general attitude sensor observations. An analyst using this approach to perform an error analysis chooses a subset of the spacecraft parameters to be 'solve-for' parameters, which are to be estimated, and another subset to be 'consider' parameters, which are assumed to have errors but not to be estimated. The result of the error analysis is an indication of overall uncertainties in the 'solve-for' parameters, as well as the contributions of the various error sources to these uncertainties, including those of errors in the a priori 'solve-for' estimates, of measurement noise, of dynamic noise (also known as process noise or plant noise), and of 'consider' parameter uncertainties. The analysis of attitude, star tracker alignment, and gyro bias uncertainties for the Gamma Ray Observatory spacecraft provide a specific example of the use of a general-purpose software package incorporating these models.

Markley, F. Landis↗
NASA NTRS1983

Uncertainty methodology for in-flight thrust determination

A methodology is proposed for the evaluation of uncertainty in the in-flight determination of aircraft thrust, which provides error traceability to a national standards laboratory, and is independent of the procedure used to calculate or measure thrust in flight, thereby yielding a consistent means for the evaluation of measurement capabilities. Attention is given to the factors of measurement error, precision, bias, uncertainty, error estimation and classification, error propagation, ground testing, and the related problems of model bias error, model precision error, and the uncertainty limit.

Adams, G. R.↗
NASA NTRS2020

Calibration Probe Uncertainty and Validation for the Hypersonic Material Environmental Test System

This paper presents an uncertainty analysis of the stagnation-point calibration probe surface predictions for conditions that span the performance envelope of the Hypersonic Materials Environmental Test System facility located at NASA Langley Research Center. A second-order stochastic expansion was constructed over 47 uncertain parameters to evaluate the sensitivities, identify the most significant uncertain variables, and quantify the uncertainty in the stagnation-point heat flux and pressure predictions of the calibration probe for a low- and high-enthalpy test condition. A sensitivity analysis showed that measurement bias uncertainty is the most significant contributor to the stagnation-point pressure and heat flux variance for the low-enthalpy condition. For the high-enthalpy condition, a paradigm shift in sensitivities revealed the computational fluid dynamics model input uncertainty as the main contributor. A comparison between the prediction and measurement of the stagnation-point conditions under uncertainty showed that there was evidence of statistical disagreement. A validation metric was proposed and applied to the prediction uncertainty to account for the statistical disagreement when compared to the possible stagnation-point heat flux and pressure measurements.

Brune, Andrew J.↗
NASA NTRS2018

Combined Error and Uncertainty Estimates for CFD Problems

Given input sources of uncertainty, non-intrusive uncertainty propagation methods quantify the uncertainty in output quantities of interest (QoI) by performing a nite number of CFD (Computational Fluid Dynamics) instance realizations needed in the calculation of output statistics. It is well known that this introduces multiple sources of error. CFD codes often utilize finite-dimensional approximation (grids, basis functions, etc.) thus incurring CFD numerical errors often approximately reinterpreted as a statistical bias. Uncertainty propagation methods calculate uncertainty statistics for output quantities of interest using a numerical method (e.g. deterministic quadrature, sampling, etc.) thus incurring UQ (Uncertainty Quantification) numerical errors. Importance of quantifying these errors in large scale scientific computing: How accurate is an output statistic?; How should additional computational resources be invested to further reduce the error in a statistic?

Posteriori↗
NASA NTRS2017

Simulating PACE Global Ocean Radiances

The NASA PACE mission is a hyper-spectral radiometer planned for launch in the next decade. It is intended to provide new information on ocean biogeochemical constituents by parsing the details of high resolution spectral absorption and scattering. It is the first of its kind for global applications and as such, poses challenges for design and operation. To support pre-launch mission development and assess on-orbit capabilities, the NASA Global Modeling and Assimilation Office has developed a dynamic simulation of global water-leaving radiances, using an ocean model containing multiple ocean phytoplankton groups, particulate detritus, particulate inorganic carbon (PIC), and chromophoric dissolved organic carbon (CDOC) along with optical absorption and scattering processes at 1 nm spectral resolution. The purpose here is to assess the skill of the dynamic model and derived global radiances. Global bias, uncertainty, and correlation are derived using available modern satellite radiances at moderate spectral resolution. Total chlorophyll, PIC, and the absorption coefficient of CDOC (aCDOC), are simultaneously assimilated to improve the fidelity of the optical constituent fields. A 5-year simulation showed statistically significant (P < 0.05) comparisons of chlorophyll (r = 0.869), PIC (r = 0.868), and a CDOC (r =0.890) with satellite data. Additionally, diatoms (r = 0.890), cyanobacteria (r = 0.732), and coccolithophores (r = 0.716) were significantly correlated with in situ data. Global assimilated distributions of optical constituents were coupled with a radiative transfer model (Ocean-Atmosphere Spectral Irradiance Model, OASIM) to estimate normalized water-leaving radiances at 1 nm for the spectral range 250-800 nm. These unassimilated radiances were within 0.074 mW/sq cm/micron/sr of MODIS-Aqua radiances at 412, 443, 488, 531, 547, and 667 nm. This difference represented a bias of 10.4% (model low). A mean correlation of 0.706 (P < 0.05) was found with global distributions of MODIS radiances. These results suggest skill in the global assimilated model and resulting radiances. The reported error characterization suggests that the global dynamical simulation can support some aspects of mission design and analysis. For example, the high spectral resolution of the simulation supports investigations of band selection. The global nature of the radiance representations supports investigations of satellite observing scenarios. Global radiances at bands not available in current and past missions support investigations of mission capability. PACE, ocean color, water-leaving radiances, biogeochemical model, radiative transfer model

