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NASA NTRS1996

Cascade Error Projection: A Learning Algorithm for Hardware Implementation

In this paper, we workout a detailed mathematical analysis for a new learning algorithm termed Cascade Error Projection (CEP) and a general learning frame work. This frame work can be used to obtain the cascade correlation learning algorithm by choosing a particular set of parameters. Furthermore, CEP learning algorithm is operated only on one layer, whereas the other set of weights can be calculated deterministically. In association with the dynamical stepsize change concept to convert the weight update from infinite space into a finite space, the relation between the current stepsize and the previous energy level is also given and the estimation procedure for optimal stepsize is used for validation of our proposed technique. The weight values of zero are used for starting the learning for every layer, and a single hidden unit is applied instead of using a pool of candidate hidden units similar to cascade correlation scheme. Therefore, simplicity in hardware implementation is also obtained. Furthermore, this analysis allows us to select from other methods (such as the conjugate gradient descent or the Newton's second order) one of which will be a good candidate for the learning technique. The choice of learning technique depends on the constraints of the problem (e.g., speed, performance, and hardware implementation); one technique may be more suitable than others. Moreover, for a discrete weight space, the theoretical analysis presents the capability of learning with limited weight quantization. Finally, 5- to 8-bit parity and chaotic time series prediction problems are investigated; the simulation results demonstrate that 4-bit or more weight quantization is sufficient for learning neural network using CEP. In addition, it is demonstrated that this technique is able to compensate for less bit weight resolution by incorporating additional hidden units. However, generation result may suffer somewhat with lower bit weight quantization.

Duong, Tuan A.↗

NASA NTRS1973

Investigation of empirical damping laws for the space shuttle

An analysis of dynamic test data from vibration testing of a number of aerospace vehicles was made to develop an empirical structural damping law. A systematic attempt was made to fit dissipated energy/cycle to combinations of all dynamic variables. The best-fit laws for bending, torsion, and longitudinal motion are given, with error bounds. A discussion and estimate are made of error sources. Programs are developed for predicting equivalent linear structural damping coefficients and finding the response of nonlinearly damped structures.

Bernstein, E. L.↗

NASA NTRS1973

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

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

Davis, J. W.↗

NASA NTRS1974

Parameter estimation for terrain modeling from gradient data

A method is developed for modeling terrain surfaces for use on an unmanned Martian roving vehicle. The modeling procedure employs a two-step process which uses gradient as well as height data in order to improve the accuracy of the model's gradient. Least square approximation is used in order to stochastically determine the parameters which describe the modeled surface. A complete error analysis of the modeling procedure is included which determines the effect of instrumental measurement errors on the model's accuracy. Computer simulation is used as a means of testing the entire modeling process which includes the acquisition of data points, the two-step modeling process and the error analysis. Finally, to illustrate the procedure, a numerical example is included.

Dangelo, K. R.↗

NASA NTRS1994

An HP Adaptive Discontinuous Galerkin Method for Hyperbolic Conservation Laws

This dissertation addresses various issues for model classes of hyperbolic conservation laws. The basic approach developed in this work employs a new family of adaptive, hp-version, finite element methods based on a special discontinuous Galerkin formulation for hyperbolic problems. The discontinuous Galerkin formulation admits high-order local approximations on domains of quite general geometry, while providing a natural framework for finite element approximations and for theoretical developments. The use of hp-versions of the finite element method makes possible exponentially convergent schemes with very high accuracies in certain cases; the use of adaptive hp-schemes allows h-refinement in regions of low regularity and p-enrichment to deliver high accuracy, while keeping problem sizes manageable and dramatically smaller than many conventional approaches. The use of discontinuous Galerkin methods is uncommon in applications, but the methods rest on a reasonable mathematical basis for low-order cases and has local approximation features that can be exploited to produce very efficient schemes, especially in a parallel, multiprocessor environment. The place of this work is to first and primarily focus on a model class of linear hyperbolic conservation laws for which concrete mathematical results, methodologies, error estimates, convergence criteria, and parallel adaptive strategies can be developed, and to then briefly explore some extensions to more general cases. Next, we provide preliminaries to the study and a review of some aspects of the theory of hyperbolic conservation laws. We also provide a review of relevant literature on this subject and on the numerical analysis of these types of problems.

