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All sourcesNASA NTRSDOE OSTI
NASA NTRS2009

Reliability Analysis of Systems Subject to First-Passage Failure

An obvious goal of reliability analysis is the avoidance of system failure. However, it is generally recognized that it is often not feasible to design a practical or useful system for which failure is impossible. Thus it is necessary to use techniques that estimate the likelihood of failure based on modeling the uncertainty about such items as the demands on and capacities of various elements in the system. This usually involves the use of probability theory, and a design is considered acceptable if it has a sufficiently small probability of failure. This report contains findings of analyses of systems subject to first-passage failure.

Lutes, Loren D.↗
NASA NTRS1994

TDRS orbit determination by radio interferometry

In support of a NASA study on the application of radio interferometry to satellite orbit determination, MITRE developed a simulation tool for assessing interferometry tracking accuracy. The Orbit Determination Accuracy Estimator (ODAE) models the general batch maximum likelihood orbit determination algorithms of the Goddard Trajectory Determination System (GTDS) with the group and phase delay measurements from radio interferometry. ODAE models the statistical properties of tracking error sources, including inherent observable imprecision, atmospheric delays, clock offsets, station location uncertainty, and measurement biases, and through Monte Carlo simulation, ODAE calculates the statistical properties of errors in the predicted satellites state vector. This paper presents results from ODAE application to orbit determination of the Tracking and Data Relay Satellite (TDRS) by radio interferometry. Conclusions about optimal ground station locations for interferometric tracking of TDRS are presented, along with a discussion of operational advantages of radio interferometry.

Pavloff, Michael S.↗
NASA NTRS1994

Application of a Monte Carlo accuracy assessment tool to TDRS and GPS

In support of a NASA study on the application of radio interferometry to satellite orbit determination, MITRE developed a simulation tool for assessing interferometric tracking accuracy. Initially, the tool was applied to the problem of determining optimal interferometric station siting for orbit determination of the Tracking and Data Relay Satellite (TDRS). Subsequently, the Orbit Determination Accuracy Estimator (ODAE) was expanded to model the general batch maximum likelihood orbit determination algorithms of the Goddard Trajectory Determination System (GTDS) with measurement types including not only group and phase delay from radio interferometry, but also range, range rate, angular measurements, and satellite-to-satellite measurements. The user of ODAE specifies the statistical properties of error sources, including inherent observable imprecision, atmospheric delays, station location uncertainty, and measurement biases. Upon Monte Carlo simulation of the orbit determination process, ODAE calculates the statistical properties of the error in the satellite state vector and any other parameters for which a solution was obtained in the orbit determination. This paper presents results from ODAE application to two different problems: (1)determination of optimal geometry for interferometirc tracking of TDRS, and (2) expected orbit determination accuracy for Global Positioning System (GPS) tracking of low-earth orbit (LEO) satellites. Conclusions about optimal ground station locations for TDRS orbit determination by radio interferometry are presented, and the feasibility of GPS-based tracking for IRIDIUM, a LEO mobile satellite communications (MOBILSATCOM) system, is demonstrated.

Pavloff, Michael S.↗
NASA NTRSDate not supplied

Sampling Functions from Gaussian Processes and Structured Covariance Gaussian Networks

When learning aerodynamic models from data, it is critical to incorporate estimates of model uncertainty. This motivates the design of probabilistic aerodynamic databases which can be sampled to generate physically and statistically plausible aerodynamic models. In this talk we discuss how to sample deterministic functions from two different kinds of probabilistic models and demonstrate their use. First, Gaussian Process Regressors (GPRs) are a widely used probabilistic kernel-based model which can be thought of as Gaussian distributions over functions. GPRs are generally trained by maximizing the marginal likelihood of seeing the training data over the kernel parameter space. Sample functions are easily generated by drawing points from the Gaussian distribution at desired input points. However, when the points are not known ahead of time, the classical sampling approach is not possible since successive function samples will generate different function realizations. We present an approach for sampling consistent function evaluations from a GPR over multiple samples. Second, we describe a neural network architecture which learns a conditional Gaussian distribution by maximizing the marginal likelihood at each point in the input space. We then discuss and compare several options for generating sample functions which match this distribution. Finally, we demonstrate the use of these probabilistic aerodynamic models in an atmospheric reentry simulation.

