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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 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
NASA NTRS2009

Stochastic Formal Correctness of Numerical Algorithms

We provide a framework to bound the probability that accumulated errors were never above a given threshold on numerical algorithms. Such algorithms are used for example in aircraft and nuclear power plants. This report contains simple formulas based on Levy's and Markov's inequalities and it presents a formal theory of random variables with a special focus on producing concrete results. We selected four very common applications that fit in our framework and cover the common practices of systems that evolve for a long time. We compute the number of bits that remain continuously significant in the first two applications with a probability of failure around one out of a billion, where worst case analysis considers that no significant bit remains. We are using PVS as such formal tools force explicit statement of all hypotheses and prevent incorrect uses of theorems.

Daumas, Marc↗
NASA NTRS2010

Altair Navigation During Trans-Lunar Cruise, Lunar Orbit, Descent and Landing

The Altair lunar lander navigation system is driven by a set of requirements that not only specify a need to land within 100 m of a designated spot on the Moon, but also be capable of a safe return to an orbiting Orion capsule in the event of loss of Earth ground support. These requirements lead to the need for a robust and capable on-board navigation system that works in conjunction with an Earth ground navigation system that uses primarily ground-based radiometric tracking. The resulting system relies heavily on combining a multiplicity of data types including navigation state updates from the ground based navigation system, passive optical imaging from a gimbaled camera, a stable inertial measurement unit, and a capable radar altimeter and velocimeter. The focus of this paper is on navigation performance during the trans-lunar cruise, lunar orbit, and descent/landing mission phases with the goal of characterizing knowledge and delivery errors to key mission events, bound the statistical delta V costs for executing the mission, as well as the determine the landing dispersions due to navigation. This study examines the nominal performance that can be obtained using the current best estimate of the vehicle, sensor, and environment models. Performance of the system under a variety sensor outages and parametric trades is also examined.

lunar lander↗
NASA NTRS2016

Investigation of Non-Equilibrium Radiation for Earth Entry

This paper presents measurements and simulations of non-equilibrium shock layer radiation relevant to high-speed Earth entry data obtained in the NASA Ames Research Center's Electric Arc Shock Tube (EAST) facility. The experiments were aimed at measuring the spatially and spectrally resolved radiance at relevant entry conditions for both an approximate Earth atmosphere (79 N2 : 21 O2) as well as a more accurate composition featuring the trace species Ar and CO2 (78.08 N2 : 20.95 O2 : 0.04 CO2 : 0.93 Ar). The experiments were configured to target a wide range of conditions, of which shots from 8 to 11.5 km/s at 0.2 Torr (26.7 Pa) are examined in this paper. The non-equilibrium component was chosen to be the focus of this study as it can account for a significant percentage of the emitted radiation for Earth entry, and more importantly, non-equilibrium has traditionally been assigned a large uncertainty for vehicle design. The main goals of this study are to present the shock tube data in the form of a non-equilibrium metric, evaluate the level of agreement between the experiment and simulations, identify key discrepancies and to promote discussion about various aspects of modeling non-equilibrium radiating flows. Radiance profiles integrated over discreet wavelength regions, ranging from the VUV through to the NIR, were compared in order to maximize both the spectral coverage and the number of experiments that could be used in the analysis. A previously defined non-equilibrium metric has been used to allow comparisons with several shots and reveal trends in the data. Overall, LAURAHARA is shown to under-predict EAST by as much as 50 and over-predict by as much as 20 depending on the shock speed. DPLRNEQAIR is shown to under-predict EAST by as much as 40 and over-predict by as much as 12 depending on the shock speed. In terms of an upper bound estimate for the absolute error in wall-directed heat flux, at the lower speeds investigated in this paper, 8 to 9 km/s, even though there are some large relative differences, the absolute error in radiance will be less then 1 Wcm2. At the highest shock speed of 11 km/s, the error will be less than 20 W/ sq cm.

Radiation↗
NASA NTRS1994

Linear Algorithms for Worst Case Identification in H infinity with Applications to Flexible Structures

This paper is concerned with linear algorithms for identification in which have been studied in [9]. It is shown that the two different linear algorithms in [9] can be unified into a single one which can be further extended to nonuniformly spaced frequency response samples with exponential convergence for the noise free case. Improved upper bounds for the corresponding identification errors are derived. Applications to the identification of lightly damped systems such as flexible structures are also considered.

linear↗
NASA NTRS1971

Optimal filtering in the presence of unmodeled time correlated driving disturbances.

In many realistic data filtering problems, the cross correlation of the state estimation error and the state forcing function is unknown due to the poor knowledge of the time history of the forcing function. In this paper, the conservative and minimal approximation to the cross correlation terms is presented. It requires only the knowledge of the estimation error covariance and the forcing function covariance, with the choice of an associated free parameter left to the user. If the estimation error covariance and/or the forcing function covariance are bounded from above but not known exactly, the cross correlation approximation using those upper bounds remains conservative. This cross correlation approximation leads to a conservative approximation to the estimation error covariance matrix differential equation between measurement times. The free parameter is determined as the analytic solution to an associated optimal control problem. The procedure is expanded to include discrete linear measurement incorporation.