Bey, Kim S.↗

NASA NTRS1989

Maximum likelihood techniques in QELS

A framework for the analysis of Quasi Elastic Light Scattering (QELS) experiments designed to be used in microgravity environment is derived. Example calculations of the type to be used to design the QELS system are given. The framework for the analysis is based on the concepts of parameter estimation typified by Maximum Likelihood Estimation methods. These methods not only serve as the template for parameter estimation algorithms, but can also be used for optimal design of the experiments. Optimal design of experiments is facilitated by the fact that these methods not only give procedures for parameter estimation, but also estimates of the errors associated with the parameter estimation.

Edwards, Robert V.↗

NASA NTRS2002

Space Radiation Cancer Risk Projections for Exploration Missions: Uncertainty Reduction and Mitigation

In this paper we discuss expected lifetime excess cancer risks for astronauts returning from exploration class missions. For the first time we make a quantitative assessment of uncertainties in cancer risk projections for space radiation exposures. Late effects from the high charge and energy (HZE) ions present in the galactic cosmic rays including cancer and the poorly understood risks to the central nervous system constitute the major risks. Methods used to project risk in low Earth orbit are seen as highly uncertain for projecting risks on exploration missions because of the limited radiobiology data available for estimating HZE ion risks. Cancer risk projections are described as a product of many biological and physical factors, each of which has a differential range of uncertainty due to lack of data and knowledge. Monte-Carlo sampling from subjective error distributions represents the lack of knowledge in each factor to quantify risk projection overall uncertainty. Cancer risk analysis is applied to several exploration mission scenarios. At solar minimum, the number of days in space where career risk of less than the limiting 3% excess cancer mortality can be assured at a 95% confidence level is found to be only of the order of 100 days.

Cucinotta, Francis↗

NASA NTRS2012

3D Drop Size Distribution Extrapolation Algorithm Using a Single Disdrometer

Determining the Z-R relationship (where Z is the radar reflectivity factor and R is rainfall rate) from disdrometer data has been and is a common goal of cloud physicists and radar meteorology researchers. The usefulness of this quantity has traditionally been limited since radar represents a volume measurement, while a disdrometer corresponds to a point measurement. To solve that problem, a 3D-DSD (drop-size distribution) method of determining an equivalent 3D Z-R was developed at the University of Central Florida and tested at the Kennedy Space Center, FL. Unfortunately, that method required a minimum of three disdrometers clustered together within a microscale network (.1-km separation). Since most commercial disdrometers used by the radar meteorology/cloud physics community are high-cost instruments, three disdrometers located within a microscale area is generally not a practical strategy due to the limitations of these kinds of research budgets. A relatively simple modification to the 3D-DSD algorithm provides an estimate of the 3D-DSD and therefore, a 3D Z-R measurement using a single disdrometer. The basis of the horizontal extrapolation is mass conservation of a drop size increment, employing the mass conservation equation. For vertical extrapolation, convolution of a drop size increment using raindrop terminal velocity is used. Together, these two independent extrapolation techniques provide a complete 3DDSD estimate in a volume around and above a single disdrometer. The estimation error is lowest along a vertical plane intersecting the disdrometer position in the direction of wind advection. This work demonstrates that multiple sensors are not required for successful implementation of the 3D interpolation/extrapolation algorithm. This is a great benefit since it is seldom that multiple sensors in the required spatial arrangement are available for this type of analysis. The original software (developed at the University of Central Florida, 1998.- 2000) has also been modified to read standardized disdrometer data format (Joss-Waldvogel format). Other modifications to the software involve accounting for vertical ambient wind motion, as well as evaporation of the raindrop during its flight time.

Lane, John↗

NASA NTRS2013

Wald Sequential Probability Ratio Test for Analysis of Orbital Conjunction Data

We propose a Wald Sequential Probability Ratio Test for analysis of commonly available predictions associated with spacecraft conjunctions. Such predictions generally consist of a relative state and relative state error covariance at the time of closest approach, under the assumption that prediction errors are Gaussian. We show that under these circumstances, the likelihood ratio of the Wald test reduces to an especially simple form, involving the current best estimate of collision probability, and a similar estimate of collision probability that is based on prior assumptions about the likelihood of collision.

