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NASA NTRS1977

Monte Carlo analysis of uncertainty propagation in a stratospheric model. 2: Uncertainties due to reaction rates

A concise stratospheric model was used in a Monte-Carlo analysis of the propagation of reaction rate uncertainties through the calculation of an ozone perturbation due to the addition of chlorine. Two thousand Monte-Carlo cases were run with 55 reaction rates being varied. Excellent convergence was obtained in the output distributions because the model is sensitive to the uncertainties in only about 10 reactions. For a 1 ppby chlorine perturbation added to a 1.5 ppby chlorine background, the resultant 1 sigma uncertainty on the ozone perturbation is a factor of 1.69 on the high side and 1.80 on the low side. The corresponding 2 sigma factors are 2.86 and 3.23. Results are also given for the uncertainties, due to reaction rates, in the ambient concentrations of stratospheric species.

Stolarski, R. S.↗

NASA NTRS1976

The uncertainty threshold principle - Fundamental limitations of optimal decision making under dynamic uncertainty

The fundamental limitations of the optimal control of dynamic systems with random parameters are analyzed by studying a scalar linear-quadratic optimal control example. It is demonstrated that optimum long-range decision making is possible only if the dynamic uncertainty (quantified by the means and covariances of the random parameters) is below a certain threshold. If this threshold is exceeded, there do not exist optimum decision rules. This phenomenon is called the 'uncertainty threshold principle'. The implications of this phenomenon to the field of modelling, identification, and adaptive control are discussed.

Athans, M.↗

NASA NTRS1977

The uncertainty threshold principle - Some fundamental limitations of optimal decision making under dynamic uncertainty

This note shows that the optimal control of dynamic systems with uncertain parameters has certain limitations. In particular, by means of a simple scalar linear-quadratic optimal control example, it is shown that the infinite horizon solution does not exist if the parameter uncertainty exceeds a certain quantifiable threshold; we call this the uncertainty threshold principle. The philosophical and design implications of this result are discussed.

Athans, M.↗

NASA NTRS1972

Study of Uncertainties of Predicting Space Shuttle Thermal Environment

Quantitative estimates of the uncertainty in predicting aerodynamic heating rates for a fully reusable space shuttle system are developed and the impact of these uncertainties on Thermal Protection System (TPS) weight are discussed. The study approach consisted of statistical evaluations of the scatter of heating data on shuttle configurations about state-of-the-art heating prediction methods to define the uncertainty in these heating predictions. The uncertainties were then applied as heating rate increments to the nominal predicted heating rate to define the uncertainty in TPS weight. Separate evaluations were made for the booster and orbiter, for trajectories which included boost through reentry and touchdown. For purposes of analysis, the vehicle configuration is divided into areas in which a given prediction method is expected to apply, and separate uncertainty factors and corresponding uncertainty in TPS weight derived for each area.

Fehrman, A. L.↗

NASA NTRS1972

Derivation of mission fluences from flux models: Propagation of uncertainties

The calculation of fluences from the flux models for spacecraft designers, and the propagation of uncertainties in the flux models to larger uncertainties in the final answer are discussed. Ionization and displacement damage in silicon, fluence, and a fluence of an equivalent energy are considered. Data in graph form are presented on stopping power and range curves for electrons and protons in silicon, relative electron and proton damage in silicon, and electron fluences expressed as 3 MeV equivalent and proton fluences expressed as 20 MeV equivalent for flybys in Jupiter's magnetic equatorial plane. It is concluded that the problem includes the uncertainty in peak flux, which has an immediate linear effect; uncertainty in the spatial distribution of the flux which gives great divergency between the upper-limit model and the nominal model and in the case of protons, may preclude any mission planning in order to make the situation better; and the uncertainty in the energy spectrum both in shape and energy location of the peak, if any, and which has little importance for mission planning if the spectrum is fairly constant.

Barengoltz, J.↗

NASA NTRS1973

Evaluation of aerodynamic heating uncertainties for Space Shuttle.

The uncertainty in heating predictions derived from ground test data correlations has been used to define the corresponding uncertainties in TPS weight for the Space Shuttle. A completely reusable Shuttle system consisting of an aluminum heat sink booster and orbiter with reusable surface insulation for thermal protection was evaluated. The largest contribution to the uncertainty in the weight of the thermal protection system for the orbiter occurred on lower surface areas due to heating and boundary layer transition uncertainties. Extension of this work to the current Shuttle system concept showed reduced weight uncertainty for the external tank compared to the reusable booster.

Masek, R. V.↗

NASA NTRS1974

Uncertainties in derived temperature-height profiles

Nomographs were developed for relating uncertainty in temperature T to uncertainty in the observed height profiles of both pressure p and density rho. The relative uncertainty delta T/T is seen to depend not only upon the relative uncertainties delta P/P or delta rho/rho, and to a small extent upon the value of T or H, but primarily upon the sampling-height increment Delta h, the height increment between successive observations of p or delta. For a fixed value of delta p/p, the value of delta T/T varies inversely with Delta h. No limit exists in the fineness of usable height resolution of T which may be derived from densities, while a fine height resolution in pressure-height data leads to temperatures with unacceptably large uncertainties.

Minzner, R. A.↗

NASA NTRS1980

Uncertainty in estimates of the number of extraterrestrial civilizations

Estimation of the number N of communicative civilizations by means of Drake's formula involves the combination of several quantities, each of which is to some extent uncertain. The uncertainty in any quantity may be represented by a probability distribution function, even if that quantity is itself a probability. The uncertainty of current estimates of N is derived principally from uncertainty in estimates of the lifetime of advanced civilizations. It is argued that this is due primarily to uncertainty concerning the existence of a "Galactic Federation" which is in turn contingent upon uncertainty about whether the limitations of present-day physics are absolute or (in the event that there exists a yet-undiscovered "hyperphysics") transient . It is further argued that it is advantageous to consider explicitly these underlying assumptions in order to compare the probable numbers of civilizations operating radio beacons, permitting radio leakage, dispatching probes for radio surveillance or dispatching vehicles for manned surveillance.

Peter A Sturrock↗

NASA NTRS1983

The effect of cross-section uncertainties on the derivation of source abundances from cosmic-ray composition observations

It is pointed out that the derivation of source abundances from the composition observed near the earth requires that the secondary contribution to the observed nuclidic abundances be calculated from a model of cosmic-ray propagation. A crucial element in such a calculation is the choice of nuclear fragmentation cross sections. Uncertainties in these cross sections give rise to uncertainties in the derived source abundances. It is shown here that the uncertainties in fragmentation cross sections can, in certain important cases, contribute significantly to the uncertainties in cosmic ray source abundances deduced from the observed composition. For this reason, it is essential that reliable estimates of the effect of cross section uncertainties be made when interpreting the source composition deduced from cosmic ray observations. In addition, formulas are presented which can be used to obtain such estimates with a minimum of computational effort.

Wiedenbeck, M. E.↗

NASA NTRS1983

Space shuttle launch vehicle aerodynamic uncertainties: Lessons learned

The chronological development and evolution of an uncertainties model which defines the complex interdependency and interaction of the individual Space Shuttle element and component uncertainties for the launch vehicle are presented. Emphasis is placed on user requirements which dictated certain concessions, simplifications, and assumptions in the analytical model. The use of the uncertainty model in the vehicle design process and flight planning support is discussed. The terminology and justification associated with tolerances as opposed to variations are also presented. Comparisons of and conclusions drawn from flight minus predicted data and uncertainties are given. Lessons learned from the Space Shuttle program concerning aerodynamic uncertainties are examined.

Hamilton, J. T.↗

NASA NTRS1983

Comet Halley ephemeris uncertainties in 1985-1986

For the planned flyby missions to Comet Halley in March 1986, the comet's ephemeris uncertainties completely dominate the spacecraft-comet miss distance. In an effort to determine realistic Comet Halley ephemeris uncertainties, a statistical covariance analysis was conducted using the actual data in 1909-1910-1911 and simulated data in 1984-1985-1986. In 1985-1986, Comet Halley's ephemeris uncertainties are very sensitive to the comet's orbital position, the optical data noise, data schedule, and whether or not the old data is included in the orbital solutions. The comet's ephemeris uncertainties in March 1986 are relatively insensitive to reasonable center of light/center of mass offsets and also to possible radar data taken in late November 1985. Accurate Space Telescope observations made in early March 1986 might significantly improve upon the comet's position uncertainties for the various intercepting spacecraft.

Yeomans, D. K.↗

NASA NTRS1972

Determination of aerothermodynamic environment uncertainties with application to space shuttle vehicles

In an effort to minimize the cost of the thermal protection system (TPS) for space shuttles, an analysis is made of environmental uncertainties. The basic categories of these uncertainties include aerodynamic heating, trajectory dispersions, atmospheric variations, and vehicle attitude variations. Also discussed are TPS design sensitivity to environmental uncertainties, and uncertainty profiles. Preliminary results indicate moderate TPS cost for a high confidence level environment may be obtained.

Scottoline, C. A.↗

NASA NTRS1976

Uncertainties in derived temperature-height soundings A summary

It is shown that high-resolution low-uncertainty temperature-height profiles cannot be deduced from pressure-height data alone because the relative uncertainty in pressure data cannot be expected to be smaller than 1% or 2% in present-day practical instrumentation. The basic equations relating temperature to pressure-height or density-height data are subjected to error analysis to determine the uncertainty introduced into computed temperature-height values by observed data. The results show that the use of density data is much more preferable than the use of pressure data if atmospheric temperature is to be determined as a function of height with a fine height resolution and a small uncertainty from the height profiles of pressure or density and if pressures and densities can be measured with comparable accuracies.

Minzner, R. A.↗

NASA NTRS1980

Analysis of uncertainties in turbine metal temperature predictions

An analysis was conducted to examine the extent to which various factors influence the accuracy of analytically predicting turbine blade metal temperatures and to determine the uncertainties in these predictions for several accuracies of the influence factors. The advanced turbofan engine gas conditions of 1700 K and 40 atmospheres were considered along with those of a highly instrumented high temperature turbine test rig and a low temperature turbine rig that simulated the engine conditions. The analysis showed that the uncertainty in analytically predicting local blade temperature was as much as 98 K, or 7.6 percent of the metal absolute temperature, with current knowledge of the influence factors. The expected reductions in uncertainties in the influence factors with additional knowledge and tests should reduce the uncertainty in predicting blade metal temperature to 28 K, or 2.1 percent of the metal absolute temperature.

Stepka, F. S.↗

NASA NTRS1981

On the uncertainty in the determination of ground reflectance and temperature from TM measurements

Uncertainties in the derivation of the ground reflectance and temperature relative to the uncertainty in the estimation of aerosol loading and water vapor amount are presented. To compute the reflectance for TM 1 (thematic mapper) through TM6, a doubling model is used, and to compute satellite-received radiance for TM7, an emission-transmission model is employed. It is shown that at a water vapor concentration of higher than 50% above normal, the relative sensitivity remains as low as 8% for ground reflectance determinations. The relative sensitivity for determining ground temperature for midlatitude summer climatological profile is less than 5%, but as the ground temperature is approximately 300 K, low sensitivity still means a variation of a few degrees. An increase in water vapor amount causes an uncertainty in ground temperature and reflectance calculations comparable to the uncertainty in aerosol loading and water vapor amount estimations.

Kiang, R. K.↗

NASA NTRS1982

A tutorial assessment of atmospheric height uncertainties for high-precision satellite altimeter missions to monitor ocean currents

Information from a number of sources is synthesized, and an error budget is deduced giving the projected overall height uncertainty correction for a suggested next-generation high-precision radar altimeter. Uncertainties deriving from the wet and dry troposphere, clouds, and the ionosphere are reviewed. It is assumed that the next generation of precision altimeters will be dual-frequency (13.5 and 6 GHz) and will be designed to correct for the ionospheric error. The altimeter-carrying satellite will have a nadir pointing near coincident-beam dual-frequency microwave radiometer for mitigating the wet tropospheric uncertainty. Whereas there are a number of caveats, the combined uncertainty in the height correction due to the atmosphere for the suggested system should be nominally 3 cm rms compared with at least 6 cm associated with the Seasat-A mission. Improvements in height resolution of the kind discussed here are considered vital for future satellite missions designed to monitor ocean currents.

Goldhirsh, J.↗

NASA NTRS1983

The development of aerodynamic uncertainties for the space shuttle orbiter

The Shuttle Program development schedule and the management decision to perform an orbital, manned mission on the first launch resulted in a requirement to develop realistic aerodynamic uncertainties for the preflight aerodynamic predictions. This paper addresses the methodology in developing two types of aerodynamic uncertainties. One involves the ability to reproduce aerodynamic results between various wind tunnel tests. The second addresses the difference between preflight aerodynamic predictions and flight results derived from analysis of past aircraft programs. Both types of uncertainties for pitching moment, lateral-directional stability, rudder power, and aileron power are presented. In addition, the application of uncertainties to flight control design and fight test planning is briefly reviewed.

Young, J. C.↗

NASA NTRS1983

Quantitative estimates of the effects of cross section uncertainties on the derivation of GCR source composition

Cosmic-ray source abundance uncertainties, resulting from the cross-section uncertainties, are calculated for the elements carbon through nickel. A significant dominance of cross-section errors in the source abundance uncertainties is found for most of the elements considered, even with uncorrelated partial cross-section errors; much larger uncertainties than those reported previously are found for Ca, N, Na, Al, and S. Propagation errors are noted to preclude a significant determination of source abundances for F, Cl, and Mn. A need for an assessment of the existing cosmic-ray propagation models - especially the propagation cross-sections which they employ - is expressed, motivated by recent improvements in the resolution and statistical accuracy of observations.

Hinshaw, G. F.↗