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At least 145 records · Page 8

Exploring Discretization Error in Simulation-Based Aerodynamic Databases

This work examines the level of discretization error in simulation-based aerodynamic databases and introduces strategies for error control. Simulations are performed using a parallel, multi-level Euler solver on embedded-boundary Cartesian meshes. Discretization errors in user-selected outputs are estimated using the method of adjoint-weighted residuals and we use adaptive mesh refinement to reduce these errors to specified tolerances. Using this framework, we examine the behavior of discretization error throughout a token database computed for a NACA 0012 airfoil consisting of 120 cases. We compare the cost and accuracy of two approaches for aerodynamic database generation. In the first approach, mesh adaptation is used to compute all cases in the database to a prescribed level of accuracy. The second approach conducts all simulations using the same computational mesh without adaptation. We quantitatively assess the error landscape and computational costs in both databases. This investigation highlights sensitivities of the database under a variety of conditions. The presence of transonic shocks or the stiffness in the governing equations near the incompressible limit are shown to dramatically increase discretization error requiring additional mesh resolution to control. Results show that such pathologies lead to error levels that vary by over factor of 40 when using a fixed mesh throughout the database. Alternatively, controlling this sensitivity through mesh adaptation leads to mesh sizes which span two orders of magnitude. We propose strategies to minimize simulation cost in sensitive regions and discuss the role of error-estimation in database quality.

Aftosmis, Michael J.

Estimation of Smoothing Error in SBUV Profile and Total Ozone Retrieval

Data from the Nimbus-4, Nimbus-7 Solar Backscatter Ultra Violet (SBUV) and seven of the NOAA series of SBUV/2 instruments spanning 41 years are being reprocessed using V8.6 algorithm. The data are scheduled to be released by the end of August 2011. An important focus of the new algorithm is to estimate various sources of errors in the SBUV profiles and total ozone retrievals. We discuss here the smoothing errors that describe the components of the profile variability that the SBUV observing system can not measure. The SBUV(/2) instruments have a vertical resolution of 5 km in the middle stratosphere, decreasing to 8 to 10 km below the ozone peak and above 0.5 hPa. To estimate the smoothing effect of the SBUV algorithm, the actual statistics of the fine vertical structure of ozone profiles must be known. The covariance matrix of the ensemble of measured ozone profiles with the high vertical resolution would be a formal representation of the actual ozone variability. We merged the MLS (version 3) and sonde ozone profiles to calculate the covariance matrix, which in general case, for single profile retrieval, might be a function of the latitude and month. Using the averaging kernels of the SBUV(/2) measurements and calculated total covariance matrix one can estimate the smoothing errors for the SBUV ozone profiles. A method to estimate the smoothing effect of the SBUV algorithm is described and the covariance matrixes and averaging kernels are provided along with the SBUV(/2) ozone profiles. The magnitude of the smoothing error varies with altitude, latitude, season and solar zenith angle. The analysis of the smoothing errors, based on the SBUV(/2) monthly zonal mean time series, shows that the largest smoothing errors were detected in the troposphere and might be as large as 15-20% and rapidly decrease with the altitude. In the stratosphere above 40 hPa the smoothing errors are less than 5% and between 10 and 1 hPa the smoothing errors are on the order of 1%. We validate our estimated smoothing errors by comparing the SBUV ozone profiles with other ozone profiling sensors.

Kramarova, N. A.

Measurement System Characterization in the Presence of Measurement Errors

In the calibration of a measurement system, data are collected in order to estimate a mathematical model between one or more factors of interest and a response. Ordinary least squares is a method employed to estimate the regression coefficients in the model. The method assumes that the factors are known without error; yet, it is implicitly known that the factors contain some uncertainty. In the literature, this uncertainty is known as measurement error. The measurement error affects both the estimates of the model coefficients and the prediction, or residual, errors. There are some methods, such as orthogonal least squares, that are employed in situations where measurement errors exist, but these methods do not directly incorporate the magnitude of the measurement errors. This research proposes a new method, known as modified least squares, that combines the principles of least squares with knowledge about the measurement errors. This knowledge is expressed in terms of the variance ratio - the ratio of response error variance to measurement error variance.

Commo, Sean A.