Gaussian process regression↗
NASA NTRS1995

Multiparameter linear least-squares fitting to Poisson data one count at a time

A standard problem in gamma-ray astronomy data analysis is the decomposition of a set of observed counts, described by Poisson statistics, according to a given multicomponent linear model, with underlying physical count rates or fluxes which are to be estimated from the data. Despite its conceptual simplicity, the linear least-squares (LLSQ) method for solving this problem has generally been limited to situations in which the number n(sub i) of counts in each bin i is not too small, conventionally more than 5-30. It seems to be widely believed that the failure of the LLSQ method for small counts is due to the failure of the Poisson distribution to be even approximately normal for small numbers. The cause is more accurately the strong anticorrelation between the data and the wieghts w(sub i) in the weighted LLSQ method when square root of n(sub i) instead of square root of bar-n(sub i) is used to approximate the uncertainties, sigma(sub i), in the data, where bar-n(sub i) = E(n(sub i)), the expected value of N(sub i). We show in an appendix that, avoiding this approximation, the correct equations for the Poisson LLSQ (PLLSQ) problems are actually identical to those for the maximum likelihood estimate using the exact Poisson distribution. We apply the method to solve a problem in high-resolution gamma-ray spectroscopy for the JPL High-Resolution Gamma-Ray Spectrometer flown on HEAO 3. Systematic error in subtracting the strong, highly variable background encountered in the low-energy gamma-ray region can be significantly reduced by closely pairing source and background data in short segments. Significant results can be built up by weighted averaging of the net fluxes obtained from the subtraction of many individual source/background pairs. Extension of the approach to complex situations, with multiple cosmic sources and realistic background parameterizations, requires a means of efficiently fitting to data from single scans in the narrow (approximately = 1.2 keV, HEAO 3) energy channels of a Ge spectrometer, where the expected number of counts obtained per scan may be very low. Such an analysis system is discussed and compared to the method previously used.

Wheaton, Wm. A.↗
NASA NTRS1996

Uncertainty and Intelligence in Computational Stochastic Mechanics

Classical structural reliability assessment techniques are based on precise and crisp (sharp) definitions of failure and non-failure (survival) of a structure in meeting a set of strength, function and serviceability criteria. These definitions are provided in the form of performance functions and limit state equations. Thus, the criteria provide a dichotomous definition of what real physical situations represent, in the form of abrupt change from structural survival to failure. However, based on observing the failure and survival of real structures according to the serviceability and strength criteria, the transition from a survival state to a failure state and from serviceability criteria to strength criteria are continuous and gradual rather than crisp and abrupt. That is, an entire spectrum of damage or failure levels (grades) is observed during the transition to total collapse. In the process, serviceability criteria are gradually violated with monotonically increasing level of violation, and progressively lead into the strength criteria violation. Classical structural reliability methods correctly and adequately include the ambiguity sources of uncertainty (physical randomness, statistical and modeling uncertainty) by varying amounts. However, they are unable to adequately incorporate the presence of a damage spectrum, and do not consider in their mathematical framework any sources of uncertainty of the vagueness type. Vagueness can be attributed to sources of fuzziness, unclearness, indistinctiveness, sharplessness and grayness; whereas ambiguity can be attributed to nonspecificity, one-to-many relations, variety, generality, diversity and divergence. Using the nomenclature of structural reliability, vagueness and ambiguity can be accounted for in the form of realistic delineation of structural damage based on subjective judgment of engineers. For situations that require decisions under uncertainty with cost/benefit objectives, the risk of failure should depend on the underlying level of damage and the uncertainties associated with its definition. A mathematical model for structural reliability assessment that includes both ambiguity and vagueness types of uncertainty was suggested to result in the likelihood of failure over a damage spectrum. The resulting structural reliability estimates properly represent the continuous transition from serviceability to strength limit states over the ultimate time exposure of the structure. In this section, a structural reliability assessment method based on a fuzzy definition of failure is suggested to meet these practical needs. A failure definition can be developed to indicate the relationship between failure level and structural response. In this fuzzy model, a subjective index is introduced to represent all levels of damage (or failure). This index can be interpreted as either a measure of failure level or a measure of a degree of belief in the occurrence of some performance condition (e.g., failure). The index allows expressing the transition state between complete survival and complete failure for some structural response based on subjective evaluation and judgment.

Ayyub, Bilal M.↗
NASA NTRS2002

The New NASA Orbital Debris Engineering Model ORDEM2000

The NASA Orbital Debris Program Office at Johnson Space Center has developed a new computer-based orbital debris engineering model, ORDEM2000, which describes the orbital debris environment in the low Earth orbit region between 200 and 2000 km altitude. The model is appropriate for those engineering solutions requiring knowledge and estimates of the orbital debris environment (debris spatial density, flux, etc.). ORDEM2000 can also be used as a benchmark for ground-based debris measurements and observations. We incorporated a large set of observational data, covering the object size range from 10 mm to 10 m, into the ORDEM2000 debris database, utilizing a maximum likelihood estimator to convert observations into debris population probability distribution functions. These functions then form the basis of debris populations. We developed a finite element model to process the debris populations to form the debris environment. A more capable input and output structure and a user-friendly graphical user interface are also implemented in the model. ORDEM2000 has been subjected to a significant verification and validation effort. This document describes ORDEM2000, which supersedes the previous model, ORDEM96. The availability of new sensor and in situ data, as well as new analytical techniques, has enabled the construction of this new model. Section 1 describes the general requirements and scope of an engineering model. Data analyses and the theoretical formulation of the model are described in Sections 2 and 3. Section 4 describes the verification and validation effort and the sensitivity and uncertainty analyses. Finally, Section 5 describes the graphical user interface, software installation, and test cases for the user.