Carpenter, J. Russell↗

NASA NTRS1991

An evaluation of water vapor radiometer data for calibration of the wet path delay in very long baseline interferometry experiments

The internal consistency of the baseline-length measurements derived from analysis of several independent VLBI experiments is an estimate of the measurement precision. The paper investigates whether the inclusion of water vapor radiometer (WVR) data as an absolute calibration of the propagation delay due to water vapor improves the precision of VLBI baseline-length measurements. The paper analyzes 28 International Radio Interferometric Surveying runs between June 1988 and January 1989; WVR measurements were made during each session. The addition of WVR data decreased the scatter of the length measurements of the baselines by 5-10 percent. The observed reduction in the scatter of the baseline lengths is less than what is expected from the behavior of the formal errors, which suggest that the baseline-length measurement precision should improve 10-20 percent if WVR data are included in the analysis. The discrepancy between the formal errors and the baseline-length results can be explained as the consequence of systematic errors in the dry-mapping function parameters, instrumental biases in the WVR and the barometer, or both.

Kuehn, C. E.↗

NASA NTRS1975

M-071 critical data analysis

A prototype balance study was conducted on earth prior to the balance studies conducted in Skylab itself. Collected were daily dietary intake data of 6 minerals and nitrogen, and fecal and urinary outputs on each of three astronauts. Essential statistical issues show what quantities need to be estimated and establish the scope of inference associated with alternative variance estimates. The procedures for obtaining the final variability due both to errors of measurement and total error (total = measurement and biological variability) are exhibited.

Hegsted, D. M.↗

NASA NTRS1977

Attitude determination system for Seasat-A mission

The attitude determination (AD) system hardware of Seasat-A consists of two sun aspect sensors, two infrared (IR) horizon scanners, related electronics, telemetry, and science sensors. The earth horizon pulse signal sensing is accomplished by a variable thresholding method intended to self-adjust for earth radiance variations. The use of sun sensors rather than star trackers for yaw determination calls for estimation rather than measurement of yaw attitude about 50% of mission time. Features of the yaw interpolation algorithm include adaptability and automatic incorporation of time-varying confidence levels of various data sources. The performance accuracy of the AD system was assessed, where it is found that the most important error source is the variation in earth atmospheric radiance. Analysis of science instrument sensitivity to AD uncertainties was performed, and the most sensitive instrument, the scatterometer system, shows only gradual degradation of performance in the vicinity of the AD accuracy requirement.

Ohtakay, H.↗

NASA NTRS1986

Application of parameter estimation to aircraft stability and control: The output-error approach

The practical application of parameter estimation methodology to the problem of estimating aircraft stability and control derivatives from flight test data is examined. The primary purpose of the document is to present a comprehensive and unified picture of the entire parameter estimation process and its integration into a flight test program. The document concentrates on the output-error method to provide a focus for detailed examination and to allow us to give specific examples of situations that have arisen. The document first derives the aircraft equations of motion in a form suitable for application to estimation of stability and control derivatives. It then discusses the issues that arise in adapting the equations to the limitations of analysis programs, using a specific program for an example. The roles and issues relating to mass distribution data, preflight predictions, maneuver design, flight scheduling, instrumentation sensors, data acquisition systems, and data processing are then addressed. Finally, the document discusses evaluation and the use of the analysis results.

Maine, Richard E.↗

NASA NTRS1994

A new approach to estimating rainwater content by radar using propagation differential phase shift

As microwaves propagate through rain, the rate of phase change with increasing distance is different depending upon whether the transmissions are polarized horizontally or vertically. This rate of change is the so-called specific propagation differential phase shift phi(sub DP). This paper demonstrates that at several frequencies and over a wide domain the ratio of phi(sub DP) to the rainwater content W is nearly linearly related to D(sub m), the mass-weighted mean drop size. An investigation of errors indicates that this new approach is likely to yield more accurate estimates of W than the other classical reflectivity factor Z, attenuation, or polarization techniques. The most accurate estimates of W are most likely at the highest frequency considered, 13.80 GHz. In lieu of such high-frequency measurements, these somewhat esoteric results are made more concrete through an analysis of 3-GHz radar measurements collected during the Convection and Precipitation Experiment in a tropical rainstorm in Florida. Among the principal advantages of using phi(sub DP) to measure rain are that an absolute calibration of the radar is no longer required and the estimates are decoupled from measurements of the radar reflectivity factor. Consequently, temporal and spatial structures of rain estimates do not simply mimic those of the reflectivity factor, as happens for classical estimation techniques using Z.