Human Error and the International Space Station: Challenges and Triumphs in Science Operations

Any system with a human component is inherently risky. Studies in human factors and psychology have repeatedly shown that human operators will inevitably make errors, regardless of how well they are trained. Onboard the International Space Station (ISS) where crew time is arguably the most valuable resource, errors by the crew or ground operators can be costly to critical science objectives. Operations experts at the ISS Payload Operations Integration Center (POIC), located at NASA's Marshall Space Flight Center in Huntsville, Alabama, have learned that from payload concept development through execution, there are countless opportunities to introduce errors that can potentially result in costly losses of crew time and science. To effectively address this challenge, we must approach the design, testing, and operation processes with two specific goals in mind. First, a systematic approach to error and human centered design methodology should be implemented to minimize opportunities for user error. Second, we must assume that human errors will be made and enable rapid identification and recoverability when they occur. While a systematic approach and human centered development process can go a long way toward eliminating error, the complete exclusion of operator error is not a reasonable expectation. The ISS environment in particular poses challenging conditions, especially for flight controllers and astronauts. Operating a scientific laboratory 250 miles above the Earth is a complicated and dangerous task with high stakes and a steep learning curve. While human error is a reality that may never be fully eliminated, smart implementation of carefully chosen tools and techniques can go a long way toward minimizing risk and increasing the efficiency of NASA's space science operations.

Harris, Samantha S.

Investigating Sources of Variability and Error in Simulations of Carbon Dioxide in an Urban Region

Greenhouse gas (GHG) emissions estimation methods that use atmospheric trace gas observations, including inverse modeling techniques, perform better when carbon dioxide (CO2) fluxes are more accurately transported and dispersed in the atmosphere by a numerical model. In urban areas, transport and dispersion is particularly difficult to simulate using current mesoscale meteorological models due, in part, to added complexity from surface heterogeneity and fine spatial/temporal scales. It is generally assumed that the errors in GHG estimation methods in urban areas are dominated by errors in transport and dispersion. Other significant errors include, but are not limited to, those from assumed emissions magnitude and spatial distribution. To assess the predictability of simulated trace gas mole fractions in urban observing systems using a numerical weather prediction model, we employ an Eulerian model that combines traditional meteorological variables with multiple passive tracers of atmospheric CO2 from anthropogenic inventories and a biospheric model. The predictability of the Eulerian model is assessed by comparing simulated atmospheric CO2 mole fractions to observations from four in situ tower sites (three urban and one rural) in the Washington DC/Baltimore, MD area for February 2016. Four different gridded fossil fuel emissions inventories along with a biospheric flux model are used to create an ensemble of simulated atmospheric CO2 observations within the model. These ensembles help to evaluate whether the modeled observations are impacted more by the underlying emissions or transport. The spread of modeled observations using the four emission fields indicates the model's ability to distinguish between the different inventories under various meteorological conditions. Overall, the Eulerian model performs well; simulated and observed average CO2 mole fractions agree within 1% when averaged at the three urban sites across the month. However, there can be differences greater than 10% at any given hour, which are attributed to complex meteorological conditions rather than differences in the inventories themselves. On average, the mean absolute error of the simulated compared to actual observations is generally twice as large as the standard deviation of the modeled mole fractions across the four emission inventories. This result supports the assumption, in urban domains, that the predicted mole fraction error relative to observations is dominated by errors in model meteorology rather than errors in the underlying fluxes in winter months. As such, minimizing errors associated with atmospheric transport and dispersion may help improve the performance of GHG estimation models more so than improving flux priors in the winter months. We also find that the errors associated with atmospheric transport in urban domains are not restricted to certain times of day. This suggests that atmospheric inversions should use CO2 observations that have been filtered using meteorological observations rather than assuming that meteorological modeling is most accurate at certain times of day (such as using only mid-afternoon observations).