Liou, Jer-Chyi↗
NASA NTRS2004

On Bayesian Inductive Inference & Predictive Estimation

We investigate Bayesian inference and the Principle of Maximum Entropy (PME) as methods for doing inference under uncertainty. This investigation is primarily through concrete examples that have been previously investigated in the literature. We find that it is possible to do Bayesian inference and PME inference using the same information, despite claims to the contrary, but that the results are not directly comparable. This is because Bayesian inference yields a probability density function (pdf) over the unknown model parameters, whereas PME yields point estimates. If mean estimates are extracted from the Bayesian pdfs, the resulting parameter estimates can differ radically from the PME values and also from the Maximum Likelihood values. We conclude that these differences are due to the Bayesian inference not assuming anything beyond the given prior probabilities and the data, whereas PME implicitly assumes that the given constraints are the only constraints that are operating. Since this assumption can be wrong, PME values may have to be revised when subsequent data shows evidence for more constraints. The entropy concentration previously "proved" by E. T. Jaynes is shown to be in error. Further, we show that PME is a generalized form of independence assumption, and so can be a very powerful method of inference when the variables being investigated are largely independent of each other.

Cheeseman, Peter↗
NASA NTRS1986

The 10Be contents of SNC meteorites

Several authors have explored the possibility that the Shergottites, Nakhlites, and Chassigny (SNC) came from Mars. The spallogenic gas contents of the SNC meteorites have been used to: constrain the sizes of the SNC's during the last few million years; to establish groupings independent of the geochemical ones; and to estimate the likelihood of certain entries in the catalog of all conceivable passages from Mars to Earth. The particular shielding dependence of Be-10 makes the isotope a good probe of the irradiation conditions experienced by the SNC meteorites. The Be-10 contents of nine members of the group were measured using the technique of accelerator mass spectrometry. The Be-10 contents of Nakhla, Governador Valadares, Chassigny, and probably Lafayette, about 20 dpm/kg, exceed the values expected from irradiation of the surface of a large body. The Be-10 data therfore do not support scenario III of Bogard et al., one in which most of the Be-10 in the SNC meteorites would have formed on the Martian surface; they resemble rather the Be-10 contents found in many ordinary chondrites subjected to 4 Pi exposures. The uncertainties of the Be-10 contents lead to appreciable errors in the Be-10 ages, t(1) = -1/lambda ln(1 Be-10/Be-10). Nonetheless, the Be-10 ages are consistent with the Ne-21 ages calculated assuming conventional, small-body production rates and short terrestrial ages for the finds. It is believed that this concordance strengthens the case for at least 3 different irradiation ages for the SNC meteorites. Given the similar half-thicknesses of the Be-10 and Ne-21 production rates, the ratios of the Be-10 and Ne-21 contents do not appear consistent with common ages for any of the groups. In view of the general agreement between the Be-10 and Ne-21 ages it does not seem useful at this time to construct multiple-stage irradiation histories for the SNC meteorites.

Pal, D. K.↗
NASA NTRS1993

Certain and possible rules for decision making using rough set theory extended to fuzzy sets

Uncertainty may be caused by the ambiguity in the terms used to describe a specific situation. It may also be caused by skepticism of rules used to describe a course of action or by missing and/or erroneous data. To deal with uncertainty, techniques other than classical logic need to be developed. Although, statistics may be the best tool available for handling likelihood, it is not always adequate for dealing with knowledge acquisition under uncertainty. Inadequacies caused by estimating probabilities in statistical processes can be alleviated through use of the Dempster-Shafer theory of evidence. Fuzzy set theory is another tool used to deal with uncertainty where ambiguous terms are present. Other methods include rough sets, the theory of endorsements and nonmonotonic logic. J. Grzymala-Busse has defined the concept of lower and upper approximation of a (crisp) set and has used that concept to extract rules from a set of examples. We will define the fuzzy analogs of lower and upper approximations and use these to obtain certain and possible rules from a set of examples where the data is fuzzy. Central to these concepts will be the idea of the degree to which a fuzzy set A is contained in another fuzzy set B, and the degree of intersection of a set A with set B. These concepts will also give meaning to the statement; A implies B. The two meanings will be: (1) if x is certainly in A then it is certainly in B, and (2) if x is possibly in A then it is possibly in B. Next, classification will be looked at and it will be shown that if a classification will be looked at and it will be shown that if a classification is well externally definable then it is well internally definable, and if it is poorly externally definable then it is poorly internally definable, thus generalizing a result of Grzymala-Busse. Finally, some ideas of how to define consensus and group options to form clusters of rules will be given.