PIC↗
NASA NTRS1988

On the appropriateness of applying chi-square distribution based confidence intervals to spectral estimates of helicopter flyover data

The validity of applying chi-square based confidence intervals to far-field acoustic flyover spectral estimates was investigated. Simulated data, using a Kendall series and experimental acoustic data from the NASA/McDonnell Douglas 500E acoustics test, were analyzed. Statistical significance tests to determine the equality of distributions of the simulated and experimental data relative to theoretical chi-square distributions were performed. Bias and uncertainty errors associated with the spectral estimates were easily identified from the data sets. A model relating the uncertainty and bias errors to the estimates resulted, which aided in determining the appropriateness of the chi-square distribution based confidence intervals. Such confidence intervals were appropriate for nontonally associated frequencies of the experimental data but were inappropriate for tonally associated estimate distributions. The appropriateness at the tonally associated frequencies was indicated by the presence of bias error and noncomformity of the distributions to the theoretical chi-square distribution. A technique for determining appropriate confidence intervals at the tonally associated frequencies was suggested.

Rutledge, Charles K.↗
NASA NTRS1991

Parametric entry corridors for lunar/Mars aerocapture missions

Parametric atmospheric entry corridor data are presented for Earth and Mars aerocapture. Parameter ranges were dictated by the range of mission designs currently envisioned as possibilities for the Human Exploration Initiative (HEI). This data, while not providing a means for exhaustive evaluation of aerocapture performance, should prove to be a useful aid for preliminary mission design and evaluation. Entry corridors are expressed as ranges of allowable vacuum periapse altitude of the planetary approach hyperbolic orbit, with chart provided for conversion to an approximate flight path angle corridor at entry interface (125 km altitude). The corridor boundaries are defined by open-loop aerocapture trajectories which satisfy boundary constraints while utilizing the full aerodynamic control capability of the vehicle (i.e., full lift-up or full lift-down). Parameters examined were limited to those of greatest importance from an aerocapture performance standpoint, including the approach orbit hyperbolic excess velocity, the vehicle lift to drag ratio, maximum aerodynamic load factor limit, and the apoapse of the target orbit. The impact of the atmospheric density bias uncertainties are also included. The corridor data is presented in graphical format, and examples of the utilization of these graphs for mission design and evaluation are included.

Ling, Lisa M.↗
NASA NTRS1992

Equivalent GPS measurements for efficient estimation process

Dual-frequency pseudorange and carrier phase data streams can be analytically combined into a single equivalent data stream, reducing the data volume and computing time in the filtering process for parameter estimation by a factor of 2 to 4. The resulting single data stream is that of carrier phase measurements with both data noise and bias uncertainty strictly defined. Based on these analytical formulas the equivalent GPS measurements can be formed by simple and efficient numerical calculations without any degradation in data strength. Formulation for the equivalent GPS measurements and their covariances are given in closed form; and a numerical simulation is performed to demonstrate the validity and effectiveness of the equivalent measurements.

Wu, S. C.↗
NASA NTRS1992

An optimal GPS data processing technique

A formula is derived to optimally combine dual-frequency GPS (Global Positioning System) pseudorange and carrier phase data streams into a single equivalent data stream, reducing the data volume and computing time in the filtering process for parameter estimation by a factor of four. The resulting single data stream is that of carrier phase measurements with both data noise and bias uncertainty strictly defined. With this analytical formula the single stream of equivalent GPS measurements can be efficiently formed by simple numerical calculations without any degradation in data strength. The formulation for the optimally combined GPS data and their covariances are given in closed form. Carrier phase ambiguity resolution, when feasible, is improved due to the preservation of the full data strength with the optimal data combining process.

Wu, S. C.↗