CO2

Rare events and Griffiths phases in topological quantum error correction

The performance of quantum error correcting (QEC) codes is often studied under the assumption of spatiotemporally uniform error rates. On the other hand, experimental implementations almost always produce heterogeneous error rates, in either space or time, as a result of effects such as imperfect fabrication and/or cosmic rays. It is therefore important to understand if and how their presence can affect the performance of QEC in qualitative ways. Here, in this work, we study the effects of nonuniform error rates in the representative examples of the 1D repetition code and the 2D toric code, focusing on when they have extended spatiotemporal correlations; these may arise, for instance, from rare events (such as cosmic rays) that temporarily elevate error rates over the entire code patch. These effects can be described in the corresponding statistical mechanics models for decoding, where long-range correlations in the error rates lead to extended rare regions of weaker coupling. For the 1D repetition code where the rare regions are linear, we find two distinct decodable phases: a conventional ordered phase in which logical failure rates decay exponentially with the code distance, and a rare-region dominated Griffiths phase in which failure rates are parametrically larger and decay as a stretched exponential. In particular, the latter phase is present when the error rates in the rare regions are above the bulk threshold. For the 2D toric code where the rare regions are planar, we find no decodable Griffiths phase: rare events which boost error rates above the bulk threshold lead to an asymptotic loss of threshold and failure to decode. Unpacking the failure mechanism implies that techniques for suppressing extended sequences of repeated rare events (which, without intervention, will be statistically present with high probability) will be crucial for QEC with the toric code.

classical statistical mechanics

Wavefront-Error Performance Characterization for the James Webb Space Telescope (JWST) Integrated Science Instrument Module (ISIM) Science Instruments

The science instruments (SIs) comprising the James Webb Space Telescope (JWST) Integrated Science Instrument Module (ISIM) were tested in three cryogenic-vacuum test campaigns in the NASA Goddard Space Flight Center (GSFC)'s Space Environment Simulator (SES). In this paper, we describe the results of optical wavefront-error performance characterization of the SIs. The wavefront error is determined using image-based wavefront sensing (also known as phase retrieval), and the primary data used by this process are focus sweeps, a series of images recorded by the instrument under test in its as-used configuration, in which the focal plane is systematically changed from one image to the next. High-precision determination of the wavefront error also requires several sources of secondary data, including 1) spectrum, apodization, and wavefront-error characterization of the optical ground-support equipment (OGSE) illumination module, called the OTE Simulator (OSIM), 2) plate scale measurements made using a Pseudo-Nonredundant Mask (PNRM), and 3) pupil geometry predictions as a function of SI and field point, which are complicated because of a tricontagon-shaped outer perimeter and small holes that appear in the exit pupil due to the way that different light sources are injected into the optical path by the OGSE. One set of wavefront-error tests, for the coronagraphic channel of the Near-Infrared Camera (NIRCam) Longwave instruments, was performed using data from transverse translation diversity sweeps instead of focus sweeps, in which a sub-aperture is translated andor rotated across the exit pupil of the system.Several optical-performance requirements that were verified during this ISIM-level testing are levied on the uncertainties of various wavefront-error-related quantities rather than on the wavefront errors themselves. This paper also describes the methodology, based on Monte Carlo simulations of the wavefront-sensing analysis of focus-sweep data, used to establish the uncertainties of the wavefront error maps.

wavefront error

Wavefront-Error Performance Characterization for the James Webb Space Telescope (JWST) Integrated Science Instrument Module (ISIM) Science Instruments

The science instruments (SIs) comprising the James Webb Space Telescope (JWST) Integrated Science Instrument Module (ISIM) were tested in three cryogenic-vacuum test campaigns in the NASA Goddard Space Flight Center (GSFC)'s Space Environment Simulator (SES) test chamber. In this paper, we describe the results of optical wavefront-error performance characterization of the SIs. The wavefront error is determined using image-based wavefront sensing, and the primary data used by this process are focus sweeps, a series of images recorded by the instrument under test in its as-used configuration, in which the focal plane is systematically changed from one image to the next. High-precision determination of the wavefront error also requires several sources of secondary data, including 1) spectrum, apodization, and wavefront-error characterization of the optical ground-support equipment (OGSE) illumination module, called the OTE Simulator (OSIM), 2) F-number and pupil-distortion measurements made using a pseudo-nonredundant mask (PNRM), and 3) pupil geometry predictions as a function of SI and field point, which are complicated because of a tricontagon-shaped outer perimeter and small holes that appear in the exit pupil due to the way that different light sources are injected into the optical path by the OGSE. One set of wavefront-error tests, for the coronagraphic channel of the Near-Infrared Camera (NIRCam) Longwave instruments, was performed using data from transverse translation diversity sweeps instead of focus sweeps, in which a sub-aperture is translated and/or rotated across the exit pupil of the system. Several optical-performance requirements that were verified during this ISIM-level testing are levied on the uncertainties of various wavefront-error-related quantities rather than on the wavefront errors themselves. This paper also describes the methodology, based on Monte Carlo simulations of the wavefront-sensing analysis of focus-sweep data, used to establish the uncertainties of the wavefront-error maps.

image analysis

Influence of Strain-Gage Balance Characteristics on the Precision Error of the Drag Coefficient

Improvements and results of a new method are presented that computes a pre-test estimate of the precision error of the drag coefficient of a wind tunnel model. The error estimate is defined as the part of the drag coefficient's precision error that is primarily associated with the precision error of the angle of attack measurement and physical characteristics of the chosen strain-gage balance. The method indirectly describes the precision error of the angle of attack measurement by using an assumed balance gage output variation of one microV/V. The physical characteristics of the balance, on the other hand, are described by partial derivatives of the axial and normal forces with respect to the strain-gage outputs. These derivatives can directly be obtained from the data reduction matrix of the balance. The precision error estimate itself is calculated by applying a simple explicit equation that uses the model reference area, the dynamic pressure, the angle of attack, the coefficients of the linear terms of the data reduction matrix, and the electrical output variation of one microvolt per volt as input. Precision errors at constant angle of attack may be visualized as contour plots by plotting them, for example, versus the Mach number and the total pressure. Characteristics of NASA's MC60E balance are used in combination with the reference area of a generic wind tunnel model in order to demonstrate that error estimates are independent of both the balance load format and the units chosen for the description of balance loads, model reference area, and the dynamic pressure. Finally, experimental data from a wind tunnel test of the Ames Check Standard Model in the NASA Ames 11-foot Transonic Wind Tunnel illustrates the application of the method to real-world test data.

precision error

A table of integrals of the error function. II - Additions and corrections.

Integrals of products of error functions with other functions are presented, taking into account a combination of the error function with powers, a combination of the error function with exponentials and powers, a combination of the error function with exponentials of more complicated arguments, definite integrals from Laplace transforms, and a combination of the error function with trigonometric functions. Other integrals considered include a combination of the error function with logarithms and powers, a combination of two error functions, and a combination of the error function with other special functions.

Geller, M.

Error analysis of bent ray radio occultation measurments

There are two types of experimental measurement errors of the Doppler data associated with the radio occultation, random and systematic. Random errors are due to thermal noise in the transmission channel, and the phase lock loop, and quantization error in the digital circuitry. These are called noise type errors. The systematic errors are due to geometric uncertainty and equipment phase instability. Considered is the amount of uncertainty, due to random measurement errors, in the refractivity profiles reconstructed by this type of indirect sensing experiment. A class of refractivity profiles is defined which approximately fit the set of measured data. Bounds are placed on the extent of this class of solution profiles. To accomplish this, the sensivity of the reconstructed refractivity profiles to errors in the measured quantity and the statistics of the errors in the measurement are examined.

Saintgermain, R. L.

Augmented burst-error correction for UNICON laser memory

A single-burst-error correction system is described for data stored in the UNICON laser memory. In the proposed system, a long fire code with code length n greater than 16,768 bits was used as an outer code to augment an existing inner shorter fire code for burst error corrections. The inner fire code is a (80,64) code shortened from the (630,614) code, and it is used to correct a single-burst-error on a per-word basis with burst length b less than or equal to 6. The outer code, with b less than or equal to 12, would be used to correct a single-burst-error on a per-page basis, where a page consists of 512 32-bit words. In the proposed system, the encoding and error detection processes are implemented by hardware. A minicomputer, currently used as a UNICON memory management processor, is used on a time-demanding basis for error correction. Based upon existing error statistics, this combination of an inner code and an outer code would enable the UNICON system to obtain a very low error rate in spite of flaws affecting the recorded data.

Lim, R. S.

Burst-error characteristics of the equatorial transionospheric channel

Analyses of AGC analog data from the Small Astronomy Satellite (SAS) at VHF (136 MHz) have shown amplitude fluctuations in the signals received at several equatorial tracking sites operated by NASA. Errors in data are shown to increase markedly for nighttime satellite passes around the periods of the two equinoxes as compared to the errors observed during other periods. Qualitative and quantitative correlations are established between the ionospheric scintillation phenomenon and the occurrence of errors. Strong time and geographic cause-and-effect relationships are established by determining the statistical correlation between scintillation indices and bit error rates. Detailed analyses of the AGC fading statistics and the fine grain error statistics, such as the block-error distribution and the bit-error autocorrelation function, establish the strong correlation between deep fades and their effects on the burst error structure associated with the transionospheric channel and the communication receiver being employed.

Blank, H. A.

Error probability performance of unbalanced QPSK receivers

A simple technique for calculating the error probability performance and associated noisy reference loss of practical unbalanced QPSK receivers is presented. The approach is based on expanding the error probability conditioned on the loop phase error in a power series in the loop phase error and then, keeping only the first few terms of this series, averaging this conditional error probability over the probability density function of the loop phase error. Doing so results in an expression for the average error probability which is in the form of a leading term representing the ideal (perfect synchronization references) performance plus a term proportional to the mean-squared crosstalk. Thus, the additional error probability due to noisy synchronization references occurs as an additive term proportional to the mean-squared phase jitter directly associated with the receiver's tracking loop. Similar arguments are advanced to give closed-form results for the noisy reference loss itself.

Simon, M. K.

Skylab water balance error analysis

Estimates of the precision of the net water balance were obtained for the entire Skylab preflight and inflight phases as well as for the first two weeks of flight. Quantitative estimates of both total sampling errors and instrumentation errors were obtained. It was shown that measurement error is minimal in comparison to biological variability and little can be gained from improvement in analytical accuracy. In addition, a propagation of error analysis demonstrated that total water balance error could be accounted for almost entirely by the errors associated with body mass changes. Errors due to interaction between terms in the water balance equation (covariances) represented less than 10% of the total error. Overall, the analysis provides evidence that daily measurements of body water changes obtained from the indirect balance technique are reasonable, precise, and relaible. The method is not biased toward net retention or loss.

Leonard, J. I.

A concatenated coding scheme for error control

In this paper, a concatenated coding scheme for error control in data communications is presented and analyzed. In this scheme, the inner code is used for both error correction and detection; however, the outer code is used only for error detection. A retransmission is requested if either the inner code decoder fails to make a successful decoding or the outer code decoder detects the presence of errors after the inner code decoding. Probability of undetected error (or decoding error) of the proposed scheme is derived. An efficient method for computing this probability is presented. Throughput efficiency of the proposed error control scheme incorporated with a selective-repeat ARQ retransmission strategy is also analyzed. Three specific examples are presented. One of the examples is proposed for error control in the NASA Telecommand System.

Kasami, T.

New dimension analyses with error analysis for quaking aspen and black spruce

Dimension analysis for black spruce in wetland stands and trembling aspen are reported, including new approaches in error analysis. Biomass estimates for sacrificed trees have standard errors of 1 to 3%; standard errors for leaf areas are 10 to 20%. Bole biomass estimation accounts for most of the error for biomass, while estimation of branch characteristics and area/weight ratios accounts for the leaf area error. Error analysis provides insight for cost effective design of future analyses. Predictive equations for biomass and leaf area, with empirically derived estimators of prediction error, are given. Systematic prediction errors for small aspen trees and for leaf area of spruce from different site-types suggest a need for different predictive models within species. Predictive equations are compared with published equations; significant differences may be due to species responses to regional or site differences. Proportional contributions of component biomass in aspen change in ways related to tree size and stand development. Spruce maintains comparatively constant proportions with size, but shows changes corresponding to site. This suggests greater morphological plasticity of aspen and significance for spruce of nutrient conditions.

Woods, K. D.

Radial orbit error reduction and sea surface topography determination using satellite altimetry

A method is presented in satellite altimetry that attempts to simultaneously determine the geoid and sea surface topography with minimum wavelengths of about 500 km and to reduce the radial orbit error caused by geopotential errors. The modeling of the radial orbit error is made using the linearized Lagrangian perturbation theory. Secular and second order effects are also included. After a rather extensive validation of the linearized equations, alternative expressions of the radial orbit error are derived. Numerical estimates for the radial orbit error and geoid undulation error are computed using the differences of two geopotential models as potential coefficient errors, for a SEASAT orbit. To provide statistical estimates of the radial distances and the geoid, a covariance propagation is made based on the full geopotential covariance. Accuracy estimates for the SEASAT orbits are given which agree quite well with already published results. Observation equations are develped using sea surface heights and crossover discrepancies as observables. A minimum variance solution with prior information provides estimates of parameters representing the sea surface topography and corrections to the gravity field that is used for the orbit generation. The simulation results show that the method can be used to effectively reduce the radial orbit error and recover the sea surface topography.

Engelis, Theodossios