Dekorvin, Andre↗
NASA NTRS2020

Spectral Range Within Global aCDOM(440) Algorithms for Oceanic, Coastal, and Inland Waters with Application to Airborne Measurements

The optically active component of dissolved organic material in aquatic ecosystems, or colored dissolved organic matter (CDOM), is represented by the coefficient of absorption due to the dissolved aquatic constituents at 440 nm, aCDOM(440). Remote sensing of aCDOM(440) enables characterization of ecosystem processes and aids in retrieval of chlorophyll a, a proxy for phytoplankton biomass. Spectrally adjacent band-ratio domains, e.g., blue to green, have previously been applied for remote sensing of aCDOM(440) in coastal and oceanic waters with similar results compared to more complex semi-analytical algorithms. Estimation of aCDOM(440) from ratios of the most spectrally separated ocean color wavebands (end members), e.g., ultraviolet (UV) to near-infrared (NIR), termed end-member analysis (EMA), has previously been shown to increase the accuracy of global aCDOM(440) retrievals from in-water observations of diffuse attenuation and to enable a unified algorithmic perspective without requiring regional adjustment of internal bio-optical parameters. EMA of above-water observations is evaluated herein, with a focus on coastal and inland waters in which increasing optical complexity and likelihood of bottom reflectance challenge the oceanic algorithms developed for deep and optically simple (case-1) waters. Analysis herein of three independent, in situ, bio-optical datasets indicates significant correlation between aCDOM(440) and end-member band ratios (next-generation 320 and 780 nm or legacy 412 and 670 nm ratios) with a coefficient of determination, R2, of 0.87 (log-scale) or higher based on a dataset spanning the dynamic range of global, conservative water bodies. For applicable wavelengths, EMA algorithms are shown to agree with case-1 relationships and to produce consistent log-scale uncertainties across more than three orders of magnitude in aCDOM(440) values (0.001–2.305 m􀀀1). EMA using UV and NIR wavelengths (320 and 780 nm) is applied to low-altitude airborne observations and satisfies 25% uncertainty based on unbiased percent differences (UPDs) within each of three dissimilar match-up sites ranging in aCDOM(440) from 0.02–0.57 m􀀀1. Results demonstrate that EMA is a useful and robust approach for the remote sensing of aCDOM(440) in coastal and inland waters, which are generally shallower, contain more optically complex environments, and span a greater range in aCDOM(440) than oceanic waters.

CDOM↗
NASA NTRS2014

The Development of a Long-Term, Continually Updated Global Solar Resource at 10 km Resolution: Preliminary Results From Test Processing and Continuing Plans

Background: Considering the likelihood of global climatic weather pattern changes and the global competition for energy resources, there is an increasing need to provide improved and continuously updated global Earth surface solar resource information. Toward this end, a project was funded under the NASA Applied Science program involving the National Aeronautics and Space Administration (NASA) Langley Research Center (LaRC), National Renewable Energy Laboratory (NREL), the State University of New York/Albany (SUNY) and the NOAA National Climatic Data Center (NCDC) to provide NREL with a global long-term advanced global solar mapping production system for improved depiction of historical solar resources and variability and to provide a mechanism for continual updates of solar resource information. This new production system is made possible by the efforts of NOAA and NASA to completely reprocess the International Satellite Cloud Climatology Project (ISCCP) data set that provides satellite visible and infrared radiances together with retrieved cloud and surface properties on a 3-hourly basis beginning from July 1983. The old version of the ISCCP data provided this information for all the world TMs available geosynchronous satellite systems and NOAA TMs AVHRR data sets at a 30 km effective resolution. This new version aims to provide a new and improved satellite calibration at an effective 10 km resolution. Thus, working with SUNY, NASA will develop and test an improved production system that will enable NREL to continually update the Earth TM solar resource. Objective and Methods: In this presentation, we provide a general overview of this project together with samples of the new solar irradiance mapped data products and comparisons to surface measurements at various locations across the world. An assessment of the solar resource values relative to calibration uncertainty and assumptions are presented. Errors resulting assumptions in snow cover and background aerosol amount are described. These uncertainties and the statistics of the agreement between the measurements and new satellite estimates are also reviewed and compared to other solar data sets. Findings and Conclusions: Preliminary results show that insolation values show an overall small bias (less than 1%) with a RMS of 25% relative to surface measurements. Exceptions at certain locations were found and will be discussed relative to the uncertainties identified above. Lastly, we will identify the next steps in the development and improvement of this production system including some accuracy goals in preparation for ultimate delivery to NREL.

Stackhouse, P.↗