Jameson, A. R.↗

NASA NTRS2003

A Treatment of Measurements of Heptane Droplet Combustion Aboard MSL-1

Results of measurements on the burning of free n-heptane droplets (that is, droplets without fiber supports) performed in Spacelab during the flights of the first Microgravity Science Laboratory (MSL-1) are presented. The droplet combustion occurred in oxidizing atmospheres which were at an ambient temperature within a few degrees of 300 K. A total of 34 droplets were burned in helium-oxygen atmospheres having oxygen mole fractions ranging from 20 to 50 percent, at pressures from 0.25 to 1.00 bar. In addition, four droplets were burned in air at 1.00 bar, bringing the total number of droplets for which combustion data were secured to 38; two of these four air tests were fiber-supported to facilitate comparisons with other fiber-support experiments, results of which also are given here. Initial diameters of free droplets ranged from about 1 to 4 mm. The primary data obtained were histories of droplet diameters, recorded in backlight on 35 mm film at 80 frames per second, and histories of flame diameters, inferred from emissions through a narrow-band interference filter centered at the 310 micron OH chemiluminescent ultraviolet band, recorded at 30 frames per second by a intensified-array camera. These data are reported here both in raw form and in a smoothed form with estimated error bars. In addition, summaries are presented of measured burning-rate constants, final droplet diameters, and final flame diameters. Both diffusive and radiative extinctions were exhibited under different conditions. Although some interpretations are reported and conclusions drawn concerning the combustion mechanisms, the principal intent of this report is to provide a complete, documented data set for future analysis.

Ackerman, M. D.↗

NASA NTRS2012

A Parameterized Inversion Model for Soil Moisture and Biomass from Polarimetric Backscattering Coefficients

A semi-empirical algorithm for the retrieval of soil moisture, root mean square (RMS) height and biomass from polarimetric SAR data is explained and analyzed in this paper. The algorithm is a simplification of the distorted Born model. It takes into account the physical scattering phenomenon and has three major components: volume, double-bounce and surface. This simplified model uses the three backscattering coefficients ( sigma HH, sigma HV and sigma vv) at low-frequency (P-band). The inversion process uses the Levenberg-Marquardt non-linear least-squares method to estimate the structural parameters. The estimation process is entirely explained in this paper, from initialization of the unknowns to retrievals. A sensitivity analysis is also done where the initial values in the inversion process are varying randomly. The results show that the inversion process is not really sensitive to initial values and a major part of the retrievals has a root-mean-square error lower than 5% for soil moisture, 24 Mg/ha for biomass and 0.49 cm for roughness, considering a soil moisture of 40%, roughness equal to 3cm and biomass varying from 0 to 500 Mg/ha with a mean of 161 Mg/ha

soil moisture↗

NASA NTRS1978

Secondary error analysis: The evaluation of analyst dot labeling

The author has identified the following significant results. From this examination of 25 test segments using Al labeling and ground truth labeling, the PCC on type 1 dots was found to be signficantly better for both types of ground truth labeled procedures than the PCC obtained using Al labeling. No significant difference in the PCC was found for type 2 dots. However, in all three treatments, the type 2 dots included pixels which fell on boundaries or were mixed pixels. This accounted for all PCC2 values being equally low. The proportion estimates achieved in these classifications showed no significant differences between procedures.

Havens, K. A.↗

NASA NTRS1970

Analysis of remote sensing data for evaluation of vegetation resources

Research has centered around: (1) completion of a study on the use of remote sensing techniques as an aid to multiple use management; (2) determination of the information transfer at various image resolution levels for wildland areas; and (3) determination of the value of small scale multiband, multidate photography for the analysis of vegetation resources. In addition, a substantial effort was made to upgrade the automatic image classification and spectral signature acquisition capabilities of the laboratory. It was found that: (1) Remote sensing techniques should be useful in multiple use management to provide a first-cut analysis of an area. (2) Imagery with 400-500 feet ground resolvable distance (GRD), such as that expected from ERTS-1, should allow discriminations to be made between woody vegetation, grassland, and water bodies with approximately 80% accuracy. (3) Barley and wheat acreages in Maricopa County, Arizona could be estimated with acceptable accuracies using small scale multiband, multidate photography. Sampling errors for acreages of wheat, barley, small grains (wheat and barley combined), and all cropland were 13%, 11%, 8% and 3% respectively.

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