Fraser, D. C.↗
NASA NTRS1972

Some effects of bias errors in redundant flight control systems.

The controllability and steady-state response of parallel-redundant flight control systems are examined. It is found that state components which appear in the parallel signal paths, e.g., individual actuator commands, are not controllable, although the sum of the command signals is well-behaved. If the response modes associated with these components are not stable, bias errors can cause the components to diverge, leading to the possibility of 'nuisance trips' in failure detection/isolation logic and eventual control system lockup (at saturation). Combining the inputs to the control computers assures that sensor bias will not cause divergence, while cross-strapping control strings bounds divergent response to all bias error inputs. Results of numerical solutions confirm the problem and its solutions.

Stengel, R. F.↗
NASA NTRS1972

Some effects of bias errors in redundant flight control systems

The controllability and steady-state response of parallel-redundant flight control systems are examined. It is found that state components which appear in the parallel signal paths, or individual actuator commands, are not controllable, although the sum of the command signals is well-behaved. If the response modes associated with these components are not stable, bias errors can cause the components to diverge, leading to the possibility of nuisance trips in failure detection/isolation logic and eventual control system lockup (at saturation). Combining the inputs to the control computers assures that sensor bias will not cause divergence, while cross-strapping control strings bounds divergent response to all bias error inputs. Results of numerical solutions confirm the problem and its solutions.

Stengel, R. F.↗
NASA NTRS1973

Some effects of bias errors in redundant flight control systems.

The controllability and steady-state response of parallel-redundant flight control systems are examined. It is found that state components which appear in the parallel signal paths, e.g., individual actuator-commands, are not controllable, although the sum of the command signals is well behaved. If the response modes associated with these components are not stable, bias errors can cause the components to diverge, leading to the possibility of nuisance trips in failure detection/isolation logic and eventual control system lockup (at saturation). Combining the inputs to the control computers assures that sensor bias will not cause divergence, while cross-strapping control strings bounds divergent response to all bias error inputs.

Stengel, R. F.↗
NASA NTRS1985

Structural error and identifiability

In most identification problems, the possibility of identifying a model from the observation of input and output is approached by first assuming that the model is an exact representation of the process. Since models are only approximations to a real process, this paper presents a concrete way of taking into account the difference in structure between the model and the process it represents. The identifiability problem is reformulated on the basis of equivalence and near-equivalence between model and process. Necessary and sufficient conditions under which the differences between the outputs of the process and a model remains within a desired bound in the presence of modeling error are given. Necessary and sufficient conditions for the identifiability of parameters are presented.

Hadaegh, F. Y.↗
NASA NTRS1985

The magnetic field at the core-mantle boundary

Models of the geomagnetic field are, in general, produced from a least-squares fit of the coefficients in a truncated spherical harmonic expansion to the available data. Downward continuation of such models to the core-mantle boundary (CMB) is an unstable process: the results are found to be critically dependent on the choice of truncation level. Modern techniques allow this fundamental difficulty to be circumvented. The method of stochastic inversion is applied to modeling the geomagnetic field. Prior information is introduced by requiring that the spectrum of spherical harmonic coefficients to fall-off in a particular manner which is consistent with the Ohmic heating in the core having a finite lower bound. This results in models with finite errors in the radial field at the CMB. Curves of zero radial field can then be determined and integrals of the radial field over patches on the CMB bounded by these null-flux curves calculated. With the assumption of negligible magnetic diffusion in the core; frozen-flux hypothesis, these integrals are time-invariant.

Bloxham, J.↗
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 NTRS2015

Extremely Low Passive Microwave Brightness Temperatures Due to Thunderstorms

Extreme events by their nature fall outside the bounds of routine experience. With imperfect or ambiguous measuring systems, it is appropriate to question whether an unusual measurement represents an extreme event or is the result of instrument errors or other sources of noise. About three weeks after the Tropical Rainfall Measuring Mission (TRMM) satellite began collecting data in Dec 1997, a thunderstorm was observed over northern Argentina with 85 GHz brightness temperatures below 50 K and 37 GHz brightness temperatures below 70 K (Zipser et al. 2006). These values are well below what had previously been observed from satellite sensors with lower resolution. The 37 GHz brightness temperatures are also well below those measured by TRMM for any other storm in the subsequent 16 years. Without corroborating evidence, it would be natural to suspect a problem with the instrument, or perhaps an irregularity with the platform during the first weeks of the satellite mission. Automated quality control flags or other procedures in retrieval algorithms could treat these measurements as errors, because they fall outside the expected bounds. But the TRMM satellite also carries a radar and a lightning sensor, both confirming the presence of an intense thunderstorm. The radar recorded 40+ dBZ reflectivity up to about 19 km altitude. More than 200 lightning flashes per minute were recorded. That same storm's 19 GHz brightness temperatures below 150 K would normally be interpreted as the result of a low-emissivity water surface (e.g., a lake, or flood waters) if not for the simultaneous measurements of such intense convection. This paper will examine records from TRMM and related satellite sensors including SSMI, AMSR-E, and the new GMI to find the strongest signatures resulting from thunderstorms, and distinguishing those from sources of noise. The lowest brightness temperatures resulting from thunderstorms as seen by TRMM have been in Argentina in November and December. For SSMI sensors carried on five DMSP satellites examined so far, the lowest thunderstorm-related brightness temperatures have been from Argentina in November - December and from Minnesota in June-July. The Minnesota cases were associated with spotter reports of large hail, significant severe wind, and tornadoes. Those locations have the record-holders for each satellite. The lowest AMSR-E 36.5 GHz brightness temperatures associated with deep convection have been in Argentina; the lowest 89.0 GHz brightness temperatures were from Typhoon Bolaven in the Philippine Sea. This paper will show examples of cases with the lowest brightness temperatures, and map the locations of these and other storms with brightness temperatures nearly as low. The study is largely motivated by the new GMI sensor on the Global Precipitation Mission core satellite, launched in February 2014, with its high resolution expected to reveal unprecedented low brightness temperatures when extreme events are encountered.

Cecil, Daniel J.↗
NASA NTRS2000

Low-dimensional Representation of Error Covariance

Ensemble and reduced-rank approaches to prediction and assimilation rely on low-dimensional approximations of the estimation error covariances. Here stability properties of the forecast/analysis cycle for linear, time-independent systems are used to identify factors that cause the steady-state analysis error covariance to admit a low-dimensional representation. A useful measure of forecast/analysis cycle stability is the bound matrix, a function of the dynamics, observation operator and assimilation method. Upper and lower estimates for the steady-state analysis error covariance matrix eigenvalues are derived from the bound matrix. The estimates generalize to time-dependent systems. If much of the steady-state analysis error variance is due to a few dominant modes, the leading eigenvectors of the bound matrix approximate those of the steady-state analysis error covariance matrix. The analytical results are illustrated in two numerical examples where the Kalman filter is carried to steady state. The first example uses the dynamics of a generalized advection equation exhibiting nonmodal transient growth. Failure to observe growing modes leads to increased steady-state analysis error variances. Leading eigenvectors of the steady-state analysis error covariance matrix are well approximated by leading eigenvectors of the bound matrix. The second example uses the dynamics of a damped baroclinic wave model. The leading eigenvectors of a lowest-order approximation of the bound matrix are shown to approximate well the leading eigenvectors of the steady-state analysis error covariance matrix.

Tippett, Michael K.↗
NASA NTRS1970

Method of statistical filtering

Minimal formula for bounding the cross correlation between a random forcing function and the state error when this correlation is unknown is used in optimal linear filter theory applications. Use of the bound results in overestimation of the estimation-error covariance.

Battin, R. H.↗
NASA NTRS1977

Minimum distortion quantizers

The well-known algorithm of Max is used to determine the minimum distortion quantizers for normal, two-sided exponential, and specialized two-sided gamma input distributions and for mean-square, magnitude, and relative magnitude error distortion criteria. The optimum equally-spaced and unequally-spaced quantizers are found, with the resulting quantizer distortion and entropy. The quantizers, and the quantizers with entropy coding, are compared to the rate distortion bounds for mean-square and magnitude error.

Jones, H. W., Jr.↗
NASA NTRS1968

Information rates for data compression.

Upper and lower bounds on required information rate for data compression fidelity criterion, comparing bounds with equivalent mean-square-error result

Davisson, L. D.↗
NASA NTRS1985

Robust state estimation with imperfect sensors

Robustness properties of extended Kalman-type filters are investigated for time-varying plants when nonlinearities or linear dynamics are present at the plant input and output. Sufficient conditions for the asymptotic stability (of the state estimation error) in the absence of noise are obtained when the nonlinearities or the linear dynamics are perfectly known. When the nonlinearities are known only within bands of uncertainty, the estimation error is shown to be ultimately bounded under certain conditions. The results obtained highlight the robustness properties of such filters, which are similar to, but not exact duals of those of linear quadratic regulators.

Joshi, S. M.↗
NASA NTRS1987

Robust time and frequency domain estimation methods in adaptive control

A robust identification method was developed for use in an adaptive control system. The type of estimator is called the robust estimator, since it is robust to the effects of both unmodeled dynamics and an unmeasurable disturbance. The development of the robust estimator was motivated by a need to provide guarantees in the identification part of an adaptive controller. To enable the design of a robust control system, a nominal model as well as a frequency-domain bounding function on the modeling uncertainty associated with this nominal model must be provided. Two estimation methods are presented for finding parameter estimates, and, hence, a nominal model. One of these methods is based on the well developed field of time-domain parameter estimation. In a second method of finding parameter estimates, a type of weighted least-squares fitting to a frequency-domain estimated model is used. The frequency-domain estimator is shown to perform better, in general, than the time-domain parameter estimator. In addition, a methodology for finding a frequency-domain bounding function on the disturbance is used to compute a frequency-domain bounding function on the additive modeling error due to the effects of the disturbance and the use of finite-length data. The performance of the robust estimator in both open-loop and closed-loop situations is examined through the use of simulations.

Lamaire, Richard Orville↗