SEARCH · Engineering Papers
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
The finite element approximation of a Dirichlet type boundary control problem for parabolic systems is considered. An approach based on the direct approximation of an input-output semigroup formula is applied. Error estimates are derived for optimal state and optimal control, and it is noted that these estimates are actually optimal with respect to the approximation theoretic properties.
The numerical solution of the Helmholtz equation is considered via finite element methods. A two-stage method which gives the same accuracy in the computed gradient as in the computed solution is discussed. Error estimates for the method using a newly developed proof are given, and the computational considerations which show this method to be computationally superior to previous methods are presented.
The Ascent Air Data System (AADS) consists of a biconic spike probe on the nose of the Space Shuttle External Tank. The final configuration of the AADS was selected on the basis of pressure measurement accuracy and simplification of the configuration. Wind tunnel calibrations were formulated to convert the 30 deg/10 deg spike measured pressures to the desired air data parameters for postflight analyses. Estimates of the system performance show that in general the user requirements for angle of attack and sideslip, and dynamic pressure are met or only slightly exceeded by the estimated errors.
Errors in the outer zone contribution to oceanic undulation differences computed from a finite set of potential coefficients based on satellite measurements of gravity anomalies and gravity disturbances are analyzed. Equations are derived for the truncation errors resulting from the lack of high-degree coefficients and the commission errors arising from errors in the available lower-degree coefficients, and it is assumed that the inner zone (spherical cap) is sufficiently covered by surface gravity measurements in conjunction with altimetry or by gravity anomaly data. Numerical computations of error for various observational conditions reveal undulation difference errors ranging from 13 to 15 cm and from 6 to 36 cm in the cases of gravity anomaly and gravity disturbance data, respectively for a cap radius of 10 deg and mean anomalies accurate to 10 mgal, with a reduction of errors in both cases to less than 10 cm as mean anomaly accuracy is increased to 1 mgal. In the absence of a spherical cap, both cases yield error estimates of 68 cm for an accuracy of 1 mgal and between 93 and 160 cm for the lesser accuracy, which can be reduced to about 110 cm by the introduction of a perfect 30-deg reference field.
Present approaches to solving the stationary Navier-Stokes equations are of limited value; however, there does exist an equivalent representation of the problem that has significant potential in solving such problems. This is due to the fact that the equivalent representation consists of a sequence of Fredholm integral equations of the second kind, and the solving of this type of problem is very well developed. For the problem in this form, there is an excellent chance to also determine explicit error estimates, since bounded, rather than unbounded, linear operators are dealt with.
There has been strong motivation to produce numerically stable formulations of the Kalman filter algorithms because it has long been known that the original discrete-time Kalman formulas are numerically unreliable. Numerical instability can be avoided by propagating certain factors of the estimate error covariance matrix rather than the covariance matrix itself. This paper documents filter algorithms that correspond to the covariance factorization P = UDU(T), where U is a unit upper triangular matrix and D is diagonal. Emphasis is on computational efficiency and numerical stability, since these properties are of key importance in real-time filter applications. The history of square-root and U-D covariance filters is reviewed. Simple examples are given to illustrate the numerical inadequacy of the Kalman covariance filter algorithms; these examples show how factorization techniques can give improved computational reliability.
Mean absolute intensities (spectral radiance) over 0.1 nm intervals between 225.2 nm and 319.6 nm at disk center and near the limb of the sun (mu = 0.23 + or - 0.04) are derived from the high spectral resolution measurements published by Kohl, Parkinson, and Kurucz. The corresponding limb-to-center ratios and spectral irradiance values are provided. A comparison with existing measurements of solar spectral radiance and spectral irradiance for the most part shows agreement within the estimated error limits, although some narrow band variations may be outside experimental errors. The contribution to the solar constant of the 230-305 nm band is derived to be 19.7 W/square m + or - 12%.
Measurements taken in 1976 from the St. Louis Regional Air Pollution Study (RAPS) data base, conducted by EPA, were analyzed to determine an optimum set of air-quality and meteorological variables for predicting maximum ozone levels for each day in 1976. A 'leaps and bounds' regression analysis was used to identify the best subset of variables. Three particular variables, the 9 a.m. ozone level, the forecasted maximum temperature, and the 6-9 a.m. averaged wind speed, have useful forecasting utility. The trajectory history of air masses entering St. Louis was studied, and it was concluded that transport-related variables contribute to the appearance of very high ozone levels. The final empirical forecast model predicts the daily maximum ozone over 341 days with a standard deviation of 11 ppb, which approaches the estimated error.
The theory, variational formulation and finite element analysis of a class of nonlinear problems arising in optimization, thin membrane deflection and compressible flows are developed. Error estimates are summarized, and representative numerical results are presented. Particular theoretical questions pertaining to the existence and uniqueness of solutions are addressed, and their implications for such applications of finite element analysis as the study of compressible flows indicated.
