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Results for “Likelihood Function”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS2018

Random Variables with Moment-Matching Staircase Density Functions

This paper proposes a family of random variables for uncertainty modeling. The variables of interest have a bounded support set, and prescribed values for the first four moments. We present the feasibility conditions for the existence of any of such variables, and propose a class of variables that conforms to such constraints. This class is called staircase because the density of its members is a piecewise constant function. Convex optimization is used to calculate their distributions according to several optimality criteria, including maximal entropy and maximal log-likelihood. The flexibility and efficiency of staircases enable modeling phenomena having a possibly skewed and/or multimodal response at a low computational cost. Furthermore, we provide a means to account for the uncertainty in the distribution caused by estimating staircases from data. These ideas are illustrated by generating empirical staircase predictor models. We consider the case in which the predictor matches the sample moments exactly (a setting applicable to large datasets), as well as the case in which the predictor accounts for the sampling error in such moments (a setting applicable to sparse datasets). A predictor model for the dynamics of an aeroelastic airfoil subject to flutter instability is used as an example. The resulting predictor not only describes the system's response accurately, but also enables carrying out a risk analysis for safe flight.

Luis G. Crespo↗
NASA NTRS1995

Gaussian statistics of the cosmic microwave background: Correlation of temperature extrema in the COBE DMR two-year sky maps

We use the two-point correlation function of the extrema points (peaks and valleys) in the Cosmic Background Explorer (COBE) Differential Microwave Radiometers (DMR) 2 year sky maps as a test for non-Gaussian temperature distribution in the cosmic microwave background anisotropy. A maximum-likelihood analysis compares the DMR data to n = 1 toy models whose random-phase spherical harmonic components a(sub lm) are drawn from either Gaussian, chi-square, or log-normal parent populations. The likelihood of the 53 GHz (A+B)/2 data is greatest for the exact Gaussian model. There is less than 10% chance that the non-Gaussian models tested describe the DMR data, limited primarily by type II errors in the statistical inference. The extrema correlation function is a stronger test for this class of non-Gaussian models than topological statistics such as the genus.

Kogut, A.↗
NASA NTRS1983

Classification by thresholding

A procedure is given which substantially reduces the processing time needed to perform maximum likelihood classification on large data sets. The given method uses a set of fixed thresholds which, if exceeded by one probability density function, makes it unnecessary to evaluate a competing density function. Proofs are given of the existence and optimality of these thresholds for the class of continuous, unimodal, and quasi-concave density functions (which includes the multivariable normal), and a method for computing the thresholds is provided for the specific case of multivariate normal densities. An example with remote sensing data consisting of some 20,000 observations of four-dimensional data from nine ground-cover classes shows that by using thresholds, one could cut the processing time almost in half.

Feiveson, A. H.↗
NASA NTRS1983

An improved push-pull voltage fed converter using a tapped output-filter inductor

A new concept of using a tapped output-filter inductor and an auxiliary commutating diode to reduce the likelihood of transformer core saturation in a push-pull, voltage-fed converter is presented. The linearized circuit model and transfer functions are derived with a hybrid approach using both state-space and circuit averaging. Operation of the new converter - including parasitic effects - is discussed, and a design equation for inductor tap ratio is established. It is predicted and experimentally confirmed that the new converter has more symmetrical transformer core operation, and the potential exits for lower transistor turnon current and reduced transistor voltage stress. These benefits reduce switching loss and enhance transistor reliability.

Wester, G. W.↗
NASA NTRS1987

Aircraft parameter estimation

The aircraft parameter estimation problem is used to illustrate the utility of parameter estimation, which applies to many engineering and scientific fields. Maximum likelihood estimation has been used to extract stability and control derivatives from flight data for many years. This paper presents some of the basic concepts of aircraft parameter estimation and briefly surveys the literature in the field. The maximum likelihood estimator is discussed, and the basic concepts of minimization and estimation are examined for a simple simulated aircraft example. The cost functions that are to be minimized during estimation are defined and discussed. Graphic representations of the cost functions are given to illustrate the minimization process. Finally, the basic concepts are generalized, and estimation from flight data is discussed. Some of the major conclusions for the simulated example are also developed for the analysis of flight data from the F-14, highly maneuverable aircraft technology (HiMAT), and space shuttle vehicles.

Kenneth W Iliff↗
NASA NTRS1987

Aircraft parameter estimation

The aircraft parameter estimation problem is used to illustrate the utility of parameter estimation, which applies to many engineering and scientific fields. Maximum likelihood estimation has been used to extract stability and control derivatives from flight data for many years. This paper presents some of the basic concepts of aircraft parameter estimation and briefly surveys the literature in the field. The maximum likelihood estimator is discussed, and the basic concepts of minimization and estimation are examined for a simple simulated aircraft example. The cost functions that are to be minimized during estimation are defined and discussed. Graphic representations of the cost functions are given to illustrate the minimization process. Finally, the basic concepts are generalized, and estimation from flight data is discussed. Some of the major conclusions for the simulated examples are also developed for the analysis of flight data from the F-14, highly maneuverable aircraft technology (HiMAT), and Space Shuttle vehicles.

Iliff, Kenneth W.↗
NASA NTRS2002

Transient Mixing Driven by Buoyancy Flows

Mixing driven by buoyancy-induced flows is of particular interest to microgravity processes, as the body force that governs the intensity of flow fields can be directly controlled. We consider a model experimental system to explore the dynamics of mixing which employs two miscible liquids inside a cavity separated initially by a divider. The two liquids are oriented vertically inside a rectangular cavity with constant width and height, and varying depths to span the range of a Hele-Shaw cell to a 3-[) configuration. The two miscible liquids can be sufficiently diluted and died, for example water and deuterium oxide, such that a distinct interface exists across the divider. The transient mixing characteristic of the two fluids is addressed by following the Lagrangian history of the interface for various aspect ratios in the z-plane (depth variation) as well as a range of pulling velocities of the divider. The mixing characteristics of the two fluids are quantified from measurement of the length stretch of the interface and its flow field using respectively image processing techniques and Particle Imaging Velocimetry. Scaling analysis shows that the length stretch depends on four governing parameters, namely the Grashof number (Gr), Schmidt number (Sc), aspect ratio (Ar), and Reynolds number (Re). Variation of the Schmidt number is taken into account through thermophysical property variation. Thus our problem reduces to a codimension three bifurcation in parametric space for Gr, Ar, and Re. Our experimental results show that for Gr on the order of 106 and a nominal cavity aspect ratio Ar = 0.2, the net effect of removal of the divider and the overwhelming buoyancy force causes an overturning motion which stretches and folds the interface to produce ml internal breakwave. The structure of the breakwave is similar to the ubiquitous Rayleigh-Taylor instability morphology. The breakwave is dissipated either through internal or wall collision depending on the impulsive velocity of the divider as prescribed by the Reynolds number. The decay of the collision event occurs through sloshing oscillations over a short time scale. The two fluids then become stably stratified with a diffusive band at the interface indicating local mass transport. The local bifurcation of the internal breakwave is investigated as a function of aspect ratio. Results show that for narrow cavities on the order of 2mm (Ar = 0.04) folding does not occur, the interface only stretches. As the cavity size increases folding occurs through a supercritical bifurcation. Insight into the mechanism of folding is obtained from measurement of the flow field which shows that in the neighborhood of the folding event, there exists hyperbolic points caused by multiple vortex interactions. The global length stretch of the interface as a function of time is nearly Gaussian; calculations of finite-time Liapunov exponents as well as construction of horseshoe maps indicate the likelihood of a chaotic transient.

W.M.B. Duval↗
NASA NTRS1976

Convolutional code performance in the Rician fading channel

The performance of short constraint length convolutional codes in conjunction with binary phase-shift keyed (BPSK) modulation and Viterbi maximum likelihood decoding on the classical Rician fading channel is examined in detail. Primary interest is in the bit error probability performance as a function of E sub b/N sub 0 parameterized by the fading channel parameters. Fairly general upper bounds on bit error probability performance in the presence of fading are obtained and compared with simulation results in the two extremes of zero channel memory and infinite channel memory. The efficacy of simple block interleaving in combating the memory of the channel is thoroughly explored. Results include the effects of fading on tracking loop performance and the subsequent impact on overall coded system performance. The approach is analytical where possible; otherwise resort is made to digital computer simulation.

Modestino, J. W.↗
NASA NTRS1989

Identification of space shuttle main engine dynamics

System identification techniques are used to represent the dynamic behavior of the Space Shuttle Main Engine. The transfer function matrices of the linearized models of both the closed loop and the open loop system are obtained by using the recursive maximum likelihood method.

Duyar, Ahmet↗
NASA NTRS1989

Identification of Space Shuttle Main Engine dynamics

System identification techniques are used to represent the dynamic behavior of the Space Shuttle Main Engine. The transfer function matrices of the linearized models of both the closed loop and the open loop system are obtained by using the recursive maximum likelihood method.

Duyar, Ahmet↗
NASA NTRS2022

Planetary protection assessment of radioisotope thermoelectric generator (RTG)-powered landed missions to ocean worlds: application to Enceladus

Landed missions to icy worlds with a subsurface liquid water ocean must meet planetary protection requirements, and ensure a sufficiently small likelihood of any microorganism-bearing part of the landed element reaching the ocean. A higher bound on this likelihood is set by the potential for radioisotope thermoelectric generator (RTG) power sources, the hottest possible landed element, to melt through the ice shell and reach the ocean. Here, we quantify this potential as a function of three key parameters: surface temperature, ice shell thickness (i.e., heat flux through the shell), and thickness of a porous (insulating) snow or regolith cover. Although the model we describe can be applied to any ocean world, we present results in the context of a landed mission concept to the south polar terrain of Saturn’s moon Enceladus. In this particular context, we discuss planetary protection considerations for landing site selection. The likelihood of forward microbial contamination of Enceladus’ ocean by an RTG-powered landed mission can be made sufficiently low to not undermine compliance with planetary protection policy.

Marc Neveu↗
NASA NTRS1972

System identification computational considerations.

System identification methods may be accurately characterized as inverse computational problems. Three approaches to the computational problem are considered. Equation error methods are based on regression analysis techniques. Attention is given to the maximum conditional likelihood estimate and the maximum unconditional likelihood (Bayesian) estimate. Gradient dependent algorithms for solving the minimization problems are discussed, taking into account Gaussian methods, quadratic model methods, and the homogeneous function model method of Jacobson and Oksman. Some advanced methods are also examined.

Bowles, R. L.↗
NASA NTRS2016

Developing Atmospheric Retrieval Methods for Direct Imaging Spectroscopy of Gas Giants in Reflected Light I: Methane Abundances and Basic Cloud Properties

Reflected light spectroscopy and photometry of cool, directly imaged extrasolar giant planets are expected to be performed in the next decade by space-based telescopes equipped with optical wavelength coronagraphs and integral field spectrographs, such as the Wide-Field Infrared Survey Telescope (WFIRST). We are developing a new atmospheric retrieval methodology to help assess the science return and inform the instrument design for such future missions, and ultimately interpret the resulting observations. Our retrieval technique employs an albedo model coupled with both a Markov chain Monte Carlo Ensemble Sampler (emcee) and a multimodal nested sampling algorithm (MultiNest) to map the posterior distribution. This combination makes the global evidence calculation more robust for any given model, and highlights possible discrepancies in the likelihood maps. Here we apply this methodology to simulated spectra of cool giant planets. As a proof-of-concept, our current atmospheric model contains 1 or 2 cloud layers, methane as a major absorber, and a H2-He background gas. This 6-to-9 parameter model is appropriate for Jupiter-like planets and can be easily expanded in the future. In addition to deriving the marginal likelihood distribution and confidence intervals for the model parameters, we perform model selection to determine the significance of methane and cloud detection as a function of expected signal-to-noise, in the presence of spectral noise correlations. After internal validation, the method is applied to realistic reflected-light spectra of Jupiter, Saturn, and HD 99492 c, a likely observing target. We find that the presence or absence of clouds and methane can be determined with high accuracy, while parameters uncertainties are model-dependent.

spectroscopy↗
NASA NTRS2018

Multidecadal Changes in Lower Stratospheric Ozone: Variability Vs. Trends

As upper stratospheric ozone appears to be recovering as a result of decreasing chlorine loading following the implementation of the Montreal Protocol and its amendments and in agreement with model projections, several recent studies report an apparent decline of ozone concentrations in the lower stratosphere in the last two decades, particularly in the extratropics. Our previous work as well as at least two other studies provide evidence that this decline results from transport changes rather than an intensification of chemical depletion. It remains unclear whether these changes represent long-term internal variability or are a consequence of a climate forcing. Here we perform free-running ensembles of the recent past (1980-2016) using the Goddard Earth Observing System Model (GEOS) at the cubed sphere C180 (approximately half degree) resolution. Two suites of 10-member ensembles are performed, one in which observed sea surface temperature (SSTs) are fully prescribed, and the other in which the linear SST trend over the recent past is removed so as to only retain internal variability. We evaluate the trends in both ozone as well as two idealized tracers with prescribed uniform loss that are used to isolate the role of transport from chemistry and emissions. Probability-distribution-functions of the trends in both ozone and idealized tracers are compared among ensemble members and with observed trends in order to evaluate the likelihood of recent observed declines in lower stratospheric ozone, relative to large internal variability. Moreover, comparisons among simulations with and without imposed SST trends indicate the extent to which dynamically-driven ozone trends reflect forced trends or internal variability in lower stratospheric dynamics.

Wargan, Krzysztof↗
NASA NTRS1986

Determination of lift and drag characteristics of Space Shuttle Orbiter using maximum likelihood estimation technique

This paper presents the technique and results of maximum likelihood estimation used to determine lift and drag characteristics of the Space Shuttle Orbiter. Maximum likelihood estimation uses measurable parameters to estimate nonmeasurable parameters. The nonmeasurable parameters for this case are elements of a nonlinear, dynamic model of the orbiter. The estimated parameters are used to evaluate a cost function that computes the differences between the measured and estimated longitudinal parameters. The case presented is a dynamic analysis. This places less restriction on pitching motion and can provide additional information about the orbiter such as lift and drag characteristics at conditions other than trim, instrument biases, and pitching moment characteristics. In addition, an output of the analysis is an estimate of the values for the individual components of lift and drag that contribute to the total lift and drag. The results show that maximum likelihood estimation is a useful tool for analysis of Space Shuttle Orbiter performance and is also applicable to parameter analysis of other types of aircraft.

Trujillo, B. M.↗
NASA NTRS1996

Improved Closed-Loop Carrier-Phase Synchronization In BPSK

Scheme motivated by maximum-likelihood approach offers advantages over other well-known schemes. Proposed signal-processing system generates error signal proportional to derivative of conditional probability density function with respect to estimated carrier phase. Signal serves as feedback signal in carrier-phase-tracking loop.

Simon, Marvin K.↗