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NASA NTRS1972

Ionosphere total electron measurements as extracted from satellite tracking data

The Goddard Range and Range Rate System (GRARR) determines the range of a spacecraft by measuring the group delay of a modulated wave and the range rate by measuring the Doppler phase shift of the carrier. An analytical technique is presented for obtaining corrections and equivalent total electron content along the vertical, using VHF GRARR data and a radial model of the ionosphere. The results of computation for a representative pass are given, and estimated accuracy is discussed from a statistical view point. Using VHF GRARR data and a radial model of the ionosphere. The results of computation for a representative pass are given, and estimated accuracy is discussed from a statistical view point. Using GRARR range, range rate, and angle tracking data from Explorer 41, values of total electron content on the order of 10 to the 17th to 10 to the 18th power (electrons/sq m) were obtained. These values agree with estimates of the total electron content from ionospheric profiles using f sub o F sub 2 predict data.

Murray, C. W., Jr.↗

NASA NTRSDate not supplied

Variational Coupled Loads Analysis using the Hybrid Parametric Variation Method

Time-domain coupled loads analysis (CLA)is used to determine the response of a launch vehicle and payload system to transient forces, such as liftoff, engine ignitions and shutdowns, jettison events, and atmospheric flight loads, such as buffet. CLA, using Hurty/Craig-Bampton (HCB)component models, is the accepted method for the establishment of design-level loads for launch systems. However, uncertainty in the component models flows into uncertainty in predicted system results. Uncertainty in the structural responses during launch is a significant concern because small variations in launch vehicle and payload mode shapes and their interactions can result in significant variations in system loads. Uncertainty quantification (UQ)is used to determine statistical bounds on prediction accuracy based on model uncertainty. In this paper uncertainty is treated at the HCB component-model level. In an effort to account for model uncertainties and statistically bound their effect on CLA predictions, this work combines CLA with UQ in a process termed variational coupled loads analysis (VCLA). The modeling of uncertainty using a parametric approach, in which input parameters are represented by random variables, is common, but its major drawback is the resulting uncertainty is limited to the form of the nominal model. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. Model-form uncertainty can be represented using a nonparametric approach based on random matrix theory (RMT). In this work, UQ is performed using the hybrid parametric variation (HPV)method, which combines parametric with nonparametric uncertainty at the HCB component model level. The HPV method requires the selection of dispersion values for the HCB fixed-interface (FI)eigenvalues, and the HCB mass and stiffness matrices. The dispersions are based upon component test-analysis modal correlation results. During VCLA, random component models are assembled into an ensemble of random systems using a Monte Carlo (MC)approach. CLA is applied to each of the ensemble members to produce an ensemble of system-level responses for statistical analysis. The proposed methodology is demonstrated through its application to a buffet loads analysis of NASA’s Space Launch System (SLS)during the transonic regime fifty seconds after liftoff. Core stage (CS)section shears and moments are recovered, and statistics are computed.

Uncertainty Quantification↗

NASA NTRS2009

Basic Diagnosis and Prediction of Persistent Contrail Occurrence using High-resolution Numerical Weather Analyses/Forecasts and Logistic Regression. Part I: Effects of Random Error

Straightforward application of the Schmidt-Appleman contrail formation criteria to diagnose persistent contrail occurrence from numerical weather prediction data is hindered by significant bias errors in the upper tropospheric humidity. Logistic models of contrail occurrence have been proposed to overcome this problem, but basic questions remain about how random measurement error may affect their accuracy. A set of 5000 synthetic contrail observations is created to study the effects of random error in these probabilistic models. The simulated observations are based on distributions of temperature, humidity, and vertical velocity derived from Advanced Regional Prediction System (ARPS) weather analyses. The logistic models created from the simulated observations were evaluated using two common statistical measures of model accuracy, the percent correct (PC) and the Hanssen-Kuipers discriminant (HKD). To convert the probabilistic results of the logistic models into a dichotomous yes/no choice suitable for the statistical measures, two critical probability thresholds are considered. The HKD scores are higher when the climatological frequency of contrail occurrence is used as the critical threshold, while the PC scores are higher when the critical probability threshold is 0.5. For both thresholds, typical random errors in temperature, relative humidity, and vertical velocity are found to be small enough to allow for accurate logistic models of contrail occurrence. The accuracy of the models developed from synthetic data is over 85 percent for both the prediction of contrail occurrence and non-occurrence, although in practice, larger errors would be anticipated.

Duda, David P.↗

NASA NTRS1980

Estimation of the accuracy of dynamic flight-determined coefficients

This paper discusses means of assessing the accuracy of maximum likelihood parameter estimates obtained from dynamic flight data. The commonly used analytical predictors of accuracy are compared from both statistical and simplified geometric standpoints. Emphasizing practical considerations, such as modeling error, the accuracy predictions are evaluated with real and simulated data. Improved computations of the Cramer-Rao bound to correct large discrepancies caused by colored noise and modeling error are presented. This corrected Cramer-Rao bound is the best available analytical predictor of accuracy. Engineering judgement, aided by such analytical tools, is the final arbiter of accuracy estimation.

Maine, R. E.↗

NASA NTRS1994

The Accuracy of Parameter Estimation in System Identification of Noisy Aircraft Load Measurement

This thesis focuses on the subject of the accuracy of parameter estimation and system identification techniques. Motivated by a complicated load measurement from NASA Dryden Flight Research Center, advanced system identification techniques are needed. The objective of this problem is to accurately predict the load experienced by the aircraft wing structure during flight determined from a set of calibrated load and gage response relationship. We can then model the problem as a black box input-output system identification from which the system parameter has to be estimated. Traditional LS (Least Square) techniques and the issues of noisy data and model accuracy are addressed. A statistical bound reflecting the change in residual is derived in order to understand the effects of the perturbations on the data. Due to the intrinsic nature of the LS problem, LS solution faces the dilemma of the trade off between model accuracy and noise sensitivity. A method of conflicting performance indices is presented, thus allowing us to improve the noise sensitivity while at the same time configuring the degredation of the model accuracy. SVD techniques for data reduction are studied and the equivalence of the Correspondence Analysis (CA) and Total Least Squares Criteria are proved. We also looked at nonlinear LS problems with NASA F-111 data set as an example. Conventional methods are neither easily applicable nor suitable for the specific load problem since the exact model of the system is unknown. Neural Network (NN) does not require prior information on the model of the system. This robustness motivated us to apply the NN techniques on our load problem. Simulation results for the NN methods used in both the single load and the 'warning signal' problems are both useful and encouraging. The performance of the NN (for single load estimate) is better than the LS approach, whereas no conventional approach was tried for the 'warning signals' problems. The NN design methodology is also presented. The use of SVD, CA and Collinearity Index methods are used to reduce the number of neurons in a layer.

Kong, Jeffrey↗

NASA NTRS1977

Performance tests of signature extension algorithms

Comparative tests were performed on seven signature extension algorithms to evaluate their effectiveness in correcting for changes in atmospheric haze and sun angle in a Landsat scene. Four of the algorithms were cluster matching, and two were maximum likelihood algorithms. The seventh algorithm determined the haze level in both training and recognition segments and used a set of tables calculated from an atmospheric model to determine the affine transformation that corrects the training signatures for changes in sun angle and haze level. Three of the algorithms were tested on a simulated data set, and all of the algorithms were tested on consecutive-day data. The classification performance on the data sets using the algorithms is presented, along with results of statistical tests on the accuracy and proportion estimates. The three algorithms tested on the simulated data produced significant improvements over the results obtained using untransformed signatures. For the consecutive-day data, the tested algorithms produced improvements in most but not all cases. The tests indicated also that no statistically significant differences were noted among the algorithms.

Abotteen, R.↗

NASA NTRS2022

Uncertainty Models for the Hybrid Parametric Variation Method of Uncertainty Quantification; Analysis

There is some level of uncertainty in every finite element model (FEM), which flows to a level of uncertainty in predicted results. The purpose of uncertainty quantification (UQ) is to provide statistical bounds on prediction accuracy based on model uncertainty. This is distinct from model updating, which attempts to modify models to improve their accuracy. UQ does not improve the accuracy of models, but accepts that the models are inherently inaccurate and attempts to quantify the impact of that inaccuracy on predicted results. Previously, an alternate method for UQ, called the Hybrid Parametric Variation (HPV) method, was applied to Space Launch System (SLS) Hurty/Craig-Bampton (HCB) components to predict system-level statistics for launch vehicle attitude control transfer functions and core stage section loads due to buffet. The HPV method combines a parametric variation of the HCB fixed-interface (FI) modal frequencies with a nonparametric variation (NPV) method that randomly varies the HCB mass and stiffness matrices as Wishart random matrix distributions using random matrix theory (RMT). Alternatively, the most common method for modeling uncertainty in the structural dynamics community is a parametric approach, which varies physical parameters in the model. However, there are several disadvantages associated with the parametric method. Determining a reduced set of parameters that have a significant impact on the system response can be time consuming, and the selected parameter probability distributions are rarely reliably known. Therefore, in practice, the parameters are surrogates for the actual errors, and the link to parameter uncertainty is unknown. Another major drawback is that the uncertainty that can be represented is limited to the form of the nominal FEM. It is the experience of the authors that based on numerous aerospace programs, almost all FEM errors are in form rather than parameter values. This hypothesis is supported by the observation of the authors that it is almost never possible to ‘tune’ a FEM to match modal test results by only modifying model parameters. Model-form uncertainty cannot be directly represented by FEM input parameters nor included in a parametric approach. However, model-form uncertainty can be modeled using RMT, where a probability distribution is developed for the matrix ensemble of interest. The major advantage of the NPV method is that it covers errors in model form. The HPV method anchors uncertainty at the HCB component level to component modal test results by matching the HCB and test modes based on mode descriptions or other methods, and then applying differing levels of frequency variation. The specific variations depend on the confidence to which a component FEM has been validated through modal testing. The NPV method is layered on the frequency variation to match modal test self-orthogonality and cross-orthogonality (XO) results. Once the component uncertainty models are identified, they are assembled, and the uncertainty is propagated to the system level using a Monte Carlo (MC) analysis approach that generates statistics for system-level predictions This provides a UQ method that can be traced to test data, which can be updated as additional data and improved correlated models become available. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The purpose of this paper is to collect and present all of the theory for HPV that has been previously published in reports and papers and to present examples of its application. Specifically, component uncertainty models based on the dispersion of corresponding mass and stiffness matrices using proposed test/analysis correlation metrics are investigated. The first example is purely academic so that the true answers are known, and the validity of the HPV method and the corresponding uncertainty models can be determined. The second example is an application to a component that is design specific to the SLS. Based on this work and other assessments, the HPV method provides another tool to the toolset used for complex system UQ analysis. From experience gathered to date using the HPV method, additional design specific applications must be investigated to provide further confidence in the validity of the HPV method of UQ analysis.

Uncertainty quantification↗

NASA NTRS2002

Fractional Snowcover Estimates from Earth Observing System (EOS) Terra and Aqua Moderate Resolution Imaging Spectroradiometer (MODIS)

The Moderate Resolution Imaging Spectroradiometer (MODIS) on the NASA Earth Observing System (EOS) Terra and Aqua missions has shown considerable capability for mapping snowcover. The typical approach that has used, along with other criteria, the Normalized Snow Difference Index (NDSI) that takes the difference between 500 meter observations at 1.64 micrometers (MODIS band 6) and 0.555 micrometers (MODIS band 4) over the sum of these observations to determine whether MODIS pixels are snowcovered or not in mapping the extent of snowcover. For many hydrological and climate studies using remote sensing of snowcover, it is desirable to assess if the MODIS snowcover observations could not be enhanced by providing the fraction of snowcover in each MODIS observation (pixel). Pursuant to this objective studies have been conducted to assess whether there is sufficient "signal%o in the NDSI parameter to provide useful estimates of fractional snowcover in each MODIS 500 meter pixel. To accomplish this objective high spatial resolution (30 meter) Landsat snowcover observations were used and co-registered with MODIS 500 meter pixels. The NDSI approach was used to assess whether a Landsat pixel was or was not snowcovered. Then the number of snowcovered Landsat pixels within a MODIS pixel was used to determine the fraction of snowcover within each MODIS pixel. The e results were then used to develop statistical relationships between the NDSI value for each 500 meter MODIS pixel and the fraction of snowcover in the MODIS pixel. Such studies were conducted for three widely different areas covered by Landsat scenes in Alaska, Russia, and the Quebec Province in Canada. The statistical relationships indicate that a 10 percent accuracy can be attained. The variability in the statistical relationship for the three areas was found to be remarkably similar (-0.02 for mean error and less than 0.01 for mean absolute error and standard deviation). Independent tests of the relationships were accomplished by taking the relationship of fractional snow-cover to NDSI from one area (e.g., Alaska) and testing it on the other two areas (e.g. Russia and Quebec). Again the results showed that fractional snow-cover can be estimated to 10 percent. The results have been shown to have advantages over other published fractional snowcover algorithms applied to MODIS data. Most recently the fractional snow-cover algorithm has been applied using 500-meter observations over the state of Colorado for a period spanning 25 days. The results exhibit good behavior in mapping the spatial and temporal variability in snowcover over that 25-day period. Overall these studies indicate that robust estimates of fractional snow-cover can be attained using the NDSI parameter over areas extending in size from watersheds relatively large compared to MODIS pixels to global land cover. Other refinements to this approach as well as different approaches are being examined for mapping fractional snow-cover using MODIS observations.

Salomonson, Vincent V.↗

NASA NTRS1982

Combining remotely sensed and other measurements for hydrologic areal averages

A method is described for combining measurements of hydrologic variables of various sampling geometries and measurement accuracies to produce an estimated mean areal value over a watershed and a measure of the accuracy of the mean areal value. The method provides a means to integrate measurements from conventional hydrological networks and remote sensing. The resulting areal averages can be used to enhance a wide variety of hydrological applications including basin modeling. The correlation area method assigns weights to each available measurement (point, line, or areal) based on the area of the basin most accurately represented by the measurement. The statistical characteristics of the accuracy of the various measurement technologies and of the random fields of the hydrologic variables used in the study (water equivalent of the snow cover and soil moisture) required to implement the method are discussed.

Johnson, E. R.↗

NASA NTRS2005

Statistical Calibration and Validation of a Homogeneous Ventilated Wall-Interference Correction Method for the National Transonic Facility

Wind tunnel experiments will continue to be a primary source of validation data for many types of mathematical and computational models in the aerospace industry. The increased emphasis on accuracy of data acquired from these facilities requires understanding of the uncertainty of not only the measurement data but also any correction applied to the data. One of the largest and most critical corrections made to these data is due to wall interference. In an effort to understand the accuracy and suitability of these corrections, a statistical validation process for wall interference correction methods has been developed. This process is based on the use of independent cases which, after correction, are expected to produce the same result. Comparison of these independent cases with respect to the uncertainty in the correction process establishes a domain of applicability based on the capability of the method to provide reasonable corrections with respect to customer accuracy requirements. The statistical validation method was applied to the version of the Transonic Wall Interference Correction System (TWICS) recently implemented in the National Transonic Facility at NASA Langley Research Center. The TWICS code generates corrections for solid and slotted wall interference in the model pitch plane based on boundary pressure measurements. Before validation could be performed on this method, it was necessary to calibrate the ventilated wall boundary condition parameters. Discrimination comparisons are used to determine the most representative of three linear boundary condition models which have historically been used to represent longitudinally slotted test section walls. Of the three linear boundary condition models implemented for ventilated walls, the general slotted wall model was the most representative of the data. The TWICS code using the calibrated general slotted wall model was found to be valid to within the process uncertainty for test section Mach numbers less than or equal to 0.60. The scatter among the mean corrected results of the bodies of revolution validation cases was within one count of drag on a typical transport aircraft configuration for Mach numbers at or below 0.80 and two counts of drag for Mach numbers at or below 0.90.

Walker, Eric Lee↗

NASA NTRS2005

Statistical Calibration and Validation of a Homogeneous Ventilated Wall-Interference Correction Method for the National Transonic Facility

Walker, Eric L.↗

NASA NTRS1986

High-accuracy computation of Delta V magnitude probability densities - Preliminary remarks

This paper describes an algorithm for the high accuracy computation of some statistical quantities of the magnitude of a random trajectory correction maneuver (TCM). The trajectory correction velocity increment Delta V is assumed to be a three-component random vector with each component being a normally distributed random scalar having a possibly nonzero mean. Knowledge of the statitiscal properties of the magnitude of a random TCM is important in the planning and execution of maneuver strategies for deep-space missions such as Galileo. The current algorithm involves the numerical integration of a set of differential equations. This approach allows the computation of density functions for specific Delta V magnitude distributions to high accuracy without first having to generate large numbers of random samples. Possible applications of the algorithm to maneuver planning, planetary quarantine evaluation, and guidance success probability calculations are described.

Chadwick, C.↗

NASA NTRS1992

A Regression Method for Comparing Launch Zone Ranges Derived From Different Sources

In modern fighter aircraft air-to-air missile launch acceptable ranges (LARs) are provided to the pilot for his launch decision. These LARs are calculated in the avionic software, using very simple algebraic equations and algorithms, that attempt to model complex missile behavior. Frequently these algorithms are revised to reflect inaccuracies discovered, when comparisons are made with missile six degree-of-freedom (6-DOF) simulations. The process of modifying this software has become expensive. In the past, these simple LAR generators were modified based only on subjective judgmental approach, with little regard to the missile range design limits. With reduced budgets a more rational methodology should be taken to assess whether or not simple fighter LAR generators need to be modified. Any LAR generator can produce large amounts of range (minimum and maximum) data over the board engagement limits of modem fighter and air-to-air missiles. This infinite population lends itself to some statistical methodology to access simple LAR accuracy and the need for software modification. The methodology should produce statistical parameters for use in the decision making process of modifying a simple fighter LAR generator. This paper presents a regression method, based on a missile range design limit philosophy. Acceptance criteria from the regression method are given that provide simple statistical parameters to aid in this decision making process.

Flight Testing↗

NASA NTRSDate not supplied

SLS Integrated Modal Test Uncertainty Quantification using the Hybrid Parametric Variation Method

Uncertainty in structural loading during launch is a significant concern in the development of spacecraft and launch vehicles. Small variations in launch vehicle and payload mode shapes and their interaction can result in significant variation in system loads. In many cases involving large aerospace systems it is difficult, not economical, or impossible to perform a system modal test. However, it is still vital to obtain test results that can be compared with analytical predictions to validate models. Instead, the “Building Block Approach” is used in which system components are tested individually. Component models are correlated and updated to agree as best they can with test results. The Space Launch System consists of a number of components that are assembled into a launch vehicle. Finite element models of the components are developed, reduced to Hurty/Craig-Bampton models and assembled to represent different phases of flight. The only opportunity to obtain modal test data from an assembled Space Launch System will be during the Integrated Modal Test. There is always uncertainty in every model, which flows into uncertainty in predicted system results. Uncertainty Quantification is used to determine statistical bounds on prediction accuracy based on model uncertainty. For the Space Launch System, model uncertainty is at the Hurty/Craig-Bampton component level. Uncertainty in the Hurty/Craig-Bampton components is quantified using the hybrid parametric variation approach that combines parametric and nonparametric uncertainty. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. This type of uncertainty cannot be represented by variations infinite element model input parameters and thus cannot be included in a parametric approach. However, model-form uncertainty can be modeled using a nonparametric approach based on random matrix theory. The hybrid parametric variation method requires the selection of dispersion values for the Hurty/Craig-Bampton fixed-interface eigenvalues, and the Hurty/Craig-Bampton stiffness matrices. Component test/analysis frequency error is used to identify the fixed-interface eigenvalue dispersions, while test/analysis cross-orthogonality is used to identify stiffness dispersion values. The hybrid parametric variation uncertainty quantification approach is applied to the Space Launch System Integrated Modal Test configuration. Monte Carlo analysis is performed, and statistics are determined for modal correlation metrics, frequency response from Integrated Modal Test shakers to selected accelerometers, as well as other metrics for determining how well target modes are excited and identified. If the predicted uncertainty envelopes future Integrated Modal Test results, then there will be increased confidence in the utility of the component-based hybrid parametric variation uncertainty quantification approach.

Uncertainty Quantification↗

NASA NTRS2012

Geospatial Method for Computing Supplemental Multi-Decadal U.S. Coastal Land-Use and Land-Cover Classification Products, Using Landsat Data and C-CAP Products

This paper discusses the development and implementation of a geospatial data processing method and multi-decadal Landsat time series for computing general coastal U.S. land-use and land-cover (LULC) classifications and change products consisting of seven classes (water, barren, upland herbaceous, non-woody wetland, woody upland, woody wetland, and urban). Use of this approach extends the observational period of the NOAA-generated Coastal Change and Analysis Program (C-CAP) products by almost two decades, assuming the availability of one cloud free Landsat scene from any season for each targeted year. The Mobile Bay region in Alabama was used as a study area to develop, demonstrate, and validate the method that was applied to derive LULC products for nine dates at approximate five year intervals across a 34-year time span, using single dates of data for each classification in which forests were either leaf-on, leaf-off, or mixed senescent conditions. Classifications were computed and refined using decision rules in conjunction with unsupervised classification of Landsat data and C-CAP value-added products. Each classification's overall accuracy was assessed by comparing stratified random locations to available reference data, including higher spatial resolution satellite and aerial imagery, field survey data, and raw Landsat RGBs. Overall classification accuracies ranged from 83 to 91% with overall Kappa statistics ranging from 0.78 to 0.89. The accuracies are comparable to those from similar, generalized LULC products derived from C-CAP data. The Landsat MSS-based LULC product accuracies are similar to those from Landsat TM or ETM+ data. Accurate classifications were computed for all nine dates, yielding effective results regardless of season. This classification method yielded products that were used to compute LULC change products via additive GIS overlay techniques.

Spruce, J. P.↗

NASA NTRS1971

Regional Land Use Mapping: the Phoenix Pilot Project

The Phoenix Pilot Program has been designed to make effective use of past experience in making land use maps and collecting land use information. Conclusions reached from the project are: (1) Land use maps and accompanying statistical information of reasonable accuracy and quality can be compiled at a scale of 1:250,000 from orbital imagery. (2) Orbital imagery used in conjunction with other sources of information when available can significantly enhance the collection and analysis of land use information. (3) Orbital imagery combined with modern computer technology will help resolve the problem of obtaining land use data quickly and on a regular basis, which will greatly enhance the usefulness of such data in regional planning, land management, and other applied programs. (4) Agreement on a framework or scheme of land use classification for use with orbital imagery will be necessary for effective use of land use data.

Anderson, J. R.↗

NASA NTRS1982

Generation of pseudo-random numbers

Practical methods for generating acceptable random numbers from a variety of probability distributions which are frequently encountered in engineering applications are described. The speed, accuracy, and guarantee of statistical randomness of the various methods are discussed.

Howell, L. W.↗

NASA NTRS1982

Performance of the spectropolarimeter for the Space Telescope faint object spectrograph

The design and preliminary test results for the spectropolarimeter for the Faint Object Spectrograph (FOS) for the Space Telescope are presented. The mechanical design and optical specifications of the spectropolarimeter are described noting that a Wollaston prism with an internal wedge angle of 20 deg is fixed behind each of two rotatable waveplate retarders of different retardations. Either waveplate/prism combination can be positioned at either of the two FOS entrance ports. Magnesium fluoride is chosen as the birefringent crystal for the polarizing elements to allow linear and circular polarization measurements down to Lyman-alpha at 1216 A. Mechanical stability and repeatability were determined by operational testing to give polarization-position angles of + or - 0.5 deg, corresponding to degree-of-polarization measurements of + or - 0.1 percent. Faint-object accuracy, dependent on photoelectron statistics and hence on observation time, is calculated to be one percent in each 100-A-wide spectral band for a 20-min observation of an AO star with V = 15th magnitude.

Allen, R. G.↗