The magnetic structure of Jupiter's magnetopause, as observed by the space probes Pioneer 10 and 11, is compared with terrestrial magnetopause structures from the OGO 5 mission. The Jovian magnetopause thickness, deduced from a rapid triple crossing, is found to lie in the range 3500-5200 km, while the adjoining plasma boundary layer was 5600-8400 km thick. Comparison with the terrestrial situation suggests that the dayside magnetopause thickness in both cases is a few times the ion gyroradius and that the dayside boundary layer is also of about the same width. The magnetopause normal vector and normal magnetic field component are determined for each crossing by use of minimum variance analysis. The results indicate a blunt and floppy magnetopause surface, for the most part with an insignificant normal magnetic field component. Only for three of the 14 crossings did this component exceed 1.5 times its error estimate. In two of these cases, the magnetic field tangential to the magnetopause displayed the characteristic features of a rotational discontinuity.
A class of Runge-Kutta formulas is examined which permit the calculation of an accurate solution anywhere in the interval of integration. This is used in a code which seldom has to reject a step; rather it takes a reduced step if the estimated error is too large. The absolute stability implications of this are examined.
The helium abundance in the Jovian atmosphere is derived from Voyager 1 data by two methods. The first method uses only infrared spectra from selected locations on the planet while the second method uses a thermal profile independently derived from radio occultation measurements and infrared spectra recorded near the occultation point. A hydrogen mole fraction of 0.897 plus or minus 0.030 is obtained from the first method, while the second method gives 0.880 plus or minus 0.036, corresponding to helium mass fractions of 0.19 plus or minus 0.05 and 0.21 plus or minus 0.06, respectively. The estimated errors for the first method are primarily due to systematic uncertainties in the H2 and He absorption coefficients, while those for the second method result mainly from errors in the radio occultation profile and are less well known. Random errors in the measured infrared spectra are found to be negligible in both cases. The results are consistent with a uniform mix of hydrogen and helium within Jupiter's interior, but a modest amount of helium depletion (Delta Y equal to or less than 0.05) cannot be excluded.
A technique is described in which all data points along an arc of the orbit may be used in an optimal numerical filter for wide-field-of-view measurements of earth emitted radiation. The statistical filter design is derived whereby the filter is required to give a minimum variance estimate of the radiative exitance at discrete points along the ground track of the satellite. An equation for the optimal numerical filter is given by minimizing the estimate error variance equation with respect to the filter weights, resulting in a discrete form of the Wiener-Hopf equation. Finally, variances of the errors in the radiant exitance can be computed along the ground track and in the cross track directions.
The kriging approach, a parametric regression method used by hydrologists and mining engineers, among others also provides an error estimate the integral of the regression function. The kriging method is explored and some of its statistical characteristics are described. The Watson method and theory are extended so that the kriging features are displayed. Theoretical and computational comparisons of the kriging and Watson approaches are offered.
The equilibrium strategy for N-person differential games can be found by studying a min-max problem subject to differential systems constraints. The differential constraints are penalized and finite elements are used to compute numerical solutions. Convergence proof and error estimates are given. Numerical results are also included and compared with those obtained by the dual method.
The work reported here addresses the important algorithm issues necessary to achieve a real-time flutter monitoring system; namely, the guidelines for choosing appropriate model forms, reduction of the parameter convergence transient, handling multiple modes, the effect of overparameterization, and estimate accuracy predictions, both online and for experiment design. An approach for efficiently computing continuous-time flutter parameter Cramer-Rao estimate error bounds has been developed. This enables a convincing comparison of theoretical and simulation results, as well as off-line studies in preparation for a flight test. Theoretical predictions, simulation and flight test results from the NASA/Dryden Drones for Aerodynamic and Structural Test (DAST) Program are compared.
All interplanetary shocks observed by ISEE-3 and either ISEE-1 or ISEE-2 or both in 1978 and 1979 are examined for evidence of upstream waves. In order to characterize the properties of these shocks it is necessary to determine accurate shock normals. An overdetermined set of equations were inverted to obtain shock normals, velocities and error estimates for all these shocks. Tests of the method indicate it is quite reliable. Using these normals the Mach number and angle were between the interplanetary magnetic field and the shock normal for each shock. The upstream waves were separated into two classes: whistler mode precursors which occur at low Mach numbers and upstream turbulence whose amplitude at Mach numbers greater than 1.5 is controlled by the angle of the field to the shock normal. The former waves are right hand circularly polarized and quite monochromatic. The latter waves are more linearly polarized and have a broadband featureless spectrum.
An alternating direction adaptive grid movement code was developed and a thesis adaptive angular meshes was directed. The alternating direction code was also established on the NASA Langley computer system and is available for use there. In essence, grid points are moved on an abstract surface above physical space by means of alternating coordinate directions. The abstract surface is formed with the salient solution properties if they can be extracted by a priori physical reasoning; or otherwise, in the absence of such reasoning, by the use of error estimates in some chosen norm. Upon formulation, all important driving properties for adaptive purposes are consolidated into one object - the abstract surface. At a basic level, a uniform distribution of surface points is equivalent to gradient resolution. This arises from a projection back down into physical space. At a higher level, a more accurate view of the abstract surface is obtained when changes in surface direction are also resolved. The appropriate measure for direction changes is normal curvature. It is defined as the rate of change of surface tangent planes as a surface coordinate curve is transversed in uniform increments